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Process Biochemistry 41 (2006) 2218–2235
A novel systems biology/engineering approach solves fundamental
molecular mechanistic problems in bioenergetics and motility
Sunil Nath *
Department of Biochemical Engineering and Biotechnology, Indian Institute of Technology, Delhi, Hauz Khas, New Delhi 110016, India
Received 13 March 2006; received in revised form 30 June 2006; accepted 4 July 2006
Dedicated to Prof. Dr. Wolf-Dieter Deckwer on the occasion of his 65th birthday
Abstract
A large number of new insights and further intricate details of the molecular mechanisms of ATP synthesis and muscle contraction have been
offered from the perspective of the torsional mechanism of energy transduction and ATP synthesis and the rotation-uncoiling-tilt (RUT) energy
storage mechanism of muscle contraction. In this paper, a new systems thermodynamics analysis of oxidative- and photo-phosphorylation has been
performed. New experimental data has been reported on the inhibition of ATP synthesis by known specific anion channel blockers: the triorganotin
compound, tributyltin chloride (TBTCl), and the stilbene compound 4,40-diisothiocyanostilbene-2,20-disulfonate (DIDS), and interpreted as
supporting the new framework. A bioinformatic analysis of the interacting a–c regions in FO has been carried out to locate the anion binding pocket
in the anion–proton symsequenceporter and insights into the coordination chemistry of the bound chloride in its internal cavity at the lipid–water
interface have been obtained. The need to look at ATP synthesis in FO as a multisubstrate reaction has been emphasized and a detailed microscopic
explanation of the mechanism of inhibition by these blockers and its relationship to the conformational cycle within FO has been postulated. Such
detailed explanations of the role of membrane elements in a lipophilic region have been shown to lead to deeper understanding and to offer a more
realistic and complete picture of biological energy transduction than considering the bilayer as ‘‘mere insulation’’, as in chemiosmotic dogma.
Details of the elementary force production events by myosin II have been provided within the novel molecular systems framework of the RUT
mechanism in which the S-1, the S-1–S-2 hinge, and the S-2 coiled coil all have essential roles in the in vivo contractile process. The new paradigm
is shown to be consistent with the great body of experiments usually considered to support the swinging crossbridge/lever arm models of muscle
contraction, because these events also occur during the cycle but as events preliminary to the occurrence of the power stroke. The crucial role of
energy storage in mechanically strained nonequilibrium conformational states of myosin, specifically as a high-energy state of S-2 with uncoiled
first few N-terminal heptads is highlighted. The propensity of these heptads to recoil and regain the resting state of the coiled coil is postulated to be
a primary driving force of the power stroke. The new paradigms of ATP synthesis/muscle contraction have been shown to remove the
inconsistencies present in previous theories and to have the sound backing of the first and second laws of thermodynamics, the principle of
electrical neutrality, the laws of Newtonian mechanics, and the great conservation laws of mechanics. A systems integration of muscle contraction
has been successfully made and a systems electrical analog constructed. The unifying laws and principles in the new theories have been further
applied to understand the functioning of other protein molecular machines such as kinesin, ncd and unconventional myosins. Finally, the major
physical, chemical, biological and technological implications arising as a result of this research have been discussed. Taken together, the new
paradigms have been shown to solve fundamental molecular mechanistic problems in bioenergetics and motility and to offer a most detailed,
unified and appealing picture of energy generation, transduction, storage and utilization processes in systems of biological molecular machines.
# 2006 Elsevier Ltd. All rights reserved.
Keywords: ATP synthase; ATP synthesis; Muscle contraction; Myosin; Molecular mechanism; Torsional mechanism; Rotation-uncoiling-tilt energy storage
mechanism; Chemiosmotic theory; Binding change mechanism; Energy transduction; Nanotechnology; Systems biology; First law of thermodynamics; Second law
of thermodynamics
* Tel.: +91 11 26857457; fax: +91 11 26582282.
E-mail address: [email protected].
1359-5113/$ – see front matter # 2006 Elsevier Ltd. All rights reserved.
doi:10.1016/j.procbio.2006.07.003
1. Introduction
The molecular mechanism of the synthesis of the universal
biological energy carrier adenosine-50-triphosphate (ATP) and
the detailed molecular mechanism of muscle contraction using
the energy of ATP hydrolysis has literally inspired an immense
S. Nath / Process Biochemistr
amount of research. Yet the detailed molecular mechanism of
these most fundamental processes in biology has proved very
difficult to solve. Here, based on a novel molecular systems
biology/engineering approach, the elusive details of the
mechanism of these processes have been offered from the
perspective of the torsional mechanism of energy transduction
and ATP synthesis and the rotation-uncoiling-tilt energy
storage mechanism of muscle contraction [1–17]. It is not
the aim here to provide an exhaustive list of references, an
impossible task on which brave attempts have been made
earlier [1–3]. However, key experimental results that are
absolutely crucial for elucidation of the detailed mechanism, in
this researcher’s opinion, but have not received the attention
they warrant, have been emphasized. New experimental data
from our laboratory that further supports the new paradigm of
ATP synthesis has been presented, and the major scientific
implications arising have been discussed.
2. Materials and methods
Spinach chloroplast thylakoid membranes were isolated and acid-base
phosphorylation carried out as described earlier in detail [1]. Briefly, the
isolated membranes were adjusted to a chlorophyll concentration of 0.5 mg/
ml. 0.5 ml of the membranes were injected into the acid stage buffer containing
0.5 mM HCl/1.0 mM succinate, pH 4.0 for 15 s. The mixture was then injected
into base stage buffer containing anion channel inhibitor DIDS (4,40-diisothio-
cyanostilbene-2,20-disulfonate) or TBTCl (tributyltin chloride) at the final
concentrations (10 or 100 nM). The phosphorylation was studied for 15, 30,
45, 60, and 75 s. For the control, tricine-NaOH buffer pH 7.4 was added to the
thylakoid membranes in place of inhibitor and phosphorylation was performed
as above. Rates of ATP synthesis were calculated and plotted against time.
3. Relationship between linear nonequilibrium
thermodynamic analysis of ATP synthesis at
macroscopic systems and single molecule levels
A linear nonequilibrium thermodynamic analysis of
oxidative and photophosphorylation has already been carried
out in detail [2,12,16,17]. Such an analysis at a macroscopic
systems level has been shown to be in harmony with the
molecular mechanism of ATP synthesis [3,5]. It would be
interesting to know why such a good correspondence between
the single molecule level, single organelle systems level (e.g. a
single mitochondrion or chloroplast thylakoid) and even the
macroscopic systems level (e.g. an ensemble of organelles/
tissue) is obtained. The derived equations for the coupled
processes of oxidative or photophosphorylation at steady state
with the original notation, and with LOP = 0, LOH = �nOLOO,
LPH = nPLPP, and LHH ¼ CH þ n2OLOO þ n2
PLPP read as [12]:
JO ¼�
LOO �n2
OL2OO
LHH
�AO þ
�nOnPLOOLPP
LHH
�AP (1)
JP ¼�
nOnPLOOLPP
LHH
�AO þ
�LPP �
n2PL2
PP
LHH
�AP (2)
or
JO ¼ L11AO þ L01AP (3)
JP ¼ L01AO þ L00AP (4)
Eqs. (1)–(4) are valid for each individual molecule pair (e.g.
redox/photosystem + ATPase). If n is the total number of
working enzyme molecules:
JwholeO ¼ nJO (5)
JwholeP ¼ nJP (6)
Substituting for JO and JP, we have for the whole organelle/
macroscopic system with n number of working redox/photo-
system + ATPase molecules:
JwholeO ¼ n½L11AO þ L01AP� ¼ Lwhole
11 AO þ Lwhole01 AP (7)
JwholeP ¼ n½L01AO þ L00AP� ¼ Lwhole
01 AO þ Lwhole00 AP (8)
because the local AO, AP = global or bulk AO, AP, respective-
ly.Therefore
Lwhole11 ¼ nL11; Lwhole
00 ¼ nL00; Lwhole01 ¼ nL01 (9)
and
Lwhole11
Lwhole00
¼ L11
L00
; etc: (10)
With X = AP/AO:
JP
JO
¼ Zqþ ZX
1þ qZX(11)
h ¼ � JP
JO
X (12)
It is readily seen that Zwhole = Z, qwhole = q, JwholeP =Jwhole
O ¼JP=JO and hwhole = h. Hence the results expressed as ratios (JP/
JO and h) are valid at both individual molecular coupling level
as well as whole organelle or macromolecular systems level
with a large number of working molecules and therefore the
correspondence between different levels holds [2,3,12]. In ATP
synthase, each FOF1 machine produces its own output (ATP)
independently of the other FOF1 molecules. Forces and torques
produced by a single FOF1 molecule are not summed up with
that produced by other FOF1 molecules. Only the ATP pro-
duced adds to the common pool. In summary, the final output is
the chemical species ATP, which is summed up. Thus, a
macroscopic consequence and novel prediction of Nath’s tor-
sional mechanism of energy transduction and ATP synthesis is
that torque produced by single ATP synthase molecules
(�40 pN nm) is independent of ATP concentration (in hydro-
lysis mode) and ADP or H+/A� concentrations or delocalized
Dc (in synthesis mode) over the entire range of concentrations
(pM–mM), even though rates of ATP synthesis/hydrolysis are a
function of these parameters of state [15]. It would be inter-
esting to find out how these relationships scale for energy
utilization by muscle, where the output is not a chemical
species but is a mechanical entity (force). We now turn to
certain molecular aspects of ATP synthesis.
y 41 (2006) 2218–2235 2219
S. Nath / Process Biochemistry 41 (2006) 2218–22352220
4. New experimental results and their interpretation by
Nath’s torsional mechanism
Recently, we have shown that several lines of biochemical
evidence from our laboratory negate the old theories and offer
further support to Nath’s torsional mechanism [1]. These include:
(i) the acid concentration dependence of the rate of ATP
synthesis, (ii) the isolation and characterization of several
uncoupler-resistant mutants of oxidative phosphorylation, (iii)
the increase in oxidative phosphorylation uncoupling efficacies
with increase in lipid solubility of the uncoupler, other things
remaining the same. Here we report new experimental data on the
inhibition of ATP synthesis by known specific anion channel
blockers: the triorganotin compound, tributyltin chloride
(TBTCl) and the stilbene compound 4,40-diisothiocyanostil-
bene-2,20-disulfonate (DIDS). Fig. 1 compares the kinetics for
incubation of spinach thylakoids in the acid stage (pH 4.0) for
15 s at an initial HCl concentration of 0.5 mM and the base stage
rates of ATP synthesis (pH 8.3) as a function of time in the
absence of TBTCl, and in the presence of 10 and 100 nM TBTCl.
A two- to four-fold inhibition of the rate of ATP synthesis was
found at the 10 nM concentration (Fig. 1). Similar trends were
found at lower TBTCl concentrations and further, similar results
were obtained with DIDS in the inhibitory range of 1–10 nM
DIDS concentrations with HCl as the acid (Agarwal and Nath, in
preparation). It is impossible to explain why specific anion
channel blockers inhibit the rate of ATP synthesis using theories
such as chemiosmosis [18] that energetically link ATP synthesis
to the translocation of a single substrate only, i.e. protons.
However, if �half the energy to synthesize ATP comes from
anion translocation (chloride being the physiological ion under
our experimental conditions in this plant system), and the other
�half is donated by proton movement through specific half-
access channels in the FO portion of ATP synthase, and both Cl�
and H+ move in a strongly coupled way (with 1:1 stoichiometry
being the most interesting case) through access pathways that
form a rigid intramembrane link, a structural union, as it were, in
the membrane for the addition and collaborative utilization of
energy and for regulation of transport and metabolism, as
predicted by the torsional mechanism [1–3,14], then such an
inhibition in the concentration range of inhibitor that does not
Fig. 1. Rates of ATP synthesis as a function of base stage (pH 8.3) phosphoryla-
tion time in spinach thylakoids incubated in 0.5 mM HCl (pH 4.0) in the acid stage
for 15 s in the absence (~) and presence of 10 nM (�) and 100 nM TBTCl (&).
saturate the membrane binding sites is in fact the expected
outcome. Thus, ATP synthesis becomes a multisubstrate reaction
involving anions and protons, and the FO portion of ATP
synthase is then a Cl�–H+ symsequencecotransporter. In fact, the
major difference then, as per the torsional mechanism of ATP
synthesis, between the molecular mechanisms in mitochondria,
chloroplasts, and bacteria is the nature of the anion (chloride,
organic anion) and cation (proton, sodium ion) to which the
energy-transducing membrane is permeable. At higher concen-
trations of TBTCl, a rate enhancement (up to eight-fold) was
consistently found (Fig. 1). Similar results were obtained with the
DIDS-HCl system in the higher 100 nM to 2 mM concentration
range, except that the rate enhancement was much lower than that
found with TBTCl, and measured less than two-fold. This is not
to suggest that the mechanisms by which DIDS and TBTCl
inhibit/enhance ATP synthesis is the same. In fact, since TBTCl
is a potent chloride channel blocker but also an anionophore, and
at higher concentrations (>10 nM) is known to mediate a Cl�–
OH� exchange [though of course it can readily inhibit the
synthase (phenomenologically similar to DIDS though mechan-
istically different from it) at doses lower than those required to
catalyze rapid rates of Cl�–OH� exchange], it may be more
insightful to focus on the class of reversible inhibitors such as
DIDS. Fig. 2 shows the rates of phosphorylation as a function of
base stage times with 1 mM succinate and 10 and 100 nM DIDS,
other conditions being the same as in Fig. 1. If the inhibitor had
blocked the chloride channel, and anion was required merely to
maintain electroneutrality, then the presence of 1 mM succinate
should have rescued the phosphorylation rates to close to control
values by permeation through alternative sites other than the
anion access channels in the FO portion of the ATP synthase. This
was not observed; rather, inhibition was obtained at both
concentrations (Fig. 2). Thus, though both chloride and
dicarboxylic acid monoanions such as succinate support ATP
synthesis in our experimental system [1], chloride gave the
maximum rates among all anions tested, and further, as Fig. 2
shows, succinate does not have the required affinity for the
binding sites to cause a rate enhancement in the presence of
DIDS, at least under the conditions studied, again pointing to the
small lipophilic Cl� as the physiological anion in this system, and
indicating an energy provision role of the anion in ATP synthesis
Fig. 2. Rates of ATP synthesis as a function of base stage (pH 8.3) phosphor-
ylation time in spinach thylakoids incubated in 1.0 mM succinate (pH 4.0) in the
acid stage for 15 s in the absence (&) and presence of 10 nM (~) and 100 nM
DIDS (�).
S. Nath / Process Biochemistry 41 (2006) 2218–2235 2221
by translocation through the membrane-bound FO portion and
binding to the protein-in-the-membrane (i.e. trapping of chloride
in its binding pocket in a lipophilic region of the membrane), and
not just a passive role to maintain electrical neutrality of bulk
aqueous phases. The properties of these lipophilic regions have
been considered and detailed molecular mechanisms developed
within FO [1–4,7,11]; such detailed explanations of the role of
membrane elements lead to deeper understanding and offer a
more realistic and complete picture of biological energy
transduction than considering the bilayer as ‘‘mere insulation’’,
as in Mitchell’s chemiosmotic theory [18].
Given the above results, any theory of ATP synthesis must be
able to explain both the inhibition of ATP synthesis at low
reversible anion inhibitor (DIDS) concentrations as well as the
enhancement in synthesis rates at higher inhibitor concentra-
tions based on a general enzymological inhibition scheme at the
macroscopic level, as well as at the microscopic level by the
DpH–Dc two mutually non-colinear half-access channel model
[3,4,7,11] within the torsional mechanism. Since DIDS has no
way of entering the membrane and affecting the inlet half-
access anion channel (linked to the inlet half-access proton
channel), it can only act on the exit half-access anion channel
(which is coupled to the exit half-access proton channel). In any
case, this is also true under the experimental conditions because
the inhibitor was added at the base stage, i.e. at the time of
phosphorylation, and the enzyme already had bound Cl� and
H+ during the acid stage. All our experimental results on ATP
synthesis can be explained by considering the inhibition to be of
mixed type, composed of competitive and uncompetitive
inhibitions, for example by the scheme E + S$ ES! P;
ES + I$ ESI with inhibition constant K 0I; E + I$ EI with
inhibition constant KI. Such a scheme is commonly encoun-
tered in multisubstrate enzyme reactions where the inhibitor is
competitive with respect to one substrate and uncompetitive
with respect to another. Inhibitor can bind to either E or ES
depending on the values of KI or K 0I. When [I]� KI, EI is
formed. Formation of ESI complex leads to decreased rates.
Since the inhibitor used is an anion channel blocker, the
inhibition can be considered uncompetitive with respect to H+
and competitive with respect to Cl�. Thus in the scheme given
above, S = H+. Let the characteristic time for unbinding of
chloride from its site be t1, the time for conformational change
and subsequent unbinding of proton from its site be t2, and the
time taken for binding of inhibitor (DIDS) to its site (which can
be different from the chloride binding site) be t3. At low
(<10 nM) inhibitor concentration, the order of the events in the
exit half-access channel is Cl� unbinding, followed by binding
of inhibitor to its site which prevents H+ unbinding. This could
happen for many reasons; for example, the chloride exit half-
access channel does not close due to the presence of bound
inhibitor in the channel, and unless the anion exit half-access
channel closes, the proton exit access half-channel does not
open and the proton does not unbind. In any case, this has to be
so from the uncompetitive nature of the inhibition with respect
to the H+: the proton cannot leave as long as the inhibitor stays
bound. Hence we obtain inhibition. In other words, for
inhibition, at the microscopic level, t3 < t2 (after Cl�
unbinding). In macroscopic terms, ESI complex is formed
and leads to decreased rates of ATP synthesis. On the other
hand, at high inhibitor concentrations (�10 nM), [I] exceeds KI
and EI is formed, i.e. the proton unbinds from its site before the
inhibitor binds to its respective site. Or, in terms of
characteristic times in the microscopic framework, t2 < t3.
Also the value of t1 itself may be smaller than the corresponding
unbinding time of chloride at low inhibitor concentrations, i.e.
the affinity of the site for chloride is lowered by the interaction
of inhibitor and Cl� unbinding is faster at high [I]. In addition to
this greater driving force for unbinding of chloride at high
inhibitor concentrations, the affinity of inhibitor for its own site
is also reduced and tight binding of DIDS is hindered due to the
changes in the microenvironment of the site at these sought-for
(and optimized) experimental conditions (leading for instance
to lowered pKa that favor unbinding of the inhibitor from the
exit aqueous pathway). In any case, H+ unbinds first, and the c-
rotor rotates by �158, and now the Cl� at the inlet access half-
channel binds rapidly to its site due to its presence at high
concentration and its high affinity for its binding site in the
microenvironment of the inlet half-access channel, following
which the H+ binds to its own site, another rotation of �158occurs and the cycle continues [1,3–5,7]. Thus, more number of
cycles occur per unit time, and a rate enhancement is obtained
under these conditions, as observed experimentally.
The use of ‘‘low’’ and ‘‘high’’ for [I] above can be
quantified. In our spinach thylakoid samples, we have 1.3 nmol
ATP synthase per milligram chlorophyll. In 0.5 ml of 0.5 mg/
ml chlorophyll concentration in the acid stage, we therefore
have, for a 0.25 mg chlorophyll basis, 1.3 � 10�9 � 6 �1023 � 0.25 or �1014 ATP synthase enzyme molecules. At
10 nM inhibitor concentration in 2 ml of base stage we have
10 � 10�9 � 2 � 10�3 � 6 � 1023 or �1013 inhibitor mole-
cules. Since [I] < [E] at this concentration and below, we
expect inhibition below 10 nM and hence 10 nM can be
considered a ‘‘low’’ concentration in this context. Thus, the
calculated value of the inhibitory dose agrees with what is
obtained experimentally (Figs. 1 and 2), and serves as a
valuable aid in the design of the ATP rate inhibition/
enhancement experiments.
5. Bioinformatic analysis to identify the anion access
channel in the FO portion of ATP synthase
Since the inception of the torsional mechanism, it was
considered that the a-Arg-210–c-Asp-61 interacting regions
form the proton access channels [7,9–11]; it is now seen that the
helix 4-a–helix 2-c interacting faces at the a–c interface of the
membrane-bound FO portion also constitute the anion access
channels. Since the A� and H+ channels should be in close
proximity to enable the direct and local energy transduction
envisaged by the torsional mechanism [1–3,14], this is logical.
Also, since the triorganotin compounds preferentially target
and block the a-subunit, and since these tin compounds are
potent inhibitors of anion channels, it logically follows that the
a-subunit entry and exit aqueous half-channels known to be
present by research work of great significance by Fillingame
S. Nath / Process Biochemistry 41 (2006) 2218–22352222
and co-worker [19] are meant for anions with the binding site/
pocket located at the a–c interface. We have already made the
novel prediction [1,14] that the conserved Arg-210 (Escher-
ichia coli numbering) residue in the polar helical segment of
helix 4 of the a-subunit at the a–c interface of the ATP synthase
forms part of the anion binding (transport) site/pocket in the
immediate vicinity of the cAsp-61 proton binding site, and that
the subunit-a access channel is an anion (e.g. Cl�) channel and
not a proton channel, as currently believed. It is possible that the
subunit-a anion access channel at the a–c interface belongs to
the family of cystic fibrosis conductance regulator (CFTR)
family of anion channels, since these channels are known to be
permeable to both Cl� and large organic anions [20], and these
properties are found in our experiments (Figs. 1 and 2). For the
occurrence of anion binding in such a scenario, it can be
predicted that a cationic group (e.g. Arg/dipole) will attract
anions into water structured around hydrophobic groups (e.g.
Leu). That is, the amide nitrogen of the peptide backbone can
form a lyotropic anion attracting group only if it lies in close
proximity to one or more hydrophobic amino acid side chains.
A bioinformatic approach to test the above prediction is
shown in Fig. 3; the sequences of the interacting a–c helical
segments were aligned with the interacting helical faces (helix
C–helix G) of the known chloride channel/pump halorhodopsin
(pHR and sHR). The key roles of the conserved Arg and the
hydrophobic Leu around this arginine residue, and the essential
nature of the Ser and Thr residues for chloride binding is clearly
revealed (Fig. 3) from the sequence alignment. The single residue
differences with the proton pump bacteriorhodopsin are also
highlighted [D versus T/R and the lack of the equivalent of a-Leu-
207 in BR (Fig. 3)]. Moreover, inspection of the sequences of the
two interacting helical arms as a whole reveals that BR contains
the negatively charged D residues in each arm (proton binding);
in HR, instead of the negatively charged D, one of the arms
contain polar T residues (anion binding), while in the
amphiphatic helical arms of a–c, the T is replaced by the
positively charged R in one arm which is ‘‘balanced’’ by the
negatively charged D in the interacting helical arm (binding
anion and proton) (Fig. 3). This progressive increase in
amphoteric character from BR to HR to the interacting groups
in the a–c subunits of FO clearly show that these FO sequences
are tailored to bind both A� and H+ at some stage of the
conformational cycle in FO. The conserved a-Arg-210 can
electrostatically (directly through its guanidinium group), but
more likely indirectly through coordination via a water cluster
interact with the bound chloride. These interactions will stabilize
the Cl� in its internal cavity/binding pocket and keep the ion
Fig. 3. Segments of interacting helix C-helix G (BR, sHR, pHR) or a-helix 4–c-
helix 2 (FO portion of Escherichia coli ATP synthase) from aligned protein
sequences for bacteriorhodopsin from Halobacterium salinarum (BR) and
halorhodopsin from H. salinarum (sHR) and halorhodopsin from Natronobac-
terium pharaonis (pHR).
solvated and also maintain the structure of the bound water. The
specificity of the anion access channel is then determined by the
steric and electrostatic properties of the Arg-210 transport site;
the inlet and outlet access pathways (the anion conducting
pathways) are relatively non-specific. The walls of these
pathways are lined with hydrophobic residues like Leu, Ile,
Val and the movement of anion through these access pathways is
akin to diffusion and is relatively non-specific. These could
reflect general properties of anion channels. Thus a-Leu-207, a-
Arg-210 and c-Asp-61 must pack together at some stage of the
conformational cycle in FO during function: this will bring the
Cl� and the H+ very close to each other. Yet they do not combine
to form a covalent bond to make HCl in the lipophilic region of
the biological membrane in mitochondria/chloroplast/bacteria,
though this bonding of the ions may occur in artificial
membranes. This combination of proton and anion also occurs
in biological membranes between an uncoupler anion U� and H+,
due to the lipid solubility of the uncoupler, as described in a new
rationale of uncoupling action [1]. This emphasizes the critical
need for the specificity of the lipophilic anion (e.g. Cl�) and the
cation (e.g. H+) for coupled symsequenceport [1–3] translocation
as separate charges without recombination in the membrane, and
for energy addition, joint energy utilization and ATP synthesis.
Thus, both the universally conserved residues of ATP synthesis –
c-Glu/Asp-61 and a-Arg-210 – possess a unique functional role,
the former as the binding site of the proton, and the latter as
constituting the binding pocket of the anion.
A role for helix 5 on a-subunit is also indicated in the ATP
synthesis process in FO. Thus, a-Arg-210 on helix 4 and a-Gln-
252 on helix 5 (not shown in Fig. 3) are packed in close
proximity because the two positions can be switched around as
in the Q-210–R-252 mutant with partial retention of function
revealed by the thoughtful experiments of Cox, Hatch and
coworkers [21]. The guanidinium group of Arg-210 can form a
hydrogen bond with the side chain of Gln-252 and further
stabilize the anion. Thus ion-ion (e.g. Arg-210–Asp-61), ion
dipole (e.g. Arg-210–Gln-252), the apolar hydrogens around
the anion (e.g. aliphatic hydrogens of Leu-207) all greatly
stabilize it in its internal cavity along with the stabilization
achieved by coordination of Arg-210 indirectly through an
intervening water cluster.
While the role of specific amino acids (Fig. 3) is of interest in
understanding anion transport through the anion access half-
channels of the A�–H+ symsequenceporter in the FO portion of
ATP synthase, the structure, specific three-dimensional
arrangement and coordination chemistry aspects are key to
anion binding. In this new view, a pentacoordinated trigonal
bipyramid structure for the chloride is predicted with
stabilization from ion–ion, ion–dipole contributions (through
direct interaction of the anion with the guanidinium group of
Arg-210 and indirectly through bound water molecules at the a–
c interface that will ensure that the anion remains solvated in
this internal site at the lipid–water a–c interface and help
maintain the correct structure of bound water, along with the
aliphatic hydrogens of the conserved non-polar Leu-207 in the
otherwise polar arm of helix 4 of a-subunit) in the very
immediate vicinity of the proton access half-channel binding
S. Nath / Process Biochemistry 41 (2006) 2218–2235 2223
site Glu/Asp-61 on helix 2 of the c-subunit of FO. The
inhibiting/ionophoric triorganotin compounds must target a-
subunit such that the structure of the polyhedron around tin
mimics the pentacoordinated trigonal bipyramid structure in
three dimensions found in the physiological case with anion
(e.g. chloride) coordination to its ligands—the amino acids Ser,
Thr and Lys, and indirectly through water the amino acids Arg,
Gln, Asp or the other Ser residues (Fig. 3). Such a novel
structural pattern as the eventual outcome is clearly visualiz-
able in three dimensions in the biochemical setting depicted in
Fig. 3. While we can catch a glimpse of the structure and
dynamics of nature’s splendid symsequenceport machinery of
anion–proton coupled translocation in the membrane-bound
portion of ATP synthase, the exact details of structure and
course of anion through the membrane must await an X-ray
structure of the a–c interface in FO, a major challenge for
structural and membrane biologists.
6. Details of Nath’s rotation-uncoiling-tilt (RUT) energy
storage mechanism of muscle contraction
Five years ago, I proposed [6] and subsequently further
developed and analyzed [1,2] and defended [22–24] a novel
mechanism of muscle contraction in which energy transduction
occurs at the elementary step of hydrolytic cleavage of bound
MgATP. A detailed mechanical analysis of this process has been
made [2]; a general thermodynamic analysis for the performance
of useful external work by open, steady state, ATP-hydrolyzing
systems has also been carried out [1]. The only major uncertainty
that remained was with the unknown sense of the torque
produced upon cleavage of the Pb–Pg bond during ATP
hydrolysis, and previously it was assumed that the sense of
the torque was so as to cause a higher energy state of myosin
associated with supercoiling of the myosin S-2 coiled coil. This
intuitively worked with a purely mechanical picture of the
coupling. While such a process may actually occur in vitro in
various motility assay protocols, a careful scrutiny of the sub-
molecular aspects of the problem and amino acid sequences of
the myosin amino terminal region suggests that, in vivo, the free
energy of ATP hydrolysis is used to uncoil the first few amino
terminus heptads of myosin S-2 coiled coil. We are then forced to
consider the state of myosin with uncoiled N-terminal S-2
heptads as a state of higher free energy with respect to the resting
state of myosin. We then progress to an electromechanical model
of the coiled coil with its solvent/ionic environment outside (e.g.
coiled coil with charges/hydrophobic residues on it at specified
spatial locations in an electrolyte medium), the packing and
interaction of hydrophobic/ionic residues within the coiled coil,
and their hydration effects, and need to consider free energy
changes. The propensity of the S-2 coiled coil to recoil is the
thermodynamic driving force of the muscle power stroke. This
recoiling of the S-2 N-terminal heptads leads to untilting and
constrained rotation of the myosin heads bound to actin filaments
which causes the power stroke exactly as detailed before [1,2,6].
The magnitude of the force generated by the elementary power
stroke obtained from thermodynamic analysis [1] is in perfect
accord with both single molecule data [25] as well as estimations
of force generated by stage 2 insect flight muscle crossbridges
using 3D electron tomographic visualization [26]. The mechan-
ism also explains the valuable anti-S-2 antibody data of Sugi and
Harrington [27]. Above all, Nath’s rotation-uncoiling-tilt (RUT)
energy storage mechanism of muscle contraction elucidates why
myosin II possesses a double-headed [1,22–24] and double-
tailed [22–24] structure, which had puzzled scientists for several
decades [28]. The thermodynamic propensity of the myosin
hydrophobic residues to repel water and regain the more stable
resting state of S-2 coiled coil is then a primary driving force for
the coiling back of myosin S-2. If S-2 were not a coiled coil but a
single helix, then no shielding of the amino acid residues in the S-
2 rod from solvent/electrolyte would have been possible: hence
we need a double tailed (coiled coil) structure for myosin II. The
double-headed structure of myosin II enables the two myosin
heads to bind to actin subunits on two different actin filaments
and permits the two heads of myosin to execute their power
strokes simultaneously upon recoiling of the S-2 coiled coil that
is common to both heads of the myosin molecule and thereby
�double the efficiency of the muscle contraction process, as
discussed earlier [1]. This raison d’etre for two heads (though not
for the coiled coil) appears to have been first suggested in a
prescient and visionary paper by Offer (termed ‘‘two-filament
interaction’’ by him) [29]. Several further details can now be
incorporated into the RUT Energy Storage Mechanism of muscle
contraction for the first time. These details further reveal the
requirement of a double-headed structure for myosin II to
perform its mechanical functions.
As discussed above, a novel prediction of the RUT
mechanism of muscle contraction is that myosin head
experiences a counterclockwise torque/rotation about its axis
(looking from the side of the myosin S-1 heads) due to the ATP
hydrolysis elementary event in one of the myosin heads [1],
which causes uncoiling of the first few N-terminal heptads of
the myosin S-2 coiled coil. This uncoiling is associated
simultaneously with tilting of myosin heads about the S-1–S-2
hinge [1,2,6,22–24] such that the heads can reach out and bind
to their binding sites on the actin filaments. The reasons why
uncoiling is favored are:
1. T
he coiled coil structure near the S-1–S-2 junction is veryweak and the weakness decreases progressively as we move
away from S-1–S-2 junction towards the carboxy-terminus.
The structure of myosin suggests that this weakness is
deliberately introduced to lower the energy barrier between
coiled and uncoiled states to make the actomyosin cycle
feasible. In other words, unlike normal canonical coiled
coils, in myosin, the free energy difference between the
coiled and uncoiled states is close to the free energy released
by ATP hydrolysis. The weakness itself is due to:
(i) P
olar residues that are buried inside the core making thecore hydrophilic (and some hydrophobic residues on the
myosin coiled coil surface), hence making the coiled
structure less stable. For example, the first three nominal
‘d’ positions of the sequence are occupied by a proline and
two glutamine residues. Moreover, the two ‘d’-position
glutamine residues pack in the core in an asymmetric
S. Nath / Process Biochemistry 41 (2006) 2218–22352224
fashion, with only one of the side chains forming a knob-
into-hole contact with the opposite helix as clearly inferred
from the recent X-ray structure of scallop striated muscle
myosin rod fragment [30]; the other side chain is oriented
towards the solvent. The residues that are exposed because
of the lack of ‘g–e’ links include the three consecutive ‘d’-
position leucines as well as other apolar core side chains
[30].
(ii) L
ack of inter-helical bridges between the two coiledhelices of myosin making the coiled structure weak.
(iii) I
nstead of following the ‘‘knobs in the holes’’ modelfollowed throughout myosin chain, the first few N-terminal
heptads do not follow the model and hence the strength of
the coiled coil is further reduced.
2. I
f there were no uncoiling then it would not have beenpossible for the myosin heads to increase the angle they
make with myosin S-2 axis. And without increasing this
angle, it is not possible for myosin heads to tilt enough to
bind with actin.
3. T
here is no tendency in the residues forming the S-1–S-2hinge to form a coil so supercoiling is impossible.
4. I
f there were supercoiling, the heads would approach closerto each other which is sterically not favorable.
5. S
Fig. 4. Representation of conformational changes in myosin upon ATP hydro-
lysis from the initial resting state (left) to the final high-energy state (right). The
first few N-terminal heptads of S-2 have uncoiled in the final state and there is
conformational strain at the S-1–S-2 hinge (right). The diagram is not to scale,
but angle g > a, angle b > a and angle g 6¼ angle b.
ince in spite of all the above factors, the uncoiled state
remains less stable than the coiled conformation, the myosin
coil starts coiling back progressively as it goes through
power stroke to rigor state and then to fully coiled structure.
This perfectly justifies the progressively decreasing strength
of the myosin coiled coil as we move towards the amino
terminus. The role of the C-terminal heptads of S-2 is to
provide rigidity to the coiled coil and thus allow the torque
upon ATP hydrolysis to cause uncoiling instead of rotation of
the entire molecule about its axis without any uncoiling.
In view of the above and earlier considerations [1,2,6], the
conformational changes in myosin head upon ATP hydrolysis
should enable the heads to rotate and tilt and allow the catalytic
domains of the heads to bind loosely (at first) to their respective
binding sites on the same or different actin filaments. If the two
heads of a myosin molecule were to bind to neighbouring
subunits on the same actin filaments, then the two myosin heads
would be bent in opposite directions (if the heads are required to
loosely bind to actin with the same conformation); such a strain
would necessarily decrease the binding strength. On this basis,
and for a number of other geometrical and steric reasons it was
suggested that the two heads bind to actin binding sites on
different actin filaments [1,29]. This was also in line with the way
the RUT mechanism was conceived originally [6] especially
keeping the novel torque element of RUT in mind and the need
for conservation of linear and angular momentum after release of
the stored energy upon coiling back of the S-2. However, it
should be noted that the mechanistic elements of RUT would
hold even if the myosin heads were to bind to the same actin
filament, as might happen for instance under invitro conditions in
the absence of the myosin–actin super-lattice structure and
supramolecular biology arrangement. Subsequently, upon Pi
release due to actomyosin interactions, the myosin head binding
to actin is known to become tight from its initial loose binding
[31]. It is also necessary that the high energy uncoiled state of
myosin be trapped in a long-living intermediate state (e.g.
M**.ADP.Pi) and the stored energy not be released until the
myosin heads have bound tightly and stereospecifically to actin.
In other words, we want to block the myosin coiled coil from
recoiling and coming back to its resting state, i.e. we wish to let it
remain in its high energy uncoiled state. To use this stored energy,
actin must first interact with the myosin head in the M**.ADP.Pi
state, and activate the next step in the series of steps in the
enzymatic pathway that will eventually unblock this high energy
‘‘latch’’ state of the crossbridge and allow it to proceed through
the lower free energy states. It is proposed here that this kinetic
block or latch is created during the ATP hydrolysis step by a kink
or bend/distortion at the S-1–S-2 hinge. This kink serves to
separate the S-2 coiled coil from the myosin S-1 such that they
act mechanically as two separate bodies and the stored energy
remains trapped in the S-2 and its milieu. We also propose for the
first time that only upon ADP release (which is subsequent to Pi
release) is this localized strain at the S-1–S-2 hinge removed to
enable the recoiling of the S-2 coiled coil, utilization of the stored
energy, and generation of the elementary power stroke.
The above analysis shows that distortion/kink or localized
conformational strain at the S-1–S-2 junction takes place during
the ATP hydrolysis elementary step due to the Pb–Pg bond
cleavage event in one of the myosin heads, i.e. it occurs due to
chemical reaction-linked conformational changes. Due to
hydrolysis-linked conformational changes, there exist rotation
of the myosin head about its axis, tilt of the head about the S-1–
S-2 hinge, and uncoiling of the first few N-terminal heptads of
the S-2 coiled coil, as per the tenets of the RUT mechanism
[1,2,6]. This is diagrammatically depicted in Fig. 4. The
rotation of the myosin head (in which the ATP hydrolysis
S. Nath / Process Biochemistry 41 (2006) 2218–2235 2225
elementary event occurs) about it axis can be communicated to
the second head of the myosin molecule (the head that was
enzymatically silent) so that the second head can also exhibit
the same rotational motion about its own axis. This is only
possible because the rotational motion of the head about its own
axis is small [2,6,31]; hence it is possible to communicate this
motion to the other head due to the common S-1–S-2 hinge and
the common S-2 coiled coil as can be readily visualized
physically upon analysis of the motion. The heads, which were
initially symmetric about the central axis of the double-headed
myosin molecule before the ATP hydrolysis reaction occurred,
become disposed dissymmetrically about the central axis/head–
rod junction (Fig. 4). Because of the absence of any mechanical
constraint from the common-hinged, coiled coil structure for
such a tilting of one head off the central axis, this tilt motion of
one myosin head will be independent of the other head and will
not be communicated to the second head. This dissymmetry is
analogous to producing a kink or bend/distortion in the myosin
neck which acts as a kinetic block or latch preventing the
uncoiled heptads of S-2 from recoiling, and hence making the
S-2 remain in a high-energy state (Fig. 4). It should be noted
that the occurrence of ATP hydrolysis in both the heads will
eliminate any possibility of dissymmetry of arrangement of
myosin heads; thus, this offers independent mechanical reasons
(separate from thermodynamic arguments in Ref. [1]) that the
two heads of myosin are functionally different [1]. This is also
in accordance with the pioneering biochemical work of
Tonomura and colleagues [32] indicating two different heads
on the myosin molecule which offered important clues to the
real molecular mechanism of muscle contraction.
The loose binding of myosin head to actin discussed above
opens a trapdoor to release Pi [33] through the 50 K cleft. Let Pi
be ejected out with velocity v (Fig. 5). If Pi were not prevented
from release during ATP hydrolysis on myosin, i.e., if it could
release without requiring loose actin binding, then the required
conformational changes described below that are necessary for
the proper functioning of the mechanism would not occur. The
50 K cleft/pocket through which Pi is ejected out is proximal to
the actomyosin interface. The conformational changes in the
myosin head should enable the catalytic domains of both heads
Fig. 5. Coordinate system for analysis of conformational changes in myosin
upon release of nucleotide from its site with velocity v at an angle u to the axial
direction (x-axis). The x-axis is along actin and the y-axis lies in a plane
perpendicular to the axial direction.
to bind tightly to their respective binding sites on actin. The
v sin u component (Fig. 5) will cause the myosin head from
which Pi was released to rotate about its own axis which helps
the catalytic domain of that head to bind to actin binding site
tightly. This motion can be communicated to the second silent
non-Pi burst head so that the second head can make a similar
rotational motion about its own axis and bind tightly to its actin-
binding site. Once again this is possible because the rotational
motion about the head’s own axis is small (only a few degrees),
and because of the presence of the common S-1–S-2 hinge and
S-2 coiled coil. Thus there also exists a small rotational motion
about the central axis (S-2 coiled coil). The v cos u (tilt)
component of the Pi release (Fig. 5) is perpendicular to the
plane of the head, hence it will cause a small rotation about the
contact between myosin and actin, as shown in Fig. 6. The axis
of this rotation is perpendicular to the central axis as well as the
head’s own axis (Fig. 6) about which the two rotations
discussed above took place. This tilt motion due to Pi release
may or may not be present—it depends on the angle of ejection
of plain inorganic phosphate, which is not available from any
experiments. We can say however that for 08 < u < 908, as u
increases, the tilt component will decrease in magnitude and it
will be in the same sense as the tilt caused by ATP hydrolysis
(define as positive tilt). For 908 < u < 1808, the tilt component
will increase in magnitude as u increases, but it will be in the
opposite sense to the tilt caused by ATP hydrolysis (define as
negative tilt). The tilt part of the motion due to Pi release can be
represented as follows for the myosin head (catalytic + regu-
latory domain)(Fig. 7). The angle between the catalytic and
regulatory domains remains the same before and after the tilt, as
diagrammed in Fig. 7. All the above rotations about their
Fig. 6. The point of rotation (P) for any v cos u (tilt) component of the motion
upon phosphate release. The axis of rotation is perpendicular to both the central
axis and the body axis and passes through P. Actin is represented by barred
vertical lines. In this and subsequent figures (i.e., Figs. 6–8), the Z-line is below
and the M-line is above.
S. Nath / Process Biochemistry 41 (2006) 2218–22352226
Fig. 7. Representation of the tilt part of the motion in myosin head due to Pi
release. The catalytic domain of myosin head is represented by a thicker line than
the regulatory domain. Bold line is before and dashed line after the conformational
change. The angle between catalytic and regulatory domains remains the same
before and after. a could be equal to b and g could be equal to d.
Fig. 8. Representation of the tilt motion of the distal portion of the crossbridge
(i.e. lever arm movement) in myosin head due to ADP release. The catalytic
domain orientation with respect to actin remains the same before and after. Bold
line represents the initial state of myosin and the dashed line represents the final
state of myosin after ADP release. The re-gaining of a symmetrical disposition
of myosin heads about the central axis is represented by the equality of the
angles D in the final state.
defined axes are the result of angular momentum conservation
upon Pi release. The physical analysis carried out here is very
general and is applicable whatever be the biochemical details of
the reactions because although there exist external forces
between actin–myosin at the actomyosin contacts, there exists
no external torque about those contacts after the ATP hydrolysis
elementary event is complete. It should also be noted that the
light chains can coordinate and stabilize the conformational
changes upon ATP hydrolysis and phosphate release discussed
here, and moreover, can help the two heads to communicate
with each other.
The tight binding of myosin heads to actin leads to release of
bound ADP from its active site through closure of the myosin
50 K cleft [6]. It is very important that ADP release not alter the
orientation of the tightly and stereoscopically bound myosin
catalytic domain on actin. To achieve this, ADP release occurs
from a different pocket/active site (‘‘front door’’) as opposed to
Pi release. This is located in the distal portion of the actin-bound
myosin head. Experiments show that upon ADP release, the
regulatory domain in smooth muscle myosin II swings �258 as
a rigid structural unit, resulting in a�3.5 nm movement about a
pivot in the vicinity of the junction of the catalytic and
regulatory domains inside the myosin motor domain [34]. The
tilt motion of the distal portion of the crossbridge (lever arm
movement) on ADP release is represented in Fig. 8. The
catalytic domain orientation with respect to actin stays the same
before and after in this representation (Fig. 8).
Thus, on ADP release, a symmetrical placement of the myosin
heads about the tail has been regained, as seen clearly from Fig. 8
(angles D are equal in the final state). Now the entire (S-1 + S-2)
behaves as a single elastic body because the kink/distortion at the
S-1–S-2 hinge has been removed. Hence recoiling of the
N-terminal heptads of S-2 takes place and the power stroke
occurs with its fulcrum at the S-1–S-2 hinge, exactly as described
in consummate detail in the RUT mechanism [1,2,6,22–24]. The
rotary motion in S-2 can be converted to the linear (translation)
motion of tightly bound myosin heads on actin due to the
presence of mechanical constraints on actin filaments which
enables only axial movement, as already explained in the
engineering analysis of this system [2].
For the case of ADP release, it is essential to have a negative
tilt (defined above) so as to restore the double-headed myosin
system to a symmetrical disposition about the head–rod
junction and thus unblock the kink/latch and allow the stored
energy to be utilized for performance of useful external work
because there is no other subsequent chemical step left that can
achieve this effect. The rotational component of ADP release
ðvADP sin uADPÞ is irrelevant to the process and may or may not
be present: moreover, experiments indicate that this is primarily
a tilt motion of the lever arm [34]. Special cases of the above
general analysis are possible. An interesting case is one where
Pi release only contributes to tight binding via a rotation of the
myosin head about its actomyosin contact and ADP release
only provides tilt of the head–rod junction in the negative sense
and removes the localized conformational strain (the marked
change in angle (tilt)) at the S-1–S-2 hinge.
The power strokes occur and the rigor state is formed with
the two heads bound to actin and with �one N-terminal S-2
heptad of the myosin molecule still in its uncoiled state, and the
binding of MgATP breaks the actomyosin complex of one of
the myosin heads with actin as described earlier [2,6]. MgATP
binding also reverses the lever arm movement in that myosin
head that had occurred upon MgADP/MgADP and Pi release.
However now, a difference in the two myosin heads arises
S. Nath / Process Biochemistry 41 (2006) 2218–2235 2227
Fig. 9. Representation of the swinging crossbridge model (left) as a transition
from the resting state to the high-energy stretched state in myosin along with
performance of useful external work (lifting of the load). The diagram on the
right shows the observed behavior in all natural systems [transition from a high-
energy state (compressed state in this diagram) to the resting state along with
performance of useful work].
because the burst head (head 1), when it disassociates from
actin due to MgATP binding, has a closed catalytic binding site
but an open 50 K cleft. This subsequently promotes the
hydrolysis of MgATP to MgADP + Pi in this myosin head
(head 1) when it is detached from actin. The remaining rotational
strain in the hinge region of the myosin molecule detaches the
second enzymatically silent non-burst head (head 2) from actin;
this silent head 2 has an open catalytic binding site but a closed
50 K cleft, unlike head 1. MgATP can bind to this non-burst head
2 when it is detached from actin, but due to the absence of actin,
the myosin catalytic site conformation upon MgATP binding is
not identical to that in the presence of interactions with actin. In
other words, we predict that MgATP is positioned differently in
the two myosin heads and the two heads are functionally
different. Thus the non-burst head (head 2) has an intrinsic
inhibition to cleavage of MgATP that can only be relieved in the
subsequent steps of the enzymatic cycle by its interaction with
actin. Thus, unless MgATP binds to the S-1 catalytic site while
the myosin head is bound to actin, it will not be in the correct
conformation to hydrolyze MgATP subsequently when myosin
head is free from actin. Thus, only one head can hydrolyze
MgATP at a time during the enzymatic cycle per two myosin
heads of a myosin molecule (i.e. per dimer).
The above novel analysis shows that only one of the myosin
heads (head 1) is able to cleave bound MgATP while it is free
from actin; the second head (head 2) cannot cleave bound
MgATP at its catalytic site when free of actin [i.e. head 2 is held
in the M.ATP (or similar) state]. The major difference between
the two myosin heads according to the RUT mechanism is in
the positioning of MgATP in the active site when actin is absent.
This intrinsic inhibition to cleavage of MgATP by head 2 can
only be overcome in steps subsequent to combination of actin
with myosin, i.e. it requires activation by actin. Other
microscopic details can also be predicted and incorporated
into the RUT’s framework. For instance, the bound heads of a
myosin molecule will be released from actin in two stages.
During the power stroke at the tightly bound actomyosin state,
the myosin heads will try to unrotate, but due to the constraint
of tight binding of myosin heads to actin complete unrotation
cannot occur, though there will be strain in the actomyosin
interactions due to this constrained unrotation [2,6]. After the
power strokes, and after MgATP binding to one of the myosin
heads’ (head 1) binding site has broken the strained actomyosin
interactions of that head with actin [2,6] and detached that head
from actin, the remaining unrotation of that myosin head (head
1) will take place as the last S-2 N-terminal heptad reforms its
initial coiled coil structure. This unrotation of head 1 is opposite
in sense to the rotation incurred during ATP hydrolysis and is in
the right sense to relieve the remaining rotational strain at the S-
1–S-2 hinge that had occurred during the hydrolysis and
subsequent processes. Thus the recoiling of S-2 to its initial
conformation and unrotation of head 1 causes the second
myosin head (head 2) to unrotate and break the strained
actomyosin interactions between the second silent non-burst
head (head 2) and actin and detaches that head from actin. In
summary, there exists a kind of cooperation between the
myosin heads through the medium of actin and the common
myosin S-1–S-2 hinge and S-2 coiled coil. Finally, both heads
of a myosin molecule have achieved their original orientation in
terms of rotation and also in terms of tilt (due to their untilting
during the power strokes [2,6]), and recoiling of the S-2 coiled
coil is also complete and a new enzymatic cycle can begin [2,6].
7. Generic differences with existing models of muscle
contraction
Detailed differences of the RUT Mechanism with other
current models of muscle contraction applicable at the
molecular level have been discussed earlier [2]. Here, more
generic and absolutely fundamental differences not treated
earlier are taken up. In the well-known swinging crossbridge
model of Huxley [28,35], increasing attraction between myosin
head and actin is the seat of the force generation by muscle.
Thus, the primary rotation of myosin head about its actomyosin
contact is the cause of the power stroke (lifting of the load) as
well as stretching of a spring/elastic element (Fig. 9). Both
these processes (stretching of the elastic element and lifting of
the load) require energy. However, in the RUT energy storage
mechanism, and in all mechanical systems that we see in nature,
it is the other way around, i.e., one of the processes releases
energy to do useful work: for example, a spring/elastic element
being restored to its resting state from a high-energy state (e.g.
compressed/stretched), thereby lifting the load (Fig. 9). This is
not to say that the swinging crossbridge is impossible: it is
possible if we supply enough energy, but the energy relations in
muscle are not as postulated in the swinging crossbridge model
(e.g. equilibrium between stepper at actomyosin and S-2
spring), and nature does not behave in the way the model
postulates. Further, in this and other such models, including the
lever arm model, distal interactions between myosin and actin
are the primary drive that passively alter the lever arm angle at a
distant S-1–S-2 hinge region of myosin. In the RUT
mechanism, there exists a bi-directional communication bet-
ween S-1 and S-2 along the helical structure of myosin, and
S. Nath / Process Biochemistry 41 (2006) 2218–22352228
angle changes about the S-1–S-2 hinge region of myosin
constitute a primary process induced by the MgATP hydrolysis
reaction and the reaction-linked conformational changes. These
movements of myosin head about the S-1–S-2 hinge due to
active MgATP bond cleavage reactions lead subsequently to
myosin head-actin interactions distal to the hinge and to loose
actomyosin binding, which is converted to strong actomyosin
binding and bond formation by conformational changes upon
chemical (e.g. inorganic phosphate) release events in the
myosin head. The power stroke takes place about the S-1–S-2
hinge in the RUT theory, unlike in all current conceptions of the
muscle contraction mechanism. Thus, primary and secondary
drives are interchanged in the new theory versus old
conceptions of the power stroke. Further, in the new paradigm,
energy changes associated with myosin–actin binding or
release, or nucleotide binding or release are not directly
coupled to the performance of useful external work. In fact,
nucleotide (e.g. MgADP) release processes only relieve the
distortion/block at the S-1–S-2 hinge and enable the power
stroke to take place, i.e. they trigger the power stroke, but are
not the true driving force of the elementary force production by
muscle. Rather, free energy released upon cleavage of the Pb–
Pg bond during the MgATP hydrolysis step in myosin S-1 is
directly transduced to conformational strain and stored as a
high energy uncoiled state in the S-2 coiled coil that is
subsequently released to execute the powerstroke and perform
useful mechanical work.
Thus, current conceptions of the molecular mechanism of
muscle contraction do not feel the need to include the aspect of
energy storage in myosin (while in the RUT Mechanism the
energy storage aspect is a central one) since in these models,
force generation and movement is directly coupled to the
release of bound ligands/nucleotides. It should also be noted
that this standpoint adopted ubiquitously by the motility field is
diametrically opposite and contradictory to the view widely
accepted within the bioenergetics community, where release of
bound nucleotides requires energy of the ion gradients/light/
redox energy, far from it being used to perform useful work, as
has been reviewed in detail [1–3]. However, neither community
has given the chemical step (synthesis/hydrolysis reaction) the
central importance that it deserves, dismissing it as energe-
tically inconsequential [35–37] (with the torsional mechanism
stating from its inception that all the elementary steps require
energy, including chemical synthesis [3,8–11]), but both
communities emphasize different physical steps (useful
external work performed by nucleotide (e.g. MgATP) binding
versus bound nucleotide (e.g. MgADP) release in bioenergetics
and motility respectively). It is only when ATP synthesis and
ATP utilization are studied together as exemplified by this
scientist-engineer’s research program of the past 15 years [1–
17] that unified and coherent theories of both processes, without
inconsistencies, emerge. Otherwise, how can we be absolutely
certain that we are not violating the universal laws of science?
Thus the torsional mechanism and the rotation-uncoiling-tilt
mechanisms have been conceived in a unified way and they are
not beset with the inconsistencies of all other previous theories,
and the several things that appear different, and the seemingly
disparate observations, are now seen and grasped as various
aspects of one underlying phenomenon.
Current conceptions of the force generation mechanism in
muscle do not attribute any role for the S-2 region unlike the
RUT Mechanism (however, see Ref. [27]). This is due in large
part to the success of in vitro motility assays. However, if the
energy is stored physically, as we propose, and not chemically,
then the linkers that couple the myosin S-1 to the substrate (e.g.
a-actinin and streptavidin) could store energy physically, for
example by acting as a torsional spring in the in vitro assays and
could thereby support motility, albeit at reduced velocities than
in vivo muscle myosin, as found. Thus, only those connectors
that in some way mimic the energy storage function of S-2
coiled coil would support motility in these assays, and the
speeds are lower than the in vivo velocities because of the
inefficiencies of the coupling in the in vitro motility system.
Yet, because of the absence of the S-2 coiled coil in these in
vitro assays one could easily be led to the false conclusion that
S-2 is not essential for motility. Moreover, the observation of
motility in these assays does not mean that the motility can only
occur by a lever arm mechanism, as tacitly assumed. Other
mechanisms are also possible. Finally, as the new paradigm
shows, the in vitro assays do not exactly match the in vivo
system of force production taking place in living muscle in each
and every way.
The fulcrum of the power stroke is different in the new
paradigm compared to current models. Thus according to the
new paradigm, the hinge at the LMM–HMM junction of
myosin II is for muscle activation, the actomyosin contact for
rotation to convert loose actomyosin to tight binding upon
phosphate release, the pivot within the myosin head at the
junction of the catalytic and regulatory domains for tilting of
the lever arm upon MgADP release to help relieve the kink/
latch state of the crossbridge, and the S-1–S-2 hinge is the
fulcrum about which the power stroke occurs. Thus a
mechanical function is ascribed to each flexible junction/hinge
known to be present in myosin II. It should be noted that the
new theory retains the pioneering and other verified aspects of
the old; for instance, it agrees completely with lever arm
theories that the postulated rotations upon phosphate release
[38] and the envisaged tilts and swings upon ADP release do
occur [34]; however in the new paradigm these are not the true
cause of the power stroke as postulated by the lever arm model,
but are merely preliminary to the power stroke. They are
precursor events that unblock the kink at the S-1–S-2 hinge and
trigger the coiling back of the N-terminal heptads of S-2 which
initiates the powerstroke. Thus, if the aim of current research
programs of muscle contraction is to understand the effect of
nucleotide binding and release steps and the conformational
changes they produce in myosin head (e.g. swings of the lever
arm and other events preceding in time to the power stroke that
serve as initiation steps to make the power stroke happen), then
the current program can be considered highly successful. But if
the aim is to understand in a unified way the cause of the
elementary force production processes during muscle contrac-
tion, and the way the powerstroke is generated on actin, then a
reorientation is necessary, and the new theory provides a way
S. Nath / Process Biochemistry 41 (2006) 2218–2235 2229
for future progress and will certainly prove a most valuable
guide for further experimentation in the field if we are willing to
listen to it with an open mind.
In the swinging crossbridge and lever arm models of muscle
contraction, ATP has a single role only, that of detaching the
crossbridge from actin and collapsing the spring/elastic element
and thereby dissipating that energy. This is not the most
efficient way of utilization of energy! This difficulty does not
arise in the RUT Mechanism because in that theory, ATP plays a
dual role. In the lever arm model, translating the head–rod
junction�5–10 nm axially need not lift the load, because there
exists a hinge inside the myosin head and the lever arm can tilt
relative to the catalytic domain, and the angle between the
catalytic domain and the lever arm can alter (Fig. 10). This
raises the crucial question: if the whole myosin head does not
tilt as one rigid entity (as envisaged by the early Huxley
swinging crossbridge models [35,36]), but rather tilting of only
part of the myosin head is involved, as conceived in later
modifications of the swinging crossbridge models by lever arm
models [38], and the angle/orientation of the catalytic domain
with respect to actin remains fixed (Fig. 10), why will the lever
arm swing move actin? In other words, the presence of the
hinge in the myosin head in the vicinity of the junction of the
catalytic and regulatory domains will not permit transmission
of the lever arm swing or axial movement of the head–rod
junction to actin filament. If the myosin head moves/tilts on
actin, the orientation of the catalytic domain relative to actin
must change, and if this orientation does not change, as
proposed by the lever arm model, then actin will not be pulled
with myosin head given the structure, architecture and
connectivity in the actin–myosin system. In fact, a pure lever
arm tilt will not generate a sufficiently large torque to cause
filament sliding and that too under external load conditions.
This conclusion is consistent with the principles of Newtonian
mechanics. We would do well not to violate it. Thus, the older
models are translation models and do not include the key role of
torque as addressed by the new mechanism where a rotary
motion (recoiling in S-2) is converted to a translation/linear
motion in S-1–actin, a mechanism that is proven in man-made
engines, and can definitely occur as per the laws of mechanics,
Fig. 10. Schematic diagram for a lever arm model representing the absorption
of energy by the internal hinge of myosin/change in angle (tilt) at the junction of
the catalytic and regulatory domains of myosin upon �axial translation of the
myosin head–rod junction during the power stroke without lifting of any load or
movement along actin.
given the architecture of the myosin–actin and the mechanical
constraints present on the system [2]. For torque to exercise its
effects, the myosin heads must be free from actin (i.e. the
myosin heads must be free to rotate about their axes in an
unconstrained way). However, the myosin heads are bound to
actin during ATP binding, and during bound phosphate/ADP
release from myosin head. Hence ATP binding or Pi/ADP
release steps cannot cause the rotation of myosin heads and
uncoiling of the N-terminal S-2 heptads. Only the ATP
hydrolysis step occurs when myosin heads are free of actin;
hence the bond scission event during the ATP hydrolysis
elementary step can readily cause the rotation-uncoiling-tilt
envisaged in the RUT mechanism, i.e. the required conforma-
tional changes, in the myosin molecules.
Finally, there is the correspondence with experiment,
especially the powerful single molecule imaging studies on
myosin II to be dealt with. The classical kinetic studies of
Tonomura and co-workers [32] on the heterogeneous nature of
the myosin dimer have already been alluded to; yet, no
consideration (let alone even a rudimentary attempt at
explanation) of the large body of his experimental work has
been given even after the passage of over three decades. More
recently, in an experiment of great technical virtuosity and
exceptional complexity, a simultaneous measurement of ATPase
and mechanical events in single myosin molecules during force
generation and interaction with actin has been pioneered by
Yanagida and co-workers [39]. The experiment shows unam-
biguously that myosin II can produce force several hundred
milliseconds after ATP hydrolysis and release of bound
nucleotides. This delay clearly points to the ability of myosin
to store chemical energy from ATP hydrolysis and subsequently
perform useful work with this stored energy. This important
finding does not support the widely accepted view that force
generation is directly coupled to the release of bound ligands.
The authors of the work predicted that ‘‘these results will prove
fundamental for understanding the mechanism of mechan-
ochemical energy transduction in molecular motors’’ [39]. The
RUT Mechanism is the only fundamental theory from first
principles that is currently available that explains these powerful
single molecule results. In summary, it can be stated that, taken
together with Nath’s torsional mechanism of energy transduction
and ATP synthesis, the rotation-uncoiling-tilt energy storage
mechanism of muscle contraction solves fundamental molecular
mechanistic problems in bioenergetics and motility and offers
a most detailed, unified and appealing picture of energy
production, transduction, storage and utilization processes in
systems of biological molecular machines.
8. Application of the general principles to other
molecular machines
The above unifying principles have been applied innova-
tively to other molecular machines, for instance the processive
cargo-carrying kinesin and ncd motors on microtubules [1]. The
general principles work for these motors, yet, because their
biological function is different from myosin II, and the nature of
mechanical constraints on the V-shaped kinesin/ncd/myosin V
S. Nath / Process Biochemistry 41 (2006) 2218–22352230
molecule is different, the specific mechanism (the rotation-twist
energy storage mechanism of processive molecular motors) is
not identical to that of myosin II [1]. However, given the detailed
development for myosin motors in Sections 6 and 7, the sense of
rotation of the two heads is opposite to that proposed earlier. Thus
ATP hydrolysis causes a clockwise rotation of the kinesin/ncd
head 1 viewed from the cargo end. The partner head (head 2 that
rotates by the ‘‘physical stroke’’ [1]) will rotate counterclockwise
viewed from the cargo end. This would also make the rotation
sense in accordance with the X-ray structures of kinesin in ATP-
like and ADP-like states and the clockwise rotation (viewed from
the cargo end) that has been proposed upon ATP hydrolysis by
these workers [40]. Such a rotation may uncoil one heptad of the
neck coiled coil. However, according to the rotation-twist energy
storage mechanism, whether there is more uncoiling or only
some (1-heptad) uncoiling, generation of twisting strain and
storage of energy as elastic (primarily twist) energy in the V-
shaped structure up to hinge 1 is similar in either case [1, 1st
column on page 15]. Experiments show that extensive neck
coiled coil unwinding does not occur during kinesin motility
[41]; hence the role of the�1-heptad unwinding may only be to
enable the heads to separate sufficiently to span the distance
between binding sites on the microtubule and bind to them. In any
case, the re-coiling of the heptad does not drive the physical
stroke of head 2 that binds to the a-tubulin site on the
microtubule; rather, the elastic (twisting) strain in the molecule
forces it to regain its resting state (page 15 of Ref. [1]). Finally,
unlike the estimation of relative speeds of the chemical and
physical strokes made for the situation invivo [1], far-sighted and
innovative in vitro experiments show that progressive shortening
of the coiled coil does not alter the time taken by the fast step, but
slows down the time for the slower step [42]. This can be
interpreted as meaning that, in vitro, with these truncated
constructs, the ‘‘physical stroke’’ [1] is the slower step, because
only the physical stroke can be affected by the mechanical/elastic
properties of the kinesin coiled coil (the chemical stroke has no
contribution from the length of coiled coil constructs but depends
only on the motor, and no alteration in the motor domains was
made in the experiments [42]). In fact, the truncated constructs
can be modeled as shorter springs/elastic elements, which do not
have sufficient elasticity on the average to overcome the barrier
for the physical stroke (and also help unbind head 2 from its
microtubule binding site). Hence these truncated constructs show
greater propensity to limp in the experiments of Block and co-
workers [42]. We predict that a higher load (vertical or backward)
will make it more difficult for the physical stroke to unbind head
2 from the microtubule and move it to its next binding site on the
microtubule. In vitro, a smaller load will reduce limping, because
the elastic strain can overcome the load and unbinding of head 2
more easily. It should be re-emphasized that the insignificant
hinge and neck/stalk rotation of kinesin/ncd/unconventional
myosin with respect to the �1808 rotation of the head is a
necessary condition for storage of elastic energy (primarily as
twist) in the V-shaped molecule as per the rotation-twist energy
storage mechanism of processive molecular motors, a require-
ment that has been spelled out very clearly [1]. The mechanism is
also consistent with other innovative experiments that showed
<308 relative rotation between microtubule and the neck/stalk of
kinesin [43]. Thus, the inchworm model is not the only
mechanism possible that is consistent with this observation. The
new mechanism is consistent with both ‘‘poles’’ of observations
[42,43]. Hence the statement on page 16 of Ref. [1] still appears
to be an accurate description in the opinion of this researcher.
The unity of the description of these molecular motors with
aspects of conventional myosin is further realized following the
key insight that the elastic strain energy accumulated in the V-
shaped molecule is by itself insufficient to enable the head that
has stepped forward by the chemical stroke (the leading head
after the stepping process) to return back and thereby relieve the
internal strain. Rather, the elastic strain needs to accumulate in
the molecule before the physical power stroke [1] takes place.
Moreover, upon stepping, the leading head, though at the right
axial position for binding to its site on the track, is in the wrong
orientation for tight, stereospecific binding. Only weak binding
of the head to its microtubule/actin track is possible in this
orientation. Hence a conformational change is needed in the
leading head to cause it to bind tightly and stereospecifically to
its binding site. It is proposed here that this occurs after release
of Pi due to microtubule/actin interaction/activation, just as in
the RUT framework for conventional myosin. Possibilities
upon Pi release from the leading head include bending of the
lever along the length of the leading head, a bending about a
pliant point in the leading head, or, most significantly, rotation
of the leading head about its axis/neck linker, or combinations
of these, until the tight binding of head to track progressively
takes place, and both motor heads face the same direction. As
this occurs, the internal elastic strain in the V-shaped molecule
increases. Further, after ATP hydrolysis, the V-shaped molecule
had bent in a second plane by tethering through the trailing
head. This prevents the trailing head from moving forward. It
can be readily visualized that in the bent structure, a component
of the torque acts downward (and hence not in a direction
perpendicular to the track); therefore, it is difficult to detach the
rear head until the motor is perpendicular to the track. This
trigger is provided by ADP release, again as in the RUT
mechanism, and now the bend/block is removed, and the
internal elastic strain applies a torque at the V-junction of the
molecule in a direction opposite to the direction of the torque
due to the ATP-motive process. The leading head, since it is
tightly and stereospecifically bound to its binding site does not
get released. The rear head bound to a-tubulin/actin detaches
and steps forward and binds to its next available binding site
and a resting state configuration of the kinesin/ncd/myosin V
molecule with both heads bound is reached (with the new
leading head containing bound MgADP, and the rear head
empty of bound nucleotide), and a new mechanochemical cycle
can begin.
9. Systems biology/engineering analysis of musclecontraction
A systems biology/engineering analysis of muscle contrac-
tion (at a certain given length) similar to that performed in
Section 3 for ATP synthesis leads to the following result [1 is
S. Nath / Process Biochemistry 41 (2006) 2218–2235 2231
the driving reaction (input), 0 is the driven mechanical
consequence (output)]:
Lwhole11 ¼ nL11 (13)
where n is the number of operating crossbridges. This is
because force on one crossbridge is 1/n times the force pro-
duced by the muscle sarcomere (neglecting internal shear
effects). Further:
Lwhole00 ¼ L00=n (14)
because the velocity of individual operating crossbridge equals
the velocity of shortening muscle in isotonic contraction.
Finally:
Lwhole01 ¼ L01 (15)
The differences with the chemical output case of Section 3 are
now clarified. In muscle, while each operating crossbridge
produces its own output (force) independently of the other
operating crossbridges, the forces produced by each cross-
bridge are summed up to produce net force output of the
half-sarcomere, which is further summed up to produce the
macroscopic effect in whole muscle. In other words, with
appropriate scaling of the variables above (per unit length,
area or volume), the result for the half-sarcomere can be readily
extended to whole muscle. However, the velocity of each
working crossbridge is equal to the velocity of contraction
of the sarcomere or in whole muscle because of the structural
relationship/arrangement between myosin and actin. Thus, the
final output is force which is summed up, and we need to know
the number of activated crossbridges, n.
The conclusion suggests itself that the overall muscle
performance is the result of two independent phenomena: that
of the individual crossbridge when activated and producing
force (under which conditions the single crossbridge behaves as
a linear energy convertor and, therefore, linear nonequilibrium
thermodynamics analysis is applicable), and the number of
operating crossbridges, n, that are activated and producing
force in the whole system [2]. We propose that the nonlinear
effects observed in the macroscopic system (e.g. whole muscle)
result from the variation in the value of n for a given
experimental condition and that n is a function of force or
velocity of isotonic contraction. We predict that the value of n
decreases with increase in velocity (because the crossbridge
will have to be disconnected faster to sustain higher velocities).
A systems (electrical) analog incorporating the above novel
concepts is shown in Fig. 11. Putting a switch (S) on is akin to
Fig. 11. Systems (electrical) analog of muscle contraction at a given length.
activating a crossbridge and increasing the number of force-
producing crossbridges (C). For a given steady state condition,
a certain number of switches are in the ‘‘on’’ state, i.e., a certain
constant number of crossbridges are activated. This number is a
function of velocity in whole muscle. Thus, Fig. 11 represents a
conservative (non-dissipative) mode of regulation [2] of the
output of the system. Using these concepts it is possible to
employ the systems approach/analog delineated in Fig. 11 and
completely determine the performance of the ‘‘system’’ in the
following progression: from submolecular elements of cross-
bridge (Sections 6 and 7) to crossbridge and actin, from
connections of crossbridge and actin in series to a myosin–actin
filament pair, from a summation of myosin–actin filament pairs
in parallel to a half-sarcomere, from a sum of half-sarcomeres
in series to a myofibril, from several myofibrils in parallel to a
muscle fiber, and finally, from the sum of muscle fibers
connected to each other in parallel to the macroscopic system of
whole muscle. Hence we have shown that the concluding
comment of other researchers on our systems approach to ATP
synthesis that ‘‘such a transition from the local to the global
level in biology is a significant achievement of the torsional
mechanism’’ [44] is applicable to the muscle system and the
RUT mechanism also.
10. Physical, chemical and biological implications
The work has a plethora of far-reaching physical, chemical
and biological implications. Specific implications have already
been dealt with in the detailed development of Sections 3–9.
Some general scientific implications resulting from the research
are discussed below as concisely as possible.
10.1. Microprocess
In various branches of engineering and science, processes
have traditionally been looked at in a macroscopic sense. This
work emphasizes the need to look at the process on a molecular,
submolecular and even microscopic level, and to seek driving
forces also at such a microlevel. The concept of the
microprocess then leads to a mechanistic, ‘‘first principles’’
understanding that can be integrated to understanding the
systems behavior at higher hierarchical levels, knowing the
systems architecture and topology.
10.2. Unity in diversity
The work shows that storage of strain energy as twist in a-
helical or uncoiling/supercoiling in coiled coil protein domains/
elements or as torsional strain in these motifs provides unified
principles for operation of protein molecular machines (and
similar principles, by extension, to DNA- and RNA-based
molecular machines). Yet, the principles manifest diverse types
of motility: the exact type of strain and localized region of energy
storage, and the exact type of motion depend on the mechanical
constraints present on the degree of freedom of the constituents
of the protein macromolecule(s). Diverse experimental observa-
tions from various fields are shown to be explained by the new
S. Nath / Process Biochemistry 41 (2006) 2218–22352232
theory in a natural way, and we have a unity of physical principle
in a diversity of biological function. The work can be seen as one
further step in revealing (in a centuries-old process of scientific
inquiry) that even the most complex processes in nature are
governed by simple, rational physical laws and principles.
10.3. First law of thermodynamics
The question was raised [1] that at which step is energy put
into ATP to raise it to a higher energy level vis-a-vis ADP + Pi?
The problem was that Boyer’s binding change mechanism [1–
3,5,8–10,37,44] did not address the questions of how and when
energy got locked into the ATP, unlike in the torsional
mechanism [1–3,4,5,7–11,13–15,44]. In current mechanisms,
the g-subunit rotates freely (e.g. ‘‘spins like a top’’); but nobody
has found a way to date to convert the rotational kinetic energy
of the spinning shaft into the stored internal energy of ATP. In
fact, as we slow the shaft, the energy will be thermalized and
dissipated as heat and not converted to useful work or stored
energy. We are then left with binding energy as the only source
of useful external work. But calculation based on experimental
Kd values [2] for the catalytic sites and use of the expression
DG = RT ln(Kd2/Kd1) reveals that the binding free energy
difference is grossly insufficient to account for the required
stabilization of�60 kJ/mol postulated by the first theory, or, for
that matter, of even the standard state value of �35 kJ/mol.
Moreover, in a tri-site mechanism, the ultra weak binding of
MgATP to site 3 (with a Kd of 23 mM) does not provide
sufficient energy to drive complete rotation of the g-subunit.
Further, binding energy is not stored energy (that is, it is not
energy stored within ATP) but is only the interaction energy of
the enzyme with the ATP. If there exists no other form of energy
storage in these systems, then, for an open system in a steady
state, we can integrate a general differential expression of the
first law involving elemental transfers over any arbitrary time
period Dt [1]. With these caveats, with the molecular machine
as the system, the binding step lies inside the system boundary,
and such a step internal to the system cannot be used to perform
useful external work outside the system boundary surface,
without violating the first law of thermodynamics for open,
steady state systems. Thus, previous theories have not
synthesized ATP but have only made ADP.Pi. It should be
noted that these are problems with the conceptions of the
earlier, first theories of ATP mechanism, and are not related to
the way the ATP synthase enzyme actually works. A clear
distinction should be made between these two. In any case, the
earlier proposals have not been cast in molecular terms and are
not sufficiently detailed to even permit a proper evaluation; the
energy transduction in these proposals remains a black box. The
new paradigm converts the black box of energy transduction
into a white box, and none of these inconsistencies without
exception arise in the new paradigms [1–17]. This work focuses
attention not only on the physics, but also on the chemistry of
the ATP hydrolysis/cleavage reaction and the chemical
hydrolysis reaction-linked conformational changes as the
elementary step at which energy transduction and storage
occurs in biological molecular machines, unlike the purely
physical interaction energies of ATP/ADP/Pi ligand binding/
release to/from the enzyme invoked in every other current
model of biological energy transduction. We can have different
theories depending on how we redistribute energy. It should
however be clearly recognized that whether ATP binding
energy, or ATP hydrolysis, or both cause rotation in the
hydrolysis mode does not really present problems for the
torsional or RUT mechanism. Since the hydrolysis step follows
the binding step on the enzyme in these processes, the
conformational changes postulated in this paper to be caused by
the hydrolysis step can readily be ascribed to the previously
occurred ATP binding step (or, for that matter, to both the ATP
binding and hydrolysis steps), and the rest of the mechanism
remains unchanged, except for a change in language and
semantics.
We now clearly see that possible violations of the first law of
thermodynamics are only revealed when we consider ATP
synthesis by the F1FO-ATP synthase and ATP utilization by a
molecular machine such as myosin–actin/kinesin/ncd (as in this
paper) together. If we consider ATP synthesis in isolation (and
never connect it with the ATP usage cycle), we can be as
inefficient as we please and simply waste redox/light energy or
the energy of ion gradients and falsely claim that we had made
ATP (e.g. by freely rotating a shaft, as in the binding change
mechanism). Unless we link ATP synthesis with the ATP
hydrolysis/utilization cycle, we would never see possible
violations of the first law of thermodynamics.
10.4. Second law of thermodynamics
From the above and earlier discussion [1–3], the energy for
useful external work must ultimately come wholly, or at least in
part, from energy stored internally (by molecular rearrange-
ments) within ATP vis-a-vis (ADP + Pi), and not only from
interaction energy steps internal to the overall system of the
molecular machine. Thus, all current mechanisms (with the
exception of Nath’s mechanisms) imply that the energy stored
in ATP is first converted into thermal motions and only then
subsequently used to perform useful external work. But this is
impossible because it would mean that useful work has been
done cyclically using heat under isothermal conditions.
According to the second law, heat cannot be an energy source
unless it flows between a source and a sink at different
temperatures.
Given the above, there are two ways to reconcile the second
law of thermodynamics with reversible processes in statistical
physics. Either we say that the second law is only applicable if,
in a volume V, the number of particles, N that have diffused into/
out of Vare greater than the average number of particles Navg in
that volume (or root mean square number of particles present in
that volume). This implies that we have specified the limits of
validity of the second law and that it is a law of large numbers.
But the fact remains that suberb state-of-the-art biological
experiments show that biological machines work as single
molecules, with discrete steps. Hence alternatively, we can say
that the second law is valid for single molecules, but we now
introduce timescales, and state the law such that it is impossible
S. Nath / Process Biochemistry 41 (2006) 2218–2235 2233
to convert energy that has spread over the thermal degrees of
freedom and equilibrated with the surroundings and reached a
Boltzmann distribution very fast (in time t < t) to a longer-
living form of (stored) energy in a (molecular) device that lasts/
stays stored in the device for a time t > t. Thus, the second law
is not violated by single molecules; rather, we have now truly
understood the meaning of the second law. A suitable concise
restatement of the second law of thermodynamics applicable to
single molecules then is, ‘‘Molecules perform useful work by
direct transduction of energy from one form to another;
thermalized energy cannot be transduced into stored energy.’’
What is thus forbidden by the second law is to take a form of
stored energy, allow it to spread over the thermal degrees of
freedom (Q), and then to try and convert this thermalized
energy Q, under isothermal conditions, to another form of
stored energy, i.e. to an energy that remains stored and lasts
longer than the time of thermal exchange. The trick of biology
then is not to allow stored energy to spread over (and exchange
freely) with the thermal (rotational, vibrational and transla-
tional) degrees of freedom of the surrounding reservoir. Such
processes that directly transduce stored energy from one form
to another are reversible too; hence there is no contradiction
with the reversibility of statistical physics.
The old forms of the second law (e.g. Kelvin-Planck and
Clausius statements) are only valid for heat engines. The
ubiquitous biological machines of molecular dimensions do not
work in the same way as heat engines and hence a new
reformulation/restatement of the second law is needed. It shows
that it is not sufficient for a fluctuation (e.g. Brownian motion)
or other perturbation to lift a microscopic (or molecular) load; it
has to keep the load lifted (or store energy in a device) for a time
t > t and not lose it to the surroundings as heat within that time.
These fundamental concepts enable us to achieve a crystal-clear
understanding of the meaning of the second law of thermo-
dynamics and to grasp what is allowed and what really is
forbidden by the second law at the molecular level. This was
chiefly because the concepts discussed in this paper and earlier
[1–3,45] allowed us to make a distinction between heat and
work/stored energy at the molecular level on the basis of
timescales applicable at even a single molecule level.
10.5. Timescales and lengthscales
The above discussion implies that conventional machines
fail when scaled down to the molecular level because the
constraint against which useful work is done is disturbed by
Brownian fluctuations and the machine cannot function at all.
Classical approaches assume the system to be ergodic, i.e. they
only consider statistical thermal degrees of freedom that are fast
enough to exchange energy with each other/with the
surroundings. However, in biological molecular machines,
this assumption is violated, and only certain specific long-
lasting (compared to the time for thermal exchange) degrees of
freedom are excited in localized spatial regions of the device
that exchange only slowly with the thermal degrees of freedom
and do not reach equilibrium with these thermal degrees of
freedom within a certain interval of time, t (these states were
called nonequilibrium conformational states or metastable
states in our earlier analyses [1–3]). Thus, these nonequilibrium
biological systems possess a deep space-time structure based on
timescales and lengthscales and their existence requires a
different, more mechanical approach to understand the
functioning of these machines.
10.6. Technological applications
The work has great potential to realize various new
technologies, including the development of new, highly
efficient (nano)devices that will play an increasingly important
role in the industrial technology of the future, as discussed
earlier in detail [2].
Finally, the major contributions already made to the world
by scientists from emerging economies (and the greater future
role and responsibilities of these societies) in the generation of
new knowledge needs to be further recognized as being
absolutely vital for the progress and future well-being of the
world in science and in all other fields of human endeavor, as
prophesized by the author [46,47]. The question arises: Can the
creative artist–scientist have a premonition of what lies in store
for him?
11. Conclusions
A comprehensive molecular mechanistic analysis of
fundamental energy transduction processes in biology has
been carried out. In particular, the molecular mechanisms of
two of the most fundamental processes in biology – ATP
synthesis and muscle contraction – have been addressed in
consummate detail in all their complexity. Currently believed
models of these fundamental processes have been analyzed and
found to be perpetual motion machines of the first and second
kinds. The former conclusion has been shown to hold because
the free energy released during the chemical ATP hydrolysis
elementary step is not employed for useful external work in
these models, and binding energy changes alone are
insufficient. The latter conclusion of current models being
Maxwell’s demon machines has been proved because, in all
those models, in effect, heat is being converted to work in a
cyclic isothermal process. The new paradigms of the torsional
mechanism of energy transduction and ATP synthesis and the
rotation-uncoiling-tilt energy storage mechanism of muscle
contraction have been shown to solve the problems in
bioenergetics and motility and to offer a most detailed, unified
and appealing picture of energy production, transduction,
storage and utilization processes in systems of biological
molecular machines. The new paradigms are in consonance
with the universal laws of science. A novel mechanism of
energy storage in biological processes different from the usual
entropic mechanism of rubber elasticity has been identified and
suggested to be of great significance in biology. In this new
mechanism, hydrophobic interactions play a very important
role. It has been proposed that upon mechanical deformation,
the extent of interface between hydrophobic protein regions and
water is increased and new protein–water interfaces are created
S. Nath / Process Biochemistry 41 (2006) 2218–22352234
by making the hydrophobic residues of the protein chain more
accessible to water, thereby storing the energy of the
mechanical torque/elastic deformation in submolecular ele-
ments of the protein machine. Free energy changes associated
with this type of hydrophobic interaction have been postulated
to provide a primary driving force for muscular contraction.
The manifold far-reaching physical, chemical, biological,
technological, social, and human implications arising from the
work have been discussed in detail.
Acknowledgements
My research program has been liberally funded by the
Department of Science and Technology, India through the
Swarnajayanti Research Project ‘‘Molecular Machines:
Mechanism and Thermodynamics’’ under the Swarnajayanti
Fellowships for ‘‘promotion of basic research of world
standard.’’ I am grateful to Dr. C. Channakeshava of the
Engineering Mechanics Research Centre, Bangalore, India for
several most helpful discussions on muscle contraction over the
years. Finally, I thank both referees for their long and detailed
reviews that have greatly helped to improve the presentation of
various aspects of the work.
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