V16 Stochastic processes in cells

16. Lecture WS 2007/08

Bioinformatics III 1

V16 Stochastic processes in cells

3 aspects of genetic circuits control dynamic cellular behaviors:

- the circuit architecture or pattern of regulatory interactions among genetic

elements

- quantitative parameter values: parameter strengths ...

- stochastic fluctuations („noise“) associated with the concentrations of cellular

components.

A fundamental biological question is how these 3 aspects of genetic circuits

combine to determine cellular behavior, its variability, and its potential to evolve.

Suel et al. Science 315, 1716 (2007)



Bacillus subtilis

Competence in B. subtilis is a stress response.

It allows cells to take up DNA from the environment.

Differentiation into competence is transient.


Competence is a probabilistic and transient differentiation process regulated by a geneticcircuit.

Pinit: The rate of entering the competent state from

the vegetative state comp: amount of time spent in the competent state

The ComK transcription factor concentration is high (pink region) when cells are competent and low (green region) when they are growing vegetatively.



Bacillus subtilis The genetic basis for this behavior is a circuit involving comK and comS.

The transcription factor ComK is necessary and sufficient for differentiation into competence.

ComK positively autoregulates its own expression but is degraded by the ClpP-ClpC-MecA

protease complex.

ComS competitively inhibits this degradation and is repressed in competent cells, forming a

negative feedback loop.

Map of the core competence circuitry. Key features include positive transcriptional autoregulation of comK and a negative feedback loop in which ComK inhibits (possibly indirectly) expression of ComS, which in turn interferes with degradation of ComK.

The graphs below the PcomK and PcomS promoters define parameters of this system: Expression rates change from K to K and from S to S respectively, as ComK concentration increases during competence.




Bacillus subtilis k and s, the basal expression rates of comK and comS, are expected to affect the behavior

of the circuit.

To manipulate these parameters, an additional copy of either comS or comK under the

control of an inducible promoter denoted Phyp generating the Hyper-k and Hyper-s,

was inserted into one chromosome.

K and S qualitatively change the

dynamics of the competence circuit and

independently tune the probability of

initiation (Pinit) and mean duration (comp) of

competence events.

(A and B) Filmstrips and PcomG-cfp time

traces (for individual cells) of competence

events obtained in Hyper-K (Phypk-comK)

and Hyper-S (Phyp-comS) strains at the

IPTG concentrations and times (hours)

indicated.

PcomG-cfp and PcomS-yfp activities are

depicted in red and green, respectively.

Sporulating cells are seen in white.

Cells that did not sporulate were prone to

lysis toward the end of movie acquisition.



K and S qualitatively change the

dynamics of the competence circuit and

independently tune the probability of

initiation (Pinit) and mean duration (comp) of

competence events.

(A and B) Filmstrips and PcomG-cfp time

traces (for individual cells) of competence

events obtained in Hyper-K (Phypk-comK)

and Hyper-S (Phyp-comS) strains at the

IPTG concentrations and times (hours)

indicated.

PcomG-cfp and PcomS-yfp activities are

depicted in red and green, respectively.

Sporulating cells are seen in white.

Cells that did not sporulate were prone to

lysis toward the end of movie acquisition.

Bacillus subtilis



Simulation model

To better understand independent tuning of Pinit and comp, as well as reliable

maintenance of excitability, use 2 simulation models of the core interactions in the

competence regulation circuitry.

- 2 continuous ODEs for the concentrations of comK and comS

- stochastic simulations that account for intrinsic noise of biochemical reactions.

Aim: analyze the continuous model to determine parameter dependence and to

identify a biologically reasonable parameter regime in which the discrete model

produced results consistent with experiments.

The continuous model is required to remain in the excitable regime as the S value

was varied by a factor of 6 and the stochastic counterpart is required to generate

the observed independent tunability of Pinit and comp.

parameter set that accounts for both maintenance of excitability at high S and

independent tunability by S and K.



Core compentence circuit K : concentration of ComK

S: concentration of ComS


S

SK

S

kKdt

dS

KSK

K

Kk

K

dt

dK

sSk

sp

s

ss

kSk

knn

k

nk

k

11

1

rearrange into



Phase diagram of continuous model



Phase diagram of continuous model






Stochastic model



Stochastic model



strong effect of K on Pinit

Within the model, increasing K increased the probability that vegetative cells reach

the minimum concentration of ComK necessary to initiate competence, explaining

the strong effect of K on Pinit.



Effect of ComS expression






To explore the effects of perturbing the circuit architecture, we reengineered the competence circuit using Rok, a protein that binds to PcomK and represses its expression. We inserted a copy of rok under the control of PcomG, creating an additional negative feedback loop onto comK (Fig. 3A).

Can one make comp more precise?



What determines Pinit?

Here, use a mutant that

grows very long cells

variations of the

concentrations become

smaller.

D: the onset probability

Pinit is clearly reduced.

Control experiments:

the expression level of

2 other genes is

unchanged



Conclusions Noise may play at least three different functional roles in competence.

First, noise could be responsible for the observed variability in duration.

Second, noise may be necessary to maintain excitability over a wide parameter

range, by inducing escape from states of high ComK concentration.

Third, noise appears to have a pivotal role in competence initiation and thus should

be considered alongside genetic parameters and circuit architecture to

comprehensively understand differentiation at the single cell level.

Quantitative analysis of a genetic system beyond its normal operating regime,

including gene expression strengths, circuit architecture, and noise levels, strongly

constrains dynamical models.

The competence regulation system maintains excitable behavior over a broad

range of parameter values. Experimentally, K and S enable Pinit and tcomp to be

tuned independently, allowing the system, in theory, to adapt to independent

selective pressures during evolution.

The circuit can also access different dynamic regimes, such as oscillation and

bistability, indicating its potential to evolve alternative qualitative behaviors.



New challenge: Electron Tomography

Method overview

a) The electron beam of an EM

microscope is scattered by the central

object and the scattered electrons are

detected on the black plate.

By tilting the object in small steps, collect

electrons scattered at different angles.

b) reconstruction in the computer.

Back-projection (Fourier method) of the

scatter-information at different angles.

The superposition generates a three-

dimensional tomogrom.

Sali et al. Nature 422, 216 (2003)



Identification of macromolecular complexes in cryoelectron tomograms of phantom cells

Frangakis et al., PNAS 99, 14153 (2002)

Idea: construct model system with well-defined properties.

Prepare „phantom cells“ (ca. 400 nm diameter) with well-defined contents:

liposomes filled with thermosomes and 20S proteasomes.

Thermosome: 933 kD, 16 nm diameter, 15 nm height,

subunits assemble into toroidal structure with 8-fold symmetry.

20S proteasome: 721 kD, 11.5 nm diameter, 15 nm height,

subunits assemble into toroidal structure with 7-fold symmetry.

Collect Cryo-EM pictures of phantom cells for a tilt series from -70º until +70º with 1.5º

increments.

Aim: identify and map the 2 types of proteins in the phantom cell.

This is a problem of matching a template, ideally derived from a high-resolution structure,

to an image feature, the target structure.



Detection and idenfication strategy


The correlation of two functions is defined as

Correlation theorem for the transform pairs:

dhtghgCorr ,

fHfGhgCorr *,



Search strategy


Adjust pixel size of templates to the pixel size of the EM 3D reconstruction.

The gray value of a voxel (volume element) containing ca. 30 atoms is obtained

by summation of the atomic number of all atoms positioned in it.

Possible search strategies:

(i) Scan reconstructed volume by using small boxes of the size of the target

structure (real space method)

(ii) Paste template into a box of the size of the reconstructed volume (Fourier

space method). This method is much more efficient.



Correlation with Nonlinear Weighting

R

nn

R

nn

R

nnn

rRrxRx

rxRrxCC

1

22

1

22

1


The correlation coefficient CC is a measure of similarity of two features e.g. a signal x

(image) and a template r both with the same size R.

Expressed in one dimension:

are the mean values of the subimage and the template.

The denominators are the variances

rx and

To derive the local-normalized cross correlation function or, equivalently, the

correlation coefficients in a defined region R around each voxel k, which belongs to a

large volume N (whereby N >> R), nonlinear filtering has to be applied.

This filtering is done in the form of nonlinear weighting.



Raw data


Central x-y slices through the 3D reconstructions of ice-embedded phantom

cells filled with

(a) 20S proteasomes,

(b) thermosomes,

(c) and a mixture of both particles.

At low magnification, the macromolecules appear as small dots.



Correlation coefficients


(a) Histogram of the correlation coefficients of the particles found in the proteasome-containing phantom cell scanned with the "correct" proteasome and the "false" thermosome template. Of the 104 detected particles, 100 were identified correctly. The most probable correlation coefficient is 0.21 for the proteasome template and 0.12 for the thermosome template.

(b) Histogram of the correlation coefficients of the particles found in the thermosome-containing phantom cell. Of the 88 detected particles, 77 were identified correctly. The most probable correlation value is 0.21 for the thermosome template and 0.16 for the proteasome template.

Detection in (a) works well, but is somehow problematic in (b) because (correct) thermosome and proteasome are not well separated.



Reconstruction of phantom cell


Volume-rendered representation of

a reconstructed ice-embedded

phantom cell containing a mixture

of thermosomes and 20S

proteasomes.

After applying the template-

matching algorithm, the protein

species were identified according to

the maximal correlation coefficient.

The molecules are represented by

their averages;

thermosomes are shown in blue,

the 20S proteasomes in yellow.

The phantom cell contained a 1:1

ratio of both proteins. The algorithm

identifies 52% as thermosomes and

48% as 20S proteasomes.



Electron tomography


- Method has very high computational cost.

- Observation: biological cells are not packed so densely as expected,

allowing the identification of single proteins and protein complexes

- Problem for real cells: molecular crowding.

Potential difficulties to identify spots.

- need to increase spatial resolution of tomograms



Reconstruction of endoplasmatic reticulum

http://science.orf.at/science/news/61666Dept. of Structural Biology, Martinsried

Picture rights shows rough

endoplasmatic reticulum

(membrane network in eukaryotic

cells that generates proteins and

new membranes) coated with

ribosomes.

The picture is taken from an intact

cell.

Membranes are shown in blue, the

ribosomes in green-yellow.

http://science.orf.at/science/news/61666



Reconstruction of the Golgi apparatus

The Golgi complex is the

organelle in which newly

synthesized lipids and

proteins are modified and

targeted for distribution to

various cellular and

extracellular destinations.

Ladinsky et al. J. Cell. Biol. 144, 1135 (1999)

HVEM tomographic reconstruction of a portion of the Golgi ribbon from a fast frozen, freeze-substitution fixed NRK cell. Two serial 4-nm slices extracted from the tomogram are shown in a and b. Comparison of the images shows how little is changed from one such slice to its neighbor; e.g., the position of the microtubule (red arrow). (a) Membranes of individual Golgi and ER cisternae are clearly seen. (b) In analyzing the data, different cisternae were modeled by placing points along the membranes that delimit them, connecting the points with colored line segments, and building closed contours that model the different membrane compartments of a given slice.





c and d are renditions of the surfaces fit to all of the contours for each object modeled in this Golgi region. The model viewed in c is in the same orientation as the tomographic slices. d shows a cisside view with the cis ER removedto provide a better view of the ERGIC elements and the underlying Golgi cisternae. The 44 elements of the ERGIC arediscontinuous, display no coated budding profiles, and do not appear to be flattened against the cis-most cisterna. Free vesicles in wells and the NCR (white) have unrestricted access to the cis side of the stack. The colors used to represent different components of the model are the same in all figures: ER, bluegray; ribosomes, small purple spheres; ERGIC, yellow; Golgi cisterna: C1, green; C2, purple; C3, rose; C4, olive; C5, pink; C6, bronze; C7, red. Polymorphic structures in the NCR are light pink and gold. Non–clathrincoated budding profiles on cisternae C1–C6, blue stippling. Clathrin-coated buds on C7, yellow stippling. Bars, 250 nm.







Mitochondria

Nicastro et al. J. Struct. Biol. 129, 48 (2000)

Surface-rendered representation of the mitochondrial reconstruction in two different orientations. The crista membrane that forms a three-dimensional network of interconnected lamellae is continuous with the inner boundary membrane (both shown in yellow). The outer membrane (magenta) is separated from the inner boundary membrane by a narrow intermembrane space of remarkably constant width.



The nuclear pore complex

Beck et al. Science 306, 1387 (2004)

Nuclear pore complexes

(NPCs) mediate the

exchange of

macromolecules between

the nucleus and the

cytoplasm. These large

assemblies (ca. 120

megadaltons in metazoa)

are constructed from about

30 different proteins, the

nucleoporins.

(E) Surfacerendered representation of a segment of nuclear envelope (NPCs in blue, membranes inyellow). The dimensions of the rendered volume are 1680 nm 984 nm 558 nm. The number of NPCs was ca. 45/m2.



The nuclear pore complex

Beck et al. Science 306, 1387 (2004)

Fig. 2. Structure of the Dictyostelium

NPC. (A). Cytoplasmic face of the NPC in

stereo view. The cytoplasmic filaments

are arranged around the central channel;

they are kinked and point toward the

CP/T.

(B) Nuclear face of the NPC in stereo

view. The distal ring of the basket is

connected to the nuclear ring by the

nuclear filaments.

(C) Cutaway view of the NPC with the

CP/T removed.



Herpes simplex virus

Grünewald et al. Science 302, 1396 (2003)

Segmented surface rendering of a single virion tomogram after denoising. (A) Outer surface showing the distribution of glycoprotein spikes (yellow) protruding from the membrane (blue). (B) Cutaway view of the virion interior, showing the capsid (light blue) and the tegument “cap” (orange) inside the envelope (blue and yellow). pp, proximal pole; dp, distal pole. Scale bar, 100 nm.(C) Segmented surface rendering of a virion portion. Tegument is orange, membrane is blue, and spikes are yellow. Scale bars, 20nm.



3D reconstruction of Saccharomyces cerevisae cell

Larabell et al. Mol. Biol. Cell 15, 957 (2004)



3D reconstruction of Saccharomyces cerevisae cell

Larabell et al. Mol. Biol. Cell 15, 957 (2004)



a nerve cell

Martone et al. J. Struct. Biol. 138, 145 (2002)

Tomographic reconstruction of neuronal spiny dendrite from the rat neostriatum (C) A surface reconstruction of the segmented volume showing the dendritic shaft in blue and the dendritic spines in red. (E) Segmented reconstruction of the node showing the major components in different colors. Yellow, compact myelin; red, axolemma; blue, paranodal loops; white, mitochondria; green, intraaxonal vesicles.



Reconstruction of actin filaments


Shown is the cytoskeleton of Dictyostelium. Apparently, filaments cross and bridge each other

at different angles, and are connected to the cell membrane (right picture).

Actin filaments are shown in brown. The cell segment left has a size of 815 x 870 x 97 nm3.

Middle: single actin filaments connected at different angles.

Right: actin filaments (brown) binding to the cell membrane (blue).

Actin filaments are structural proteins – they form filaments which span the entire cell.

They stabilize the cellular shape, are required for motion, and are involved in important

cellular transport processes (molecular motors like kinesin walk along these filaments).




Science fiction


Reconstruct proteome of real biological cells.

Required steps:

(1) obtain EM maps of isolated (e.g. 6000 yeast) proteins

(2) enhance resolution of tomography

(3) speed up detection algorithm




Summary

The structural characterization of large multi-protein complexes and the

resolution of cellular architectures will likely be achieved by a combination of

different methods in structural biology:- X-ray crystallography and NMR for high-resolution structures of single

proteins and pieces of protein complexes- (Cryo) Electron Microscopy to determine medium-resolution structures of

entire protein complexes- Stained EM for still pictures at medium-resolution of cellular organells- (Cryo) Electron Tomography for 3-dimensional reconstructions of biological

cells and for identification of the individual components.

Mapping and idenfication steps require heavy computation.

Employ protein-protein docking as a help to identify complexes?

teams of experimentalists and bioinformaticians

- Sali & Baumeister, Sali & Chu

- Russell & Böttcher

- Wriggers & J. Frank, M. Radermacher & J. Frank

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V16 Stochastic processes in cells