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Closing the Loop on ProteinClosing the Loop on Protein--DNA InteractionsDNA Interactions
Institute for Mathematics and its ApplicationsUniversity of Minnesota
September 17, 2007
Stephen Levene, Ph.D.Departments of Molecular and Cell Biology and Physics
University of Texas at Dallas
AcknowledgmentsAcknowledgments
SupportSupport:: NIH (GM 47898, GM 55871, GM 67242), NIH (GM 47898, GM 55871, GM 67242), Texas Advanced Technology ProgramTexas Advanced Technology Program
SiteSite--specific specific RecombinationRecombination
Alexandre VetcherAlexandre VetcherAbbye McEwenAbbye McEwen
Farah BardaiFarah BardaiIsabel DarcyIsabel Darcy11
Yuri LyubchenkoYuri Lyubchenko22
Alex LushnikovAlex Lushnikov22
Yongli ZhangYongli Zhang88
Don CrothersDon Crothers66
DNA Topology and SupercoilingDNA Topology and Supercoiling
Hua TsenHua TsenIsabel DarcyIsabel Darcy11
Andreas HankeAndreas Hanke77
Rob SchareinRob Scharein55
RepeatedRepeated--sequencesequenceDNADNA
Sima ZeinSima ZeinRichard SindenRichard Sinden33
Woody WrightWoody Wright44Jerry ShayJerry Shay44
1Dept. of Mathematics, Univ. of Iowa 7Dept. of Physics and2Dept. of Pharm. Sciences, Univ. of Neb. Med. School Astronomy, UT-Brownsville3IBT, Texas A&M Univ. 8Phys. Biosci. Div., Lawrence4UT-Southwestern School of Med. Berkeley Laboratory5Hypnagogic Software, Vancouver, BC6Depts. of Chemistry, Mol. Biophys. & Biochem., Yale Univ.
15-5
0 kb
picoscalenanoscale mesoscale
DNA Biophysics in the 21DNA Biophysics in the 21stst
CenturyCentury
©© 2007 S.D. Levene. All rights reserved.2007 S.D. Levene. All rights reserved.
• Role of DNA looping in biology
• General principles of DNA looping deduced from statistical mechanics
• Applications to loop-mediated gene repression: the lacoperon
• Looping in site-specific recombination and implications for DNA topology
OutlineOutline
©© 2007 S.D. Levene. All rights reserved.2007 S.D. Levene. All rights reserved.
DNA Looping in BiologyDNA Looping in Biology
• Gene regulation
Repression: ara, deo, gal, lacoperonsActivation: glnALG operonMany eukaryotic examples (e.g., β-globin locus)
• Intramolecular site-specific recombination (Int, Cre, Flp, Gin/Hin, etc.)
• Transposition (Mu)
• Type-II restriction enzymes (SfiI, NgoMIV)
• DNA mismatch repair (MutHSL)
©© 2007 S.D. Levene. All rights reserved.2007 S.D. Levene. All rights reserved.
Courtesy of Mike White, UCSD
DNA size, bp
103
J, m
ol L
-1
10-9
10-8
10-7
200
A
DNA size, bp235 240 245 250 255
J, m
ol L
-1
10-9
10-8
B
Relationship to DNA CyclizationRelationship to DNA Cyclization
Levene, Nature ELS (http://www.els.net)
©© 2007 S.D. Levene. All rights reserved.2007 S.D. Levene. All rights reserved.
• J drops precipitously with DNA size for small DNAs
• Near 200 bp, J varies by ~100-fold over a full helical turn
• J values are extremely sensitive to the presence of intrinsic bends
Solving the DNASolving the DNA--looping Problemlooping Problem
©© 2007 S.D. Levene. All rights reserved.2007 S.D. Levene. All rights reserved.
( )21 3
21 1
Nij ij
i j ij
x xHβ
σ
−
= =
−= ∑∑Hamiltonian:
= instantaneous rotation angle (tilt, roll, or twist) of the i-th rigid body relative to (i-1)-st
= variance of rotation angle
= corresponding mechanical-equilibrium angle
ijx2ijσ
ijx
{ }( )( ) : 1, , 1; 1, ,3 0; 1, ,6kijf x i N j k= − = = =… … …Non-linear constraints:
-2
6B
8 e expkdet( )det( )
sEloopG
JT
π
π
Δ⎡ ⎤= = −⎢ ⎥
⎣ ⎦A F
Harmonic-approximation solution for the J factor:
• The J factor is:
Proportional to Keq for the formation of a closed loop from an open chainEffective concentration of one loop end in the vicinity of anotherRatio of statistical-mechanical partition functions for closed and open loops
Zhang & Crothers Biophys J
(2003)
©© 2007 S.D. Levene. All rights reserved.2007 S.D. Levene. All rights reserved.
Parameterization of DNA Parameterization of DNA ConformationsConformations
Tilt
θ
Roll
φ
Twist
τ
©© 2007 S.D. Levene. All rights reserved.2007 S.D. Levene. All rights reserved.
φDPτPP ≈ 0
φPD
τPP = -60°
τPP = -60°
Zhang et al. Biophys J (2006)
©© 2007 S.D. Levene. All rights reserved.2007 S.D. Levene. All rights reserved.
1 6 8 1 7 2 1 7 6 1 8 0 1 8 4 1 8 8 1 9 2
1
1 0
1 0 0
(b(a )N
J
fact
or (n
M)
D N A leng th (bp )
0 ° 6 0 ° 1 2 0 °
1 6 8 1 7 2 1 7 6 1 8 0 1 8 4 1 8 8 1 9 2
1
1 0
1 0 0
(b(a )N
J
fact
or (n
M)
D N A leng th (bp )
0 ° 6 0 ° 1 2 0 °
Coupling of Twist and Writhe in Coupling of Twist and Writhe in DNA LoopingDNA Looping
Zhang et al. Biophys J (2006)
©© 2007 S.D. Levene. All rights reserved.2007 S.D. Levene. All rights reserved.
Effects of DNAEffects of DNA--sequence Symmetrysequence Symmetry
1
10
100
168 172 176 180 184 188 1920.1
1
10
100
J fa
ctor
(nM
)
+90 -90 Sum
(d(c)
(b(a)
J fa
ctor
(nM
)
DNA length (bp)
+45 -135 Sum
Zhang et al. Biophys J (2006)
• Two distinct looped conformations contribute to the J factor• Dramatically reduced phase dependence – cannot rule out looping
Summary Summary –– Part IPart I
• Numerical approach to computing looping free energies based on harmonic approximation is 104-fold more efficient than Monte Carlo simulation
• DNA looping is distinguished from cyclization by strong coupling of twist and writhe
• Relationship between Tw and Wr in small loops can generate phase shifts such that the most energetically favorable loops involve non-integral numbers of helical turns
• Negligible helical-phase dependencies do not necessarily imply absence of DNA looping
©© 2007 S.D. Levene. All rights reserved.2007 S.D. Levene. All rights reserved.
©© 2007 S.D. Levene. All rights reserved.2007 S.D. Levene. All rights reserved.
Intact E. coli cellV ≈ 1 fL = 1·10-12 cm3
50x to 100x
≈1 μ
m
E. coli genome4.6·106 bpL = 1.6 mm
= 6·10-11 cm3
2 3 / 24 3V S= < >
Architectural DNAArchitectural DNA--bending Proteins in bending Proteins in Genome Organization and RegulationGenome Organization and Regulation
HU-DNA cocrystal structureSwinger et al. Embo J (2003)
E. coli architectural DNA-bending proteins:
HU ≈ Fis > IHF > H-NS > StpA > Dps
O1
O3
O1
O2
O1O3 O2
92 bp 401 bp
4 (LacR)
DNA Looping and Regulation of DNA Looping and Regulation of the the laclac OperonOperon
• Looping between the primary operator, O1, and auxiliary operators, O2and O3, enhances repression by increasing the effective concentration of LacR at the promoter
©© 2007 S.D. Levene. All rights reserved.2007 S.D. Levene. All rights reserved.
+
Structure of the Structure of the LacRLacR TetramerTetramer
©© 2007 S.D. Levene. All rights reserved.2007 S.D. Levene. All rights reserved.
y
xH
C
T
DP/PD PD/DPPP
“V-shaped” tetramerLewis et al. Science (1996)
“Extended” tetramerRuben & Roos Microsc Res Tech (1997)
137-bp DNA loop mediated by extended tetramer
PDPP
DP
The The ““VV--shapedshaped”” Repressor Forms Repressor Forms Multiple Loop Geometries Multiple Loop Geometries
©© 2007 S.D. Levene. All rights reserved.2007 S.D. Levene. All rights reserved.
J = 0.42 nMΔGloop = 53.5 kJ mol-1
“WT”179 bp
(+), J = 0.01 nMΔGloop = 62.8 kJ mol-1
(-), J = 2.1 nMΔGloop = 49.5 kJ mol-1
“WA”179 bp
“WA”163 bp
(-), J = 0.75 nMΔGloop = 52.0 kJ mol-1
(+), J = 0.78 nMΔGloop = 52.0 kJ mol-1
“LB”163 bp
(-), J = 15 nMΔGloop = 44.6 kJ mol-1
0 nMJ ≅(+),ΔGloop > 100 kJ mol-1
Zhang et al. PLoS One (2006)
The Extended The Extended LacRLacR Tetramer is Tetramer is the Dominant Form in Small Loopsthe Dominant Form in Small Loops
©© 2007 S.D. Levene. All rights reserved.2007 S.D. Levene. All rights reserved.
DNA length (bp)60 80 100 120 140 160 180
J (n
M)
0.001
0.01
0.1
1
10
100
1000
SL (15,30) LB (0,0)Sum
-ΔG
0 loop
/kBT
-28
-26
-24
-22
-20
-18
-16
-14
DNA length (bp)130 140 150 160 170 180
J (n
M)
0.001
0.01
0.1
1
10
LBWAWTSum
-ΔG
loop
/kBT
-26
-24
-22
-20
-18
Zhang et al. PLoS One (2006)
Thermodynamic Model for Thermodynamic Model for LacRLacRRepressionRepression
©© 2007 S.D. Levene. All rights reserved.2007 S.D. Levene. All rights reserved.
12
12 1212
12
K1 K2
K2 K1
Kc(1)Kc
(2)
1 2 1 2( )c t
t t t
d JPD K K K K J P P
λλ
=+ + + +
( )( )1 2
1 1noloop t
loop t t
E JPR JE K P K P
λ= = + ≡ + Γ
+ +
( )( )
1 2
1 2 1 2
tloop
t t
K K PE
K K K K J P Pλ+
=+ + + +
1
1noloop
t
KEK P
=+
1 2( )( )t
t t
PK P K P
λΓ =
+ +
0( ,DNA flex., protein flex.)J J h=
(known)
(4 params)
Zhang et al. PLoS One (2006)
Analyzing Experimental DataAnalyzing Experimental Data
©© 2007 S.D. Levene. All rights reserved.2007 S.D. Levene. All rights reserved.
Data of Müller et al.J Mol Biol (1996)
Data of Becker et al.J Mol Biol (2005)
Zhang et al. PLoS One (2006)
Analyzing Experimental Data Analyzing Experimental Data (cont(cont’’d)d)
©© 2007 S.D. Levene. All rights reserved.2007 S.D. Levene. All rights reserved.
16 (± 1)10.95 (± 0.03)0.8 (± 0.1)128 (± 2)1.04.66b25Becker et al. [18]ΔHU
19 (± 1)11.08 (± 0.04)0.7 (± 0.1)95 (± 3)1.14.66b26Becker et al. [18]WT
20.7 (± 0.5)11.60 (± 0.01)1.1 (± 0.1)95 (± 1)1.01.17a51Müller et al. [5]
Protein flexibility,
deg.
Helical repeat,
bp·turn-1
Torsional rigidity, 10-19
erg·cm
Persistence length, bp
Best-fit valuesFitting errorΓ, x 102
No. of data
points,Nd
Data Set
Zhang et al. PLoS One (2006)
Looping, Looping, LacRLacR flexibility, and HUflexibility, and HU--dependent Bending Dramatically dependent Bending Dramatically Increase Repression EfficiencyIncrease Repression Efficiency
©© 2007 S.D. Levene. All rights reserved.2007 S.D. Levene. All rights reserved.Zhang et al. PLoS One (2006)
Summary Summary –– Part IIPart II
©© 2007 S.D. Levene. All rights reserved.2007 S.D. Levene. All rights reserved.
• Small loops ( 200 bp) between lac operators are predominantly mediated by the extended LacR tetramer conformation
• LacR-dependent regulation in vivo is facilitated by enhanced DNA flexibility in the presence of HU protein
• HU binding and protein flexibility are both important factors that promote DNA looping over short distances
<
3' 5'
Mechanism of Tyrosine SiteMechanism of Tyrosine Site--specific specific RecombinasesRecombinases
a b
a b
a b
a b
Cleavage, strandexchange
Isomerization (?),HJ resolution
X
a b
a b
5' 3'
5' 3'
5'3'
Holliday-junctionintermediate
©© 2007 S.D. Levene. All rights reserved.2007 S.D. Levene. All rights reserved.
3-noded knot3-noded knot
DNA Knotting via SiteDNA Knotting via Site--specific specific RecombinationRecombination
©© 2007 S.D. Levene. All rights reserved.2007 S.D. Levene. All rights reserved.
well
unknotted,nicked plasmid
7-noded knot5-noded knot
9-noded knotsc plasmid
linear plasmid4-kb linear
3-kb linear
kb-ladder
supercoiled plasmid
kb-ladder
knotted plasmid
supercoiled plasmid
knotted plasmid
linear p
lasmid
unresolvedknots
=
Electron micrograph of a (+3) DNA knot Tsen & Levene, unpublished
Topology of Topology of CreCre Recombination is Recombination is Inconsistent with a Planar IntermediateInconsistent with a Planar Intermediate
©© 2007 S.D. Levene. All rights reserved.2007 S.D. Levene. All rights reserved.
TATTGAAGCATATCGTA
ATAACTTCGTATAGCAT ACATTATACGAAGTTAT
TGTAATATGCTTCAATA
ATAACTTCGTATAATGT
TATTGAAGCATATTACA
ATGCTATACGAAGTTAT
TACGATATGCTTCAATA
(11)abθ
(12)baθ
TATTGAAGCATATCGTA
ATAACTTCGTATAGCAT ACATTATACGAAGTTAT
TGTAATATGCTTCAATA
ATAACTTCGTATAATGT
TATTGAAGCATATTACA
ATGCTATACGAAGTTAT
TACGATATGCTTCAATA
TATTGAAGCATATCGTA
ATAACTTCGTATAGCAT
TATTGAAGCATATCGTA
ATAACTTCGTATAGCAT ACATTATACGAAGTTAT
TGTAATATGCTTCAATA
ACATTATACGAAGTTAT
TGTAATATGCTTCAATA
ATAACTTCGTATAATGT
TATTGAAGCATATTACA
ATAACTTCGTATAATGT
TATTGAAGCATATTACA
ATGCTATACGAAGTTAT
TACGATATGCTTCAATA
ATGCTATACGAAGTTAT
TACGATATGCTTCAATA
(11)abθ
(12)baθ
Cre-HJ cocrystal structureGuo et al. Nature (1997)
AtomicAtomic--force Microscopy of force Microscopy of CreCre Synaptic Synaptic ComplexesComplexes
©© 2007 S.D. Levene. All rights reserved.2007 S.D. Levene. All rights reserved.
(80%)
(97%)
Vetcher et al. J Mol Biol (2006)
ConclusionsConclusions
©© 2007 S.D. Levene. All rights reserved.2007 S.D. Levene. All rights reserved.
• Development of comprehensive theory for DNA looping that accounts for DNA and protein conformation, protein flexibility, thermal fluctuations, and helical phasing
• Small regulatory loops ( 200 bp) in the lac operon are mediated by the extended LacR tetramer conformation and regulation in vivo is facilitated by enhanced DNA flexibility in the presence of HU
• Understanding DNA looping is vital for rigorously interpreting results of topological experiments
• Loop-closure kinetics is an emerging tool for analyzing the structure of complex nucleoprotein assemblies
<
Nick Cozzarelli1938 - 2006
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