Mechanisms of Accuracy in Homologous Recombination

• Recognition processes in homologous recombination

in the presence of competition and noise.

• Mechanism 1: Kinetic Proofreading.

• Mechanism 2: Conformational Proofreading.

• Conformational changes (induced fit) may enhance recognition.

• Possible tests?

Institute Curie, April 2008

RecA-mediated Homologous Recombination

• Essential for genome integrity via repair machinery.

• Molecular engine of genetic diversity via crossover and sex

(horizontal transfer).

• Key role in evolution: control of speciation and genetic isolation.

• Proteins mediate homologous recombination.

• RecA superfamily: RecA (E.coli), Rad51 (yeast), hRad51 (human).

• Structure and function conserved from bacteria to human.

Molecular recognition in Homologous Recombination

RecA Polymerization

Homologous search

Strand exchange

50-60%

• Recombination is a three-stage process:

(1) RecA is polymerized along ssDNA.

• RecA extends ssDNA by 50-60% - conserved.

(2) Homologous search: recognition of homologous DNA

sequence within many lookalikes.

• Homologous search may occur even without ATP

hydrolysis.

(3) Formation of synapse and strand exchange.

Challenge of molecular recognition

• Noisy, crowded milieu.

• Recognizer and target fluctuate.

• Many competing lookalikes.

• Relatively weak recognition interactions.

• Challenge:

How to find and identify targets ?

David Goodsell

How to enhance recognition during recombination?

• The recognition problem is twofold:

• Global-scale: How to approach the target?

• Parallel search (finds target within 200,000

competitors in 15 minutes)

• Local-scale: How to recognize the homologous sequence?

• Two suggested mechanisms:

– Kinetic Proofreading (Libchaber, Bar-Ziv, Stavans, Sagi & TT, 2002-6)

– Conformational Proofreading (Savir & TT, 2007-8)David Goodsell

(Dorfman, Fulconis, Dutreix,Viovy, PRL 2004)

1st mechanism: Kinetic Proofreading

• Kinetic Proofreading (Hopfield, Ninio, 1974-5) = Energy consuming

mechanism for sensitivity amplification in biological processes.

• Allows discrimination between two similar targets (~ free energies)

with an error << naive thermodynamic bound ~ exp(-ΔF).

• Intermediate irreversible stages (coupling to energy source).

TargetsRight product

0 1 Wrong product2Right product

Wrong product

+

+

Hint: Kinetic Proofreading in filament formation

• RecA binding-unbinding dynamics:

Polymerization/depolymerization (ATP).

• Detects minute sequence differences.

0

1

2

final

[ TT, Bar-Ziv, Libchaber PNAS 2002, PRL 2004 ]

Kinetic Proofreading in Recombination

• Experimental hints (Sagi, Stavans & TT, NAR 2006):

• Homology recognition

• FRET measurements of exchange fraction

with heterologous sequences.

• Dependence on the number of

mismathches and their location.

mismatches

Strand exchange depends strongly on location and distribution of mismatches

• Small fraction of mismatches can reduce

significantly the exchange (even << 10%).

• Exchange is directional: more vulnerable to

mismatches close to the 3’ end.

• Contiguous mismatches have stronger effect.

mismatch

Model: Kinetic Proofreading Cascade

• Sequential check and exchange.

• Cascade of N irreversible stages.

• Exchange can abort at each stage.

• Mismatches reduce forward rate.

• Multiplicative effect of mismatches.

→ Exponential decay of exchange 1 1t j j j j j j jp p p pα α β− −∂ = − + −

1

0

success = jN

j j j

pp

αα β

−=+∏

fraction ~ exp( )Lμ− µ – mismatch probability, L – length

Experimental evidence and hints

• Minimum efficient processing segment (MEPS) of 20-30 bp.

• Exponential dependence of successful exchange in vivo

(Vulic Tadei Radman, PNAS 1997; Majewski Zawadzki Pickerill Cohan Dowson, J Bact 2000).

• Such sensitivity sets a well-defined genetic barrier between species.

MEPS ~ 20-30 bp. Red

uctio

n of

exc

hang

e

Role of DNA extension in homologous search?

• Costs significant deformation energy,

3-4 kBT per base-pair (kBT = 0.6 kcal/mol).

• Structural reason: exposing bases?

• Increasing effective target size?(Klapstein Chou Bruinsma 2004)

• Conformational Proofreading?

mechanism to detect DNA in large pool of similar targets, using conformation changes.

Why induced fit?

• Induced fit: Recognizers change their shape upon binding. • Can molecular recognition gain from induced fit?

• Quality measures: specificity = [Right]/[Wrong] =• What is the optimal recognition strategy?

Lock-and-key or induced fit ?

WW

W

WR

Induced fit(Koshland 1958)

?

?

Conformational Proofreading:When off-target is right on

• Structural mismatch reduces Right, but also reduces Wrong even more.

• Result: Enhancement of specificity and other quality measures.

• Optimal specificity at finite mismatch.

• Quantitative example: Homologous Recombination.

recognizersize

RightWrong

Specificity

binding

• Induced fit enhances recognition. • Optimal recognizer is off-target• Not lock-and-key.

Optimal

recognizersize

Molecular recognition as a decision problem

• Natural measure for the performance of molecular recognition .

• Each possible binding event has a cost/benefit of identification and

misidentification.

• Cost = Cost(event)×Prob(event) = correct + miss + false-alarm.

• Cost depends on structural parameters and can be optimized.

No Bind

Bind

Noise

DecisionUnit

Right, Wrong WrongRightTarget

Decision

False Alarm CWBCorrect, CRBBind

Correct, CWNMiss, CRNNo Bind

Cost depends on structural parameters

N base pairs

m mismatches

Extension energy

ΔGext

Gain from correct bp: specific interactions

ΔGs

Gain form incorrect bp: nonspecific interactions

ΔGns

( , ) ( , , , ),binding ext s nsP N m F N m G G G= Δ Δ Δ

• Binding probability for N base pairs and m mismatches :

ssDNA+RecA filament

dsDNA

( , )1 ( · ( )· · )

1binding

ext s nsP N m

exp N G N m G m G=

+ Δ − − Δ − Δ

Cost balances Right and Wrong binding

• Tolerance t measures relative cost of error.

• t increases → system less tolerant to errors

• Cost depends on structural

parameters and binding energetics:

(hom) ( hom)binding bindingCost P t P non= − + × −

Maximize Right detection + Minimize Wrong detection

extGΔ extension

sGΔ specific interactionsnsGΔ nonspecific interactions

mis s nsG G GΔΔ = Δ − Δ

Optimal extension minimizes detection cost

• Minimization of the cost reveals an optimal extension (t = 1):

ext

s

GG

ΔΔ

2ext s mis

mG G GN

Δ = Δ − ΔΔ

ns

s

GG

ΔΔ

1

12mN

−

Unstable

complex

NonspecificV

Specific

1

• Optimal extension energy ~ Specific binding energy.

Extension by a factor of

~ Constant force (Bustamante et al.,2000):stretchGΔ~ 4 5 BsG k T−Δ

~ 1.5 3.5s n BsG G k TΔ − −Δ

χ

Interfacial energy

(Cizeau Viovy, 1997).

~ 3.6 (at 1.7)Bint k TG χ =Δ

Structural parameters are measured

(Xiao Lee Singleton, 2006)

(Malkov Camerini-Otero, 1998)

Cost exhibits minimum at optimal extension

, 13, 3 ,1 mis BN G T tm k= = Δ = =ΔOne RecA monomer, one mismatch, symmetric:

• Well-defined valley ~ 50-60%

Analytic approximation for the cost

linear with good approximation

2

4 ( )· 2[ 1 1]2 ·

int s misstr

int str

mG G GN G NG N G

χΔ Δ − ΔΔΔ

= + −Δ Δ

2· ( 1) ( 1)ext str intG N G Gχ χΔ = Δ − + Δ −

interfacial interaction

stretching interactionspecific interactions

destabilization due to mismatch

1 3[ 1 (10 ) 1]6N m

N Nχ ≅ + − −⇒

(Fulconis Dutreix Viovy, 2005)

Conformational and Kinetic Proofreading

Kinetic Proofreading:Time delay (additional steps)

Energy-consuming non-equilibrium.

Conformational Proofreading:Spatial mismatch. Quasi-equilibrium.

• Kinetic and Conformational proofreading use the same generalstrategy: Reduce production of both Right and Wrong, but .reduction of Wrong product is larger and specificity improves.

• Recent evidence in recombination.

Sagi, Tlusty, Stavans (2006 ) NAR

0 1 2 final

0 0

Savir, Tlusty (2007-8 ) PLoS ONE, IEEE…

Possible experimental tests?

Conformational Proofreading:

• Binding curves as a function of

controlled extension.

• Predicting increase of binding

fraction with extension.

• But optimal cost at zero extension.

homologous Non-homologous

1 1.5

1 1.5

%hom %non-hom−

% b

ound

Extension

hom

Non-hom

Extension

(Fulconis, Mine, Bancaud, Dutreix, Viovy

EMBO J 2006 )

Possible experimental tests?

Kinetic Proofreading:

• Single molecule measurements of sequential

and directional processes.

• For example, asymmetric correlation etc.

(Fulconis, Mine, Bancaud, Dutreix, Viovy

EMBO J 2006 )

Typical KPR dynamics

Summary and outlook

• Suggestion: Homologous recombination combines

Kinetic Proofreading + Conformational Proofreading.

• Indirect experimental evidence. Direct evidence?

• Conformational Proofreading: conformational changes (induced fit)

may enhance the quality of molecular recognition.

• Analogy between molecular recognition and decision problem may

explain the extreme DNA extension by 50-60%.

• Outlook: Application of Conformational Proofreading to other systems:

tRNA, transcription, enzymes… (in progress).

[ Savir & Tlusty, PLoS ONE 2007; IEEE J Signal Processing 2008; RecA – submitted ]

Optimal extension is not sensitive to tolerance

3, 1 1 5 3, . ,s B mis BN m G k k TT G= = Δ = ΔΔ =

mism Gct e ΔΔ≅

• t increases → system less tolerant to errors

Cost balances correct and incorrect binding 1 .

1 ( · · ) 1 ( · · · )ext s ext s mis

tCostexp N G N G exp N G N G m G

−= +

+ Δ − Δ + Δ − Δ + ΔΔ

Maximize correct detection + Minimize incorrect detection

extGΔ extension

sGΔ specific interactionsnsGΔ nonspecific interactions

mis s nsG G GΔΔ = Δ − Δ

• t – Tolerance of the System

correct

incorrect

· (hom)· (hom)· (non-hom)· (non-hom)

h f

h f

c p pc p p

t = −

Cost Occurrence functionality

t increases the system is less tolerant to errors

Cost exhibits minimum at optimal extension

, 13, 3 ,1 mis BN G T tm k= = Δ = =Δ• One RecA monomer, one mismatch, symmetric:

Homologues Recombination

• Genome repair• Generating genetic diversity

Bugreev et al, Nature Structural & Molecular Biology 14, 746 - 753 (2007)