Error correc'on through catastrophes Arvind Murugan Physics and - PowerPoint PPT Presentation

Error correc'on through catastrophes Arvind Murugan Physics and the James Franck Ins3tute University of Chicago

Kine%c Proofreading Stochas%c algorithms Search strategies

Errors in enzyma'c reac'ons T G C T A - C - A - G - C - T - T - G - T - C - G - A - A - A - G - C DNA polymerase

Errors in enzyma'c reac'ons T G C A - C - A - G - C - T - T T - G - T - C - G - A - A - A - G - C DNA polymerase

Errors in enzyma'c reac'ons T C T G A - C - A - G - C - T - T - G - T - C - G - A - A - A - G - C DNA polymerase E ( A ≡ G ) − E ( A ≡ T ) = ∆

Errors in enzyma'c reac'ons

Errors in enzyma'c reac'ons T C T G A - C - A - G - C - T - T - G - T - C - G - A - A - A - G - C DNA polymerase E ( A ≡ G ) − E ( A ≡ T ) = ∆

Errors in enzyma'c reac'ons • Protein synthesis • tRNA charging • T-cell receptors • …. e − ∆ How do you reduce effec?ve error rate below kT (Fixed Δ )

John Hopfield (1974) Kine'c Proofreading Jacques Ninio (1975) Enzyme E + Wrong + Right (wrong substrate)W + E + R (right substrate) Substrate W Substrate R EW E 1 R 1 EW i E R i EW i+1 ER i+1 EW Wrong ER Product Right Wrong product + E !Δ Product Energy difference Delta Right product + E

John Hopfield (1974) Kine'c Proofreading Jacques Ninio (1975) Enzyme E + Wrong + Right (wrong substrate, eg. ‘G’)W + E + R (right substrate, eg. ‘T’) Substrate W Substrate R EW 1 ER 1 EW i ER i e ∆ e ∆ EW i+1 ER i+1 EW ER f f Wrong Right Product Wrong product + E Right product + E Product η ∼ e − 2 ∆

A.M, D.Huse, S.Leibler, PNAS 2012 General Principle R W E EW ER EW 1 ER 1 EW i ER i ER j EW j ER 2 EW 2 W-Product + E R-Product + E

A.M, D.Huse, S.Leibler, PNAS 2012 General Principle ∆ e ∆ e R W ∆ e E ∆ e EW ER - ∆ e EW 1 ER 1 ER i EW i e ∆ ER j EW j ER 2 EW 2 e ∆ W-Product + E R-Product + E

General network Red lines –checkpoints, in Start parallel. e ∆ e ∆ e ∆ e ∆ e ∆ e ∆ e ∆ Finish Can n parallel paths, each with a failure rate η ∼ e − ∆ be combined to give η ∼ e − n ∆

Error correc'ng kine'c limit E+S Reac?on is completed only along green path. Reac?on interrupted at red checkpoints – ‘ catastrophe ’ To finish: ES must get past all red checkpoints. Exponen?ally unlikely.

Error correc'ng kine'c limit E+S L ES Reac?on coordinate (a measure of reac?on progress)

Reac'on coordinate & progress Finish Exponen?ally unlikely -> catastrophe L Start %me

Catastrophes at checkpoints E+S d ∆ d e ES f f EW i ER i f f p R p W Forward > forw. = forw. = e ∆ d + f d + f ! n p W forw. ! e − n ∆ when f ⌧ d, e ∆ d Need η ⇠ p R forw. when f ⌧ d, e ∆ d Low error rate but very slow comple%on rate

Catastrophes and rescues Finish E+S Exponen?ally unlikely -> catastrophe L ES Start %me rescue

Catastrophes and rescues f cat < f res unbounded L f cat > f res bounded t

Reac'on coordinate & progress p R cat. < p res. < p W p R cat. < p W p res. ⌧ p R cat. < p W cat. < p res. cat. cat. Error rate R Dissipa?on/Time W η ∼ e − n ∆ , η ∼ e − ∆ , η ∼ e − n ∆ 0 , T ∼ Λ n T ∼ n γ T ∼ n κ Lowest error, High error, Low error, Highest ?me Low ?me Low ?me

Energy vs Error Rate tradeoff E+S D T T D T D # of fu?le cycles ~ # of ATP molecules used ~ dissipa?on ES

Dynamic instability of microtubules unbounded L bounded t Tim Mitchison (HMS)

Non-equilibrium growth of microtubules

Microtubule growth regimes f cat < f res unbounded L f cat > f res bounded t

Microtubule growth as a search strategy chromosome microtubule Wrong direc3on Right direc3on Proposal: Set <catastrophe rate> ~ <rescue rate> Bounded Signaling molecule cat. > rescue (lowers cat.) Unbounded cat. < rescue Bounded-unbounded transi?on point

Microtubules and foraging Foraging ants Microtubules When should you return home and try again? Kirschner/Gerhart

Algorithms that get stuck

Algorithms that get stuck Stuck Start Finish Stuck Stuck Restarts cut tail of first passage ?me distribu?on Example: Simulated annealing on a glassy landscape

Duality: Errors vs (first passage) Time Wrong finish Start Right Finish Wrong finish Wrong finish Restarts cut tail of first passage ?me distribu?on Example: Simulated annealing on a glassy landscape

Summary Proofreading = Dynamic instability in chemical space (catastrophes and rescues) Happy medium in error-energy tradeoff Happy medium in returns home (search, stochas?c algorithms..)