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Physics of nano-motors: from cargo transport to gene expression

Physics of nano-motors: from cargo transport to gene expression. Debashish Chowdhury Physics Department, Indian Institute of Technology, Kanpur. Home page: http://home.iitk.ac.in/~debch/profile_DC.html.

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Physics of nano-motors: from cargo transport to gene expression

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  1. Physics of nano-motors: from cargo transport to gene expression Debashish Chowdhury Physics Department, Indian Institute of Technology, Kanpur Home page: http://home.iitk.ac.in/~debch/profile_DC.html

  2. Motor Transport System = Motor + Track + Fuel Fundamental questions: (A) Properties of single-motor: (i) Composition and structure (inventory of parts and architectural design) (ii) Structural/conformational and bio-chemical dynamics (operational mechanism driven by mechano-chemical cycles): power-stroke or Brownian ratchet? (iii) Control systems and regulators of operation. (B) Collective properties: (i) Machines within machines, e.g., replisome (DNA replication factory): Helicase + primase + polymerase + ligase + clamp & clamp loader (ii) Collective phenomena: coordination, cooperation and competition (iii) Effects of steric interactions on the spatio-temporal organization

  3. The operational mechanism of a real molecular motor may involve a combination of power stroke and Brownian ratchet Power-stroke versus Brownian ratchet Joe Howard, Curr. Biol. 16, R517 (2006).

  4. Power Stroke Input energy drives the motor forward Random Brownian force tends to move motor both forward and backward. Input energy merely rectifies backward movements. Mechanisms of energy transduction by molecular motors Brownian ratchet A Brownian motor operates by converting random thermal energy of the surrounding medium into mechanical work!! Such systems are far from thermodynamic equilibrium and, therefore, do NOT violate second law of thermodynamics.

  5. q Totally Asymmetric Simple Exclusion Process (TASEP) Discretized position, discrete velocity (0 or 1) and discrete time A particle moves forward, with probability q, iff the target site is empty. Simplest Model of InteractingSelf-Driven Particles in 1-d Steric interactions of the motors are often captured in the theoretical models by appropriate extensions of We plot phase diagrams in planes spanned by exprimentally accessible parameters.

  6. Outline of the talk 1. Introduction 2. Brief overview of the motors of our current interest 3. Single-headed motor traffic on microtubule track 4. Ribosome traffic on mRNA track 5. RNA polymerase traffic on DNA 6. Summary and conclusion

  7. Brief overview of molecular motors of our current interest

  8. Cytoskeletal Molecular Motors: Cargo transport Kinesin-1 on Microtubule Myosin-V on F-actin Porters Animated cartoon: MCRI, U.K. Ribbon diagram of the two heads of kinesin-1 (also called conventional kinesin)

  9. Not all kinesins have two-heads. KIF1A kinesins are single-headed (“lame” porters); These motors are physical realizations of Brownian ratchets Distribution of Step sizes of KIF1A Okada et al. Nature (2003) (1) +Ve and –Ve steps sizes, i.e., both forward and backward steps. (2) Step sizes are distributed around multiples of 8 nm

  10. Molecular mechanism of processivity of KIF1A Processivity depends on the K-loop; the larger the number of lysines, the higher is the processivity. KIF1A becomes practically non-processive on E-hook-digested MT Okada and Hirokawa, PNAS (2000) Experiments on a series of KIF1A mutants with different number of lysines in the K-loop and with E-hook digested microtubules Both +vely charged K-loop of KIF1A and the –vely charged E-hook of MT are essential for the processive movement of KIF1A.

  11. K KT KDP KD K ATP P ADP Strongly Attached to MT Weakly Attached to MT State 1 State 2 Brownian ratchet mechanism of movement of single KIF1A (Diffusive) In the weakly-attached state, because of the electrostatic attraction between E-hook of the microtubule and the K-loop of the kinesin, the motor remains tethered while executing Brownian motion along its track. This corresponds to the diffusive part of the dynamics of a Brownian ratchet.

  12. KIF1A (Red) MT (Green) 10 pM 100 pM 1000pM 2 mM of ATP 2 mm Many motors are moving simultaneously on the same track; similarity with traffic Nishinari, Okada, Schadschneider and Chowdhury, Phys. Rev. Lett. 95, 118101 (2005) Greulich, Garai, Nishinari, Schadschneider, Chowdhury, Phys. Rev. E, 77, 041905 (2007) Chowdhury, Garai and Wang, Phys. Rev. E (Rapid Commun.), 77, 050902(R) (2008)

  13. wd wa wf 1 1 2 2 2 2 1 2 wb wb Model of interacting KIF1A on a single MT protofilament Greulich, Garai, Nishinari, Okada, Schadschneider, Chowdhury MT track = 1-d lattice; motor-binding site on MT = lattice site KIF1A traffic on MT = TASEP for particles with “internal” states + Attachments & Detachments Current occupation Occupation at next time step

  14. Low-density region High-density region Density Position Greulich, Garai, Nishinari, Schadschneider, Chowdhury, Phys. Rev. E, 77, 041905 (2007) Mean-field theory versus computer simulations A new “probe-particle” method developed for locating the domain wall Co-existence of high-density and low-density regions, separated by a fluctuating domain wall (or, shock): Molecular motor traffic jam !! Non-trivial effects of lane changing on the flux of the KIF1A motors Chowdhury, Garai and Wang, Phys. Rev. E (Rapid Commun.), 77, 050902(R) (2008)

  15. Not all motors are cargo transporters SHREDDERS: walk/diffuse and depolymerize the track Dependence of MT-length distribution on depolymerase concentration Govindan, Gopalakrishnan and Chowdhury, Europhys. Lett. 83, 40006 (2008) Kip3p: a member of kinesin-8 family MCAK, KLP10A and KLP59C : members of kinesin-13 family www.nature.com/.../n9/thumbs/ncb0906-903-f1.jpg www.nature.com/.../v7/n3/thumbs/ncb1222-F7.gif

  16. Not all motors move on tracks made of filamentous proteins Track Filamentous Protein Nucleic Acid strand Microtubule F-actin DNA RNA Example: DNA helicase that unzips a double-stranded DNA and translocates on one of the single strands. Garai, Chowdhury and Betterton, Phys. Rev. E 77, 061910 (2008).

  17. But, today I’ll talk about the “real engines of creation”, the motors which also polymerize the macromecules of life (e.g., RNA and proteins), from the respective templates which also serve as the corresponding tracks.

  18. Motor traffic on Nucleic Acid Tracks

  19. Central dogma of Molecular Biology and assemblers Simultaneous Transcription and Translation in bacteria DNA Transcription (RNA polymerase) RNA Translation (Ribosome) Protein Rob Phillips and Stephen R. Quake, Phys. Today, May 2006. Many motors move on the same track; similarity with traffic

  20. We model only elongation stage in detail. initiation termination a b Three Stages of transcription / translation Initiation (Start), Elongation, Termination (Stop) RNAP/Ribosome traffic = TASEP for RODS with “internal states” OPEN boundary conditions Av. speed of a ribosome = Av. speed of synthesis of a single protein Flux = No. of ribosomes detected at the stop codon per unit time = Total no. of proteins synthesized per unit time

  21. Ribosome traffic on mRNA track; pause-and-translocation of ribosomes A. Basu and D. Chowdhury, Phys. Rev. E 75, 021902 (2007) A. Garai, D. Chowdhury and T.V. Ramakrishnan, Phys. Rev. E (under review) (2008)

  22. TASEP-like models of ribosome traffic L = 2 a b mRNA track = lattice; codon (triplet of nucleotides) = a lattice site. Ribosome = a hard rod that covers L lattice sites; moves by one site. Entire mechano-chemical cycle is captured by the single hopping parameter q. q q MacDonald and Gibbs (1969); Lakatos and Chou (2003); Shaw, Zia and Lee (2003); Shaw, Sethna and Lee (2004), Shaw, Kolomeisky and Lee (2004), Dong, Schmittmann and Zia (2007)

  23. BUT, a ribosome is not a “particle”; it’s mechanical movement is coupled to its biochemical cycle

  24. Ribosome: a mobile workshop http://www.mpasmb-hamburg.mpg.de/ Ribosome mRNA Protein A motor that moves along mRNA track, decodes genetic message, polymerizes protein using mRNA as a template. http://www.molgen.mpg.de/~ag_ribo/ag_franceschi/

  25. The Ribosome www.cancerquest.org • The ribosome has two subunits: large and small The small subunit binds with the mRNA track The synthesis of protein takes place in the larger subunit Processes in the two subunit are well coordinated B Alberts et al Mol. Biol of the Cell

  26. tRNA, an adapter molecule, helps in the coordination of the operations of the two subunits Interacts with LARGER s.u. Amino acid (Monomer of protein) Interacts with SMALLER s.u. Anti-codon Codon = Triplet of nucleotides on mRNA Correct codon-anticodon matching guarantees correct amino acid species

  27. Three main stages in the mechano-chemical cycle of a ribosome Cryo-electron microscopy: Frank et al. PNAS, 104, 19671 (2007). A toy model: Basu and Chowdhury, Amer. J. Phys. (2007) For simplicity, I explain the process schematically assuming L = 1 Codon (Triplet of nucleotides) Ribosome Large subunit Small subunit mRNA track i - 1 i i + 1

  28. A toy model of Ribosome Traffic on a mRNA template during protein synthesis Basu and Chowdhury, Amer. J. Phys. (2007) wa Arrival of cognate tRNA mRNA track i - 1 i i + 1

  29. A toy model of Ribosome Traffic on a mRNA template during protein synthesis Basu and Chowdhury, Amer. J. Phys. (2007) wfl Peptide bond forms and Larger s.u. moves forward mRNA track i - 1 i i + 1

  30. A toy model of Ribosome Traffic on a mRNA template during protein synthesis Basu and Chowdhury, Amer. J. Phys. (2007) Smaller s.u. pulled forward wfs mRNA track i - 1 i i + 1

  31. A toy model of Ribosome Traffic on a mRNA template during protein synthesis Basu and Chowdhury, Amer. J. Phys. (2007) wfl Smaller s.u. pulled forward Peptide bond forms and Larger s.u. moves forward wfs wa Arrival of cognate tRNA Large subunit Small subunit mRNA track i - 1 i i + 1

  32. E P A But, a ribosome is not simply two pieces of rods connected by a spring Three binding sites for tRNA: E, P, A Two GTPases (engines which hydrolyze “fuel” molecules GTP) control movement of tRNA from one binding site to the next: Elongation-factor (EF)-Tu and Elongation-factor (EF)-G

  33. E E E P P P A A A Initiation α Theoretical model of ribosome traffic and protein synthesis A. Basu and D. Chowdhury, Phys. Rev. E 75, 021902 (2007) Codon (Triplet of nucleotides on mRNA track) β Termination

  34. Master eqn. for ribosome traffic for arbitrary l > 1 Position of a ribosome indicated by that of the LEFTmost site. dP1(i;t)/dt = wh2 P5(i-1;t) Q(i-1|i-1+l) + wp P2(i;t) – wa P1(i;t) dP2(i;t)/dt = wa P1(i;t) – [ wp + wh1] P2(i;t) dP3(i;t)/dt = wh1 P2(i;t) – k2 P3(i;t) dP4(i;t)/dt = k2 P3(i;t) – wg P4(i;t) dP5(i;t)/dt = wg P4(i;t) – wh2 Q(i|i+l) P5(i;t) P(i|j) = Conditional prob. that, given a ribosome at site i, there is another ribosome at site j = 1 - Q(i|j)

  35. Steady-state solution with periodic boundary conditions J = wh2 P5 Q(i|i+l) = wh2 P5 Q(1|1+l) P(1|1+l) = Z(L-2l,N-2, l)/Z(L-l,N-1, l) = (N-1)/(L+N-Nl-1) Where Z(L,N, l) = (N+L-Nl)!/[N! (L-Nl)!] = No. of ways of arranging N ribosomes and N-Nl gaps. P5 = P/[1 + {wh2 keff-1 (L-Nl )/(L+N-Nl -1)}] Where keff-1 = wg-1 + k2-1 + wh1-1 + wa-1 + wpwa-1wh1-1 J = {wh2r (1-rl)}/{(1+r-rl) + Wh2(1-rl)}, Where Wh2 = wh2/keff.

  36. Effects of sequence inhomogeneity of real mRNA Genes crr and cysK of E-coli (bacteria)K-12 strain MG1655 “Hungry codons” are the bottlenecks Basu and Chowdhury, Phys. Rev. E 75, 021902 (2007)

  37. Phase diagram of TASEP with Open B. C. a q b Phase diag. for q=1 and RSU LD: j is independent of b. HD: j is independent of a. MC: j is independent of both a, b

  38. (b = 1) Open Boundary Condition and Phase Diagrams Using Extremum current principle (Popkov and Schutz, 1999) A novel way of creating high-density phase: reduce fuel supply to the motors!! TASEP aa-tRNA conc. aa-tRNA conc. Pwa Pwa a Pwh ribosome conc. GTP conc.

  39. Manipulation of translation by a single ribosome Dwell Time Wen,…, Noller, Bustamante and Tinoco Jr., Nature (March, 2008) Translocation Time

  40. Comparison between theory and experiment SIMUL.: Garai, Chowdhury and Ramakrishnan, PRE (under review) (2008) EXPT.: Wen,…, Noller, Bustamante and Tinoco Jr., Nature (March, 2008) Dwell Time Dwell Time

  41. RNAP traffic on DNA and transcriptional bursts Tripathi and Chowdhury, Phys. Rev. E, 77, 011921 (2008) Tripathi and Chowdhury, Europhys. Lett. (in press) (2008)

  42. RNA polymerase: a mobile workshop RNA polymerase DNA RNA A motor that moves along DNA track, decodes genetic message, polymerizes RNA using DNA as a template. Roger Kornberg Nobel prize in Chemistry (2006)

  43. Theoretical model of RNAP and RNA synthesis T. Tripathi and D. Chowdhury, Phys. Rev. E 77, 011921 (2008) RNAP + RNAn→RNAP + RNAn + NTP → RNAP.RNAn+1.PPi → RNAP + RNAn+1 Transcription-elongation complex (TEC) = RNAP + DNA template + mRNA transcript Mechano-chemistry of each RNAP + Steric interactions

  44. RNAP traffic and rate of RNA synthesis Flux= Total rate of RNA synthesis (No./second) Open Boundary conditions Periodic Boundary conditions Coverage density NTP (RNA subunit concentration)

  45. Conclusions from single-cell experiments on transcription in-vivo: Relatively long periods of transcriptional inactivity are interspersed with brief periods of transcriptional bursts. Golding et al. Cell 123, 1025 (2005): prokaryotes (E-coli bacteria) Chubb et al. Curr. Biol. 16, 1018 (2006): eukaryotes (amoeba Dictyostelium) Raj et al. PLoS Biol. 4(10): e309 (2006): eukaryotes (chinese hamster ovary) Agents responsible (speculation): In prokaryotes, unbinding and binding of transcription repressor molecules In eukaryotes, chromatin remodeling enzymes Such a universal feature indicates a generic mechanism

  46. A Generic model: Transcriptional burst caused by gene switching Tripathi and Chowdhury, Europhys. Lett. (in press) (2008) A typical time series in our model Sort the events into separate bursts: members of the same burst are separated from the immediate preceding and succeeding events by time gaps smaller than Dt while the time gap between any pair of successive bursts is at least Dt. Two choices: Dt = 0.5 min. and 2.5 min. “ON” “OFF”

  47. Theory: Tripathi and Chowdhury, EPL (2008) Experiment: Chubb, Trcek, Shenoy and Singer, Curr. Biol. 16, 1018 (2006) won exp(- won tdur) Burst DURATION Burst DURATION woff exp(- woff tint) Distr. Of burst duration and intervals depend only on the rates of switching Burst INTERVAL Burst INTERVAL

  48. Burst-size Distribution P(n) = [1- exp(- woff /keff)] exp(-nwoff/keff) where keff = weff/l, and weff = w12w21f/(w12 + w21f) Burst-size distribution depends on the rate constants in the elongation cycle. Burst Size

  49. Summary and Conclusion • We have developed models for template-dictated polymerization of macromolecules of life by incorporating • mechano-chemistry of individual machines + steric interactions • between the machines. These efforts go beyond the earlier works on single-machine modeling and models of “ribosome traffic” (TASEP for hard rods). (2) We have not only calculated the average rate of polymerization and average density profile, but also studied transcriptional and translational noise. Our models account for transcriptional “bursts” observed in single-cell experiments. These models go beyond the earlier models of noise in gene expression (at the single gene level) as the roles of the machinery are captured explicitly.

  50. Thank You

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