Molecular Machines: Packers and Movers, Assemblers and Shredders

1. Molecular Machines: Packers and Movers, Assemblers and Shredders Debashish Chowdhury Physics Department, Indian Institute of Technology, Kanpur Home page: http://home.iitk.ac.in/~debch/profile_DC.html 2nd IITK REACH Symposium, March 2008

2. “Nature, in order to carry out the marvelous operations in animals and plants, has been pleased to construct their organized bodies with a very large number of machines, which are of necessity made up of extremely minute parts so shaped and situated such as to form a marvelous organ, the composition of which are usually invisible to the naked eye, without the aid of microscope”- Marcello Malpighi (seventeenth century); As quoted by Marco Piccolino, Nature Rev. Mol. Cell Biology 1, 149-152 (2000). Marcello Malpighi (March 10, 1628 - September 30, 1694) Founder of microscopic anatomy http://en.wikipedia.org/wiki/Marcello_Malpighi

3. “The entire cell can be viewed as a factory that contains an elaborate network of interlocking assembly lines, each of which is composed of a set of large protein machines…. Why do we call the large protein assemblies that underline cell function protein machines? Precisely because, like machines invented by humans to deal efficiently with the macroscopic world, these protein assemblies contain highly coordinated moving parts” - Bruce Alberts, Cell 92, 291 (1998). President of the National Academy of Sciences USA (1993-2005) Editor-in-chief, SCIENCE (March, 2008 - )

4. Input Output Machine Input Motor Mechanical Output

5. “Natural” Nano-machines within a living cell Designs of molecular machines have been perfected by Nature over millions or billions of years on the principles of evolutionary biology. Understanding mechanisms through experiments and theoretical modeling Design using artificial components synthesized in the laboratory Design using natural components extracted from living cells “Artificial” Nano-machines for practical applications All the design and manufacturing completed so far have succeeded only in establishing “proof-of-principle”, but still far from commercial prototypes.

6. “Natural” Nano-machines within a living cell Understanding mechanisms through experiments and theoretical modeling In THIS TALK

7. Outline of the talk 1. Introduction 2. Examples of molecular motors I. Cytoskeletal motors II. Nucleic acid-based motors 3. Methods of quantitative modeling to understand mechanisms 4. Some fundamental questions on mechanisms of molecular motors 5. Theoretical model of single-headed kinesin motor KIF1A 6. Theoretical models of RNA polymerase and Ribosome 7. Examples of molecular motors III: Membrane-associated rotary motors 8. Conclusion

8. Examples of molecular motors I: Cytoskeletal Motors

9. Cytoskeleton of a cell Required for mechanical strength and intra-cellular transportation. Alberts et al., Molecular Biology of the Cell

10. Cytoskeletal Motor Transport System = Motor + Track + Fuel

11. Protofilament TRACK Track: Microtubule Track: F-actin a-b dimer http://www.cryst.bbk.ac.uk/PPS2/course/section11/actin2.gif Diameter of a tubule: ~ 25 nm.

12. Superfamilies of Cytoskeletal MOTORS Woehlke and Schliwa (2000) http://www.proweb.org/kinesin/CrystalStruc/Dimer-down-rotaxis.jpg

13. Cytoskeletal Motors Porters Rowers Myosin-V Myosin-II Kinesin-1 Animated cartoon: MCRI, U.K. Science, 27 June (2003)

14. Cytoskeletal Motors Porters My research group works on “PORTERS”. Kinesin-1: Smallest BIPED Animated cartoon: MCRI, U.K.

15. SHREDDERS: walk/diffuse and depolymerize Theoretical modeling by Govindan, Gopalakrishnan and Chowdhury (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. Examples of molecular motors II: Nucleic acid-based Motors

17. Central dogma of Molecular Biology and assemblers Simultaneous Transcription and Translation DNA Transcription (RNA polymerase) RNA Translation (Ribosome) Protein Rob Phillips and Stephen R. Quake, Phys. Today, May 2006.

18. 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)

19. 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/

20. Methods of Quantitative modeling to understand mechanisms

21. Brownian level: Langevin eqn. for the individual proteins (equivalent: Fokker-Planck or Master equations) Levels of Description Coarse-grained level: Dynamical equations for local densities of motors; Too coarse to maintain individual identities of the motors. Molecular level: Classical Newton’s equations for protein + molecules of the aqueous environment; Classical Molecular Dynamics (MD) (inadequate for length and time scales relevant for motor protein dynamics) Atomic level: Quantum mechanical calculation of structures; numerical works based on software packages (Quantum Chemistry)

22. Brownian level: Master eqn./Fokker-Planck eqn. for the individual proteins Level of Description adopted in our theoretical works

23. State Space Chem. State Position

24. State Space Chem. State Translocation Position

25. State Space Chem. State Chem. reaction Position

26. State Space Chem. State Mechano- Chemical transition Position

27. Mechano-chemical transitions in “state-space” Translate into Mathematical language Master equations Numerical protocols Analytical solution Computer simulation Theoretical predictions Numerical predictions Compare Compare Compare Experimental data

28. Some Fundamental questions on mechanisms of molecular motors

29. Size: Nano-meters; Force: Pico-Newtons Question I: Is the mechanism of molecular motors identical to those of their macroscopic counterparts (except for a difference of scale)? NO. (1) Far from equilibrium (2) Made of soft matter (3) Dominant forces are non-inertial “…gravitation is forgotten, and the viscosity of the liquid,…,the molecular shocks of the Brownian movement, …. Make up the physical environment….The predominant factor are no longer those of our scale; we have come to the edge of a world of which we have no experience, and where all our preconceptions must be recast”. - D’Arcy Thompson, “On Growth and Form” (1942).

30. FORCES on molecular motors Random thermal forces; bombardment by water molecules (“Brownian”-type motion) Viscous forces; inertial forces are negligibly small (Low-Reynold’s number).

31. Question II: What is the mechanism of energy transduction ?

32. Power Stroke S.A. Endow, Bioessays, 25, 1212 (2003)

33. Power-stroke versus Brownian ratchet Joe Howard, Curr. Biol. 16, R517 (2006).

34. 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!!

35. Smoluchowski-Feynman ratchet-and-pawl device Feynman Lectures in Physics. R.D.Astumian ,Scientific American, July 2001 Using the ratchet-and-pawl device, Feynman showed that it is impossible to extract mechanical work spontaneously from thermal energy of the surrounding medium if the device is in equilibrium (consequence of the 2nd law of thermodynamics). A Brownian motor does not violate 2nd law of thermodynamics as it operates far from equilibrium where the 2nd law is not applicable.

36. Question III: Why are the porters processive? (i.e., how does a porter cover a long distance without getting detached from the track?) Answer: The “fuel burning” (ATP hydrolysis) by the two heads of a 2-headed kinesin are coordinated in such a way that at least one remains attached when the other steps ahead. Then, why is a single-headed kinesin processive?

37. Theoretical model of Single-headed kinesin motor KIF1A

38. For processivity of a molecular motor two heads are not essential. Single-headed kinesin KIF1A is processive because of the electrostatic attraction between the “K-loop” of the motor and “E-hook” of the track. Nishinari, Okada, Schadschneider and Chowdhury, Phys. Rev. Lett. 95, 118101 (2005).

39. Enzymatic cycle of a single KIF1A motor K KT KDP KD K ATP P ADP Strongly Attached to MT Weakly Attached to MT (Diffusive) State 1 State 2

40. wd wa i-1 i i+1 1 1 1 ws wf wh wb wb 2 2 2 1,2 Two “chemical” states “State-space” of KIF1A and the mechano-chemical transitions Binding site on Microtubule position Chemical state

41. wd wa wf 1 1 2 2 2 2 1 2 Model of interacting KIF1A on a single protofilament Greulich, Garai, Nishinari, Okada, Schadschneider, Chowdhury wb wb Current occupation Occupation at next time step

42. Master eqns. for KIF1A traffic in mean-field approximation Si = Probability of finding a motor in the Strongly-bound state. Wi = Probability of finding a motor in the Weakly-bound state. dSi(t)/dt = wa(1-Si-Wi) + wf Wi-1(1-Si-Wi) + ws Wi – wh Si – wd Si GAIN terms LOSS terms dWi(t)/dt = wh Si + wb Wi-1 (1-Si-Wi) + wb Wi+1 (1-Si-Wi) - wb Wi {(1-Si+1-Wi+1)+ (1-Si-1-Wi-1)} – ws Wi – wf Wi(1-Si+1-Wi+1) i = 1,2,…,L

43. Validation of the model of interacting KIF1A Nishinari, Okada, Schadschneider and Chowdhury, Phys. Rev. Lett. 95, 118101 (2005) Low-density limit Excellent agreement with qualitative trends and quantitative data obtained from single-molecule experiments.

44. Greulich, Garai, Nishinari, Schadschneider, Chowdhury, Phys. Rev. E, 77, 041905 (2007) Low-density region High-density region Density Position Co-existence of high-density and low-density regions, separated by a fluctuating domain wall (or, shock): Molecular motor traffic jam !!

45. Lane-changing by single-headed kinesin KIF1A motors Chowdhury, Garai and Wang (2008) W(x,y) → W(x,y+1) with wbl+ W(x,y) → W(x,y-1) with wbl- W(x,y) → S(x,y+1) with wfl+ W(x,y) → S(x,y-1) with wfl- Lane-change allowed from weakly-bound state Y X Lane = Protofilament

46. Effect of lane changing on the flux of KIF1A motors Chowdhury, Garai and Wang (2008) Flux (per lane) wfl/wf New prediction: Flux can increase or decrease depending on the rate of fuel consumption.

47. Theoretical models of RNA polymerase and Ribosome

48. Theoretical model of RNAP and RNA synthesis T. Tripathi and D. Chowdhury, Phys. Rev. E 77, 011921 (2008) “Transcriptional bursts in noisy gene expression”, T. Tripathi and D. Chowdhury (2008), submitted for publication

49. The Ribosome Cartoon of a ribosome; E, P, A: three binding sites for tRNA 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 by tRNA

50. Biochemical cycle of ribosome during polypeptide elongation E P A Basu and Chowdhury (2007) t-RNA t-RNA t-RNA-EF-Tu (GTP) t-RNA t-RNA-EF-Tu (GDP+P) t-RNA t-RNA t-RNA t-RNA EF-G (GTP) t-RNA t-RNA-EF-Tu (GDP) i t-RNA t-RNA t-RNA i+1