Molecular Machines: Molecular Machines: Packers and Movers, Assemblers and Packers and Movers, Assemblers and

ShreddersShredders 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

“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).

(March 10, 1628 - September 30, 1694)

http://en.wikipedia.org/wiki/Marcello_Malpighi

Founder of

microscopic anatomy

Marcello Malpighi

“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 - )

MachineInput Output

MotorInput

Output

Mechanical

“Natural” Nano-machines within a living cell

“Artificial” Nano-machines for practical applications

Understanding mechanisms through experiments and theoretical modeling

Design using natural components extracted from living cells

Design using artificial components synthesized in the laboratory

All the design and manufacturing completed so far have succeeded only in establishing “proof-of-principle”, but still far from commercial prototypes.

Designs of molecular machines have been perfected by Nature over millions or billions of years on the principles of evolutionary biology.

“Natural” Nano-machines within a living cell

Understanding mechanisms through experiments and theoretical modeling

In THIS TALK

Outline of the talk

Introduction

2. Examples of molecular motors

I. Cytoskeletal motors

II. Nucleic acid-based motors

3. Methods of quantitative modeling to understand mechanisms

8. Conclusion

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

Examples of molecular motors I:

Cytoskeletal Motors

Cytoskeleton of a cell

Alberts et al., Molecular Biology of the Cell

Required for mechanical strength

and intra-cellular transportation.

Cytoskeletal Motor Transport System = Motor + Track + Fuel

- dimer

Protofilament

Diameter of a tubule: ~ 25 nm.

Track: Microtubule Track: F-actin

http://www.cryst.bbk.ac.uk/PPS2/course/section11/actin2.gif

TRACK

Woehlke and Schliwa (2000)

Superfamilies of Cytoskeletal MOTORS

http://www.proweb.org/kinesin/CrystalStruc/Dimer-down-rotaxis.jpg

Cytoskeletal Motors

Porters Rowers

Animated cartoon: MCRI, U.K.

Kinesin-1

Myosin-V Myosin-

II

Science, 27 June (2003)

Cytoskeletal Motors

Porters

Animated cartoon: MCRI, U.K.

Kinesin-1: Smallest BIPED

My research group works on “PORTERS”.

MCAK, KLP10A and KLP59C :

members of kinesin-13 family

Kip3p:

a member of kinesin-8 family

SHREDDERS: walk/diffuse and depolymerizeTheoretical modeling by Govindan, Gopalakrishnan and Chowdhury (2008)

www.nature.com/.../v7/n3/thumbs/ncb1222-F7.gifwww.nature.com/.../n9/thumbs/ncb0906-903-f1.jpg

Examples of molecular motors II:

Nucleic acid-based Motors

(RNA polymerase)

Translation

(Ribosome)

DNA

RNA

Protein

Transcription

Central dogma of Molecular Biology and assemblers

Simultaneous Transcription and Translation

Rob Phillips and Stephen R. Quake, Phys. Today, May 2006.

RNA polymerase: a mobile workshop

DNA RNA

decodes genetic message,

RNA polymerase

polymerizes RNA using DNA as a template.

A motor that moves along DNA track,

Roger Kornberg

Nobel prize in Chemistry (2006)

Ribosome: a mobile workshop

http://www.molgen.mpg.de/~ag_ribo/ag_franceschi/

mRNA Protein

decodes genetic message,

Ribosome

polymerizes protein using mRNA as a template.

A motor that moves along mRNA track,

http://www.mpasmb-hamburg.mpg.de/

Methods of Quantitative modeling

to

understand mechanisms

Atomic level: Quantum mechanical calculation of structures; numerical works based on software packages

(Quantum Chemistry)

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)

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.

Brownian level:

Master eqn./Fokker-Planck eqn. for the individual proteins

Level of Description adopted in our theoretical works

Chem. State

Position

State Space

Translocation

State Space

Chem. State

Position

Chem. reaction

Chem. State

Position

State Space

Mechano-

Chemical transition

Chem. State

Position

State Space

Translate into

Mathematical language

Master equations Numerical protocols

Analytical

solution Computer

simulation

Theoretical predictions Numerical predictions

Experimental data

CompareCompa

re

Mechano-chemical transitions in

“state-space”

Compare

Some

Fundamental questions

on

mechanisms

of

molecular motors

Question I: Is the mechanism of molecular motors identical to those of their macroscopic counterparts (except for a difference of scale)?

Size: Nano-meters; Force: Pico-Newtons

NO.

Far from equilibrium

Made of soft matter

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).

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).

Question II: Question II:

What is the mechanism of energy What is the mechanism of energy transduction ?transduction ?

Power Stroke

S.A. Endow, Bioessays, 25, 1212 (2003)

Power-stroke versus Brownian ratchet

Joe Howard, Curr. Biol. 16, R517 (2006).

Brownian ratchetPower 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

A Brownian motor operates by converting random thermal energy of the surrounding medium into mechanical work!!

R.D.Astumian ,Scientific American, July 2001

Smoluchowski-Feynman ratchet-and-pawl device

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).

Feynman Lectures in Physics.

A Brownian motor does not violate 2nd law of thermodynamics as it operates far from equilibrium where the 2nd law is not applicable.

Question III: Question III: Why are the porters processive? Why are the porters processive? (i.e., how does a porter cover a (i.e., how does a porter cover a long distance without getting long distance without getting

detached from the track?)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?

Theoretical model

of

Single-headed kinesin motor KIF1A

For processivity of a molecular motor two heads are not essential.

Nishinari, Okada, Schadschneider and Chowdhury, Phys. Rev. Lett. 95, 118101 (2005).

Single-headed kinesin KIF1A is processive because of the

electrostatic attraction between the

“K-loop” of the motor and “E-hook” of the track.

K KT KDP KD K

ATP P ADP

State 1 State 2

Strongly Attached to MT

(Diffusive)

Weakly Attached to MT

Enzymatic cycle of a single KIF1A motor

Binding site on Microtubule

ii-1 i+1

h

s

1 11

2 2 2bb

f

a

d

1,2 Two “chemical” states

“State-space” of KIF1A and the mechano-chemical transitions

position

Chemical state

Model of interacting KIF1A on a single protofilament

b b

Current occupation

Occupation at next time step

fd a

1 2 2 21 2 21

Greulich, Garai, Nishinari, Okada, Schadschneider, Chowdhury

Master eqns. for KIF1A traffic in mean-field approximation

dSi(t)/dt = a(1-Si-Wi) + f Wi-1(1-Si-Wi) + s Wi – h Si – d Si

dWi(t)/dt = h Si + b Wi-1 (1-Si-Wi) + b Wi+1 (1-Si-Wi)

- b Wi {(1-Si+1-Wi+1) + (1-Si-1-Wi-1)}

– s Wi – f Wi(1-Si+1-Wi+1)

i = 1,2,…,L

Si = Probability of finding a motor in the Strongly-bound state.

Wi = Probability of finding a motor in the Weakly-bound state.

GAIN terms LOSS terms

Validation of the model of interacting KIF1A

Excellent agreement with qualitative trends and quantitative data obtained from single-molecule experiments.

Low-density limit

Nishinari, Okada, Schadschneider and Chowdhury, Phys. Rev. Lett. 95, 118101 (2005)

ATP(mM)ATP(mM)

∞∞0.90.9

0.33750.3375

0.150.15

Position

Density

Greulich, Garai, Nishinari, Schadschneider, Chowdhury, Phys. Rev. E, 77, 041905 (2007)

Co-existence of high-density and low-density regions, separated by a fluctuating domain wall (or, shock): Molecular motor traffic jam !!

Low-density region High-density region

X

Y

W(x,y) → W(x,y+1) with bl+

W(x,y) → W(x,y-1) with bl-

W(x,y) → S(x,y+1) with fl+

W(x,y) → S(x,y-1) with fl-

Lane-changing by single-headed kinesin KIF1A motorsChowdhury, Garai and Wang (2008)

Lane = Protofilament

Lane-change allowed from weakly-bound state

Chowdhury, Garai and Wang (2008)

flf

Flux

(per lane)

New prediction:

Flux can increase or decrease depending on the rate of fuel consumption.

Effect of lane changing on the flux of KIF1A motors

Theoretical models

of

RNA polymerase

and

Ribosome

T. Tripathi and D. Chowdhury, Phys. Rev. E 77, 011921 (2008)

Theoretical model of RNAP and RNA synthesis

“Transcriptional bursts in noisy gene expression”,

T. Tripathi and D. Chowdhury (2008), submitted for publication

The Ribosome

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

Cartoon of a ribosome;

E, P, A: three binding sites for tRNA

Biochemical cycle of ribosome during polypeptide elongation

Basu and Chowdhury (2007)E P A

t-RNA t-RNA t-RNA-EF-Tu (GTP) t-RNA t-RNA-EF-Tu (GDP+P)

t-RNA t-RNA-EF-Tu (GDP) t-RNA t-RNA EF-G (GTP)t-RNA t-RNA

t-RNA t-RNA

i

i+1

t-RNA

α

β

E P A E P A E P A E P A

Theoretical model of ribosomes and rates of protein synthesisA. Basu and D. Chowdhury, Phys. Rev. E 75, 021902 (2007)

Initiation

Termination

Codon

(Triplet of nucleotides on mRNA track)

dP1(i;t)/dt = h2 P5(i-1;t) Q(i-1|i-1+l) + p P2(i;t) – a P1(i;t)

dP2(i;t)/dt = a P1(i;t) – [ p + h1] P2(i;t)

dP3(i;t)/dt = h1 P2(i;t) – k2 P3(i;t)

dP4(i;t)/dt = k2 P3(i;t) – g P4(i;t)

dP5(i;t)/dt = g P4(i;t) – h2 Q(i|i+l) P5(i;t)

Master eqn. for ribosome traffic for arbitrary l > 1Position of a ribosome indicated by that of the LEFTmost site.

P(i|j) = Conditional prob. that, given a ribosome at site i, there is another ribosome at site j = 1 - Q(i|j)

Basu and Chowdhury, Phys. Rev. E 75, 021902 (2007)

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)

Rate of

protein synthesis

Rate of fuel consumption

Examples of molecular motors III:

Membrane-associated Rotary Motors

Viral DNA packaging machine

Pressure in a Phi-29 viral capsid ~ 60 Atmospheric pressure

~ 10 times the pressure in a champagne bottle

The machine consists of a 10 nm diameter ring of RNA molecule sandwiched between two protein rings.

The rotation of the rings pull the DNA just as a rotating nut can pull in a bolt.

Fuel: ATP

The packaging motor can generate a force large enough to withstand this pressure!!

www.biologie.uni-osnabrueck.de/biophys/Junge/pictures/ATPaseVideo/Synthase.Mov

Movie

•Produces three ATPs per twelve protons passing through the it

ATP synthase

Bacterial

Flagellar

motor

Membrane-associated Rotary Motors

10 nm

ocw.mit.edu

Conclusion

Combination of powerful techniques from several disciplines has already provided some insight into the mechanisms of natural nano-machines.

“Does life provide us with a model for nanotechnology that we should try and emulate- are life’s soft machines simply the most effective way of engineering in the unfamiliar environment of the very small?”- R.A.L. Jones, Soft Machines (OUP, 2007).

Molecular Machines

Chemistry Molecular Cell Biology

Physics

Nano-technology

Thank You

AcknowledgementsCollaborators (Last 4 years):

On Ribosome: Aakash Basu*, Ashok Garai, T.V. Ramakrishnan (IITK/IISc/BHU).

On RNA Polymerase: Tripti Tripathi, Prasanjit Prakash.On Helicase: Ashok Garai, Meredith D. Betterton (Phys., Colorado). On Chromatin-remodeling enzymes: Ashok Garai, Jesrael Mani.On KIF1A: Ashok Garai, Philip Greulich (Th. Phys., Univ. of Koln), Andreas Schadschneider (Th. Phys., Univ. of Koln), Katsuhiro Nishinari (Engg, Univ. of Tokyo), Yasushi Okada (Med., Univ. of Tokyo), Jian-Sheng Wang (Phys., NUS). On MCAK & Kip3p: Manoj Gopalakrishnan (HRI), Bindu Govindan (HRI).

On MT-Motor tug-of-war: Dipanjan Mukherjee, Debasish Chaudhuri (MPI-PKS Dresden).

Funding: CSIR (India), MPI-PKS (Germany).

Discussions: Roop Mallik (TIFR) Krishanu Ray (TIFR)Stephan Grill (MPI-PKS and MPI-CBG, Dresden)Joe Howard (MPI-CBG, Dresden)Frank Julicher (MPI-PKS, Dresden) Gunter Schuetz (FZ, Juelich)

Now at Stanford University

Support: IITK-TIFR MoU, IITK-NUS MoU.