Transcript Molecular Machines: Packers and Movers, Assemblers and Shredders Debashish Chowdhury Physics Department,

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
“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);
Marcello Malpighi
(March 10, 1628 September 30, 1694)
Founder of
microscopic anatomy
As quoted by Marco Piccolino, Nature Rev.
Mol. Cell Biology 1, 149-152 (2000).
http://en.wikipedia.org/wiki/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 - )
Input
Input
Machine
Motor
Output
Mechanical
Output
“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 natural components
extracted from living cells
Design using artificial components
synthesized in the laboratory
“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.
“Natural” Nano-machines within a living cell
Understanding mechanisms through experiments and theoretical modeling
In THIS TALK
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
Examples of
molecular motors I:
Cytoskeletal Motors
Cytoskeleton of a cell
Required for mechanical strength
and intra-cellular transportation.
Alberts et al., Molecular Biology of the Cell
Cytoskeletal Motor Transport System = Motor + Track + Fuel
TRACK
Track: Microtubule
Track: F-actin
a-b dimer
Protofilament
http://www.cryst.bbk.ac.uk/PPS2/course/section11/actin2.gif
Diameter of a tubule: ~ 25 nm.
Superfamilies of Cytoskeletal MOTORS
Woehlke and Schliwa (2000)
http://www.proweb.org/kinesin/CrystalStruc/Dimer-down-rotaxis.jpg
Cytoskeletal Motors
Porters
Rowers
Myosin-V
Myosin-II
Kinesin-1
Animated cartoon: MCRI, U.K.
Science, 27 June (2003)
Cytoskeletal Motors
Porters
My research group
works on “PORTERS”.
Kinesin-1: Smallest BIPED
Animated cartoon: MCRI, U.K.
SHREDDERS: walk/diffuse and depolymerize
Theoretical modeling by Govindan, Gopalakrishnan and Chowdhury (2008)
Kip3p:
MCAK, KLP10A and KLP59C :
a member of kinesin-8 family
members of kinesin-13 family
www.nature.com/.../n9/thumbs/ncb0906-903-f1.jpg
www.nature.com/.../v7/n3/thumbs/ncb1222-F7.gif
Examples of
molecular motors II:
Nucleic acid-based
Motors
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.
DNA
RNA polymerase: a mobile workshop
RNA polymerase
A motor that moves along DNA track,
RNA
decodes genetic message,
polymerizes RNA using DNA as a template.
Roger Kornberg
Nobel prize in Chemistry (2006)
Ribosome: a mobile workshop
http://www.mpasmb-hamburg.mpg.de/
mRNA
Ribosome
A motor that moves along mRNA track,
Protein
decodes genetic message,
polymerizes protein using mRNA as a template.
http://www.molgen.mpg.de/~ag_ribo/ag_franceschi/
Methods of
Quantitative modeling
to
understand
mechanisms
Levels of Description
Coarse-grained level: Dynamical equations for local densities of motors;
Too coarse to maintain individual identities of the motors.
Brownian level: Langevin eqn. for the individual proteins
(equivalent: Fokker-Planck or Master equations)
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)
Level of Description adopted in our theoretical works
Brownian level:
Master eqn./Fokker-Planck eqn. for the individual proteins
State Space
Chem.
State
Position
State Space
Chem.
State
Translocation
Position
State Space
Chem.
State
Chem. reaction
Position
State Space
Chem.
State
Mechano- Chemical transition
Position
Mechano-chemical transitions
in
“state-space”
Translate into
Master equations
Mathematical language
Numerical protocols
Computer
Analytical solution
Theoretical predictions
simulation
Numerical predictions
Compare
Compare Compare
Experimental data
Some
Fundamental questions
on
mechanisms
of
molecular motors
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)?
(1) Far from equilibrium
NO.
(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).
FORCES
on
molecular motors
Random thermal forces;
Viscous forces;
bombardment by
water molecules
(“Brownian”-type motion)
inertial forces are
negligibly small
(Low-Reynold’s number).
Question II:
What is the mechanism of energy transduction ?
Power Stroke
S.A. Endow, Bioessays, 25, 1212 (2003)
Power-stroke versus Brownian ratchet
Joe Howard, Curr. Biol. 16, R517 (2006).
Mechanisms of energy transduction by molecular motors
Power Stroke
Input energy drives the
motor forward
Brownian ratchet
Random Brownian force
tends to move motor both
forward and backward.
Input energy merely rectifies
backward movements.
A Brownian motor operates by converting random thermal
energy of the surrounding medium into mechanical work!!
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.
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?
Theoretical model
of
Single-headed kinesin
motor KIF1A
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).
Enzymatic cycle of a single KIF1A motor
K
KT
KDP
KD
K
ATP
P
Strongly
Attached to MT
Weakly
Attached to MT
(Diffusive)
State 1
State 2
ADP
“State-space” of KIF1A and the mechano-chemical transitions
wd
wa
i-1
i
i+1
1
1
1
ws
2
1,2
Binding site on Microtubule
wb
wh
2
Two “chemical” states
position
wf
wb
Chemical
state
2
Model of interacting KIF1A on a single protofilament
Greulich, Garai, Nishinari, Okada, Schadschneider, Chowdhury
wd wa
1
1
wf
2
wb
2
2
2
1
2
wb
Current occupation
Occupation at next time step
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
Validation of the model of interacting KIF1A
Nishinari, Okada, Schadschneider and Chowdhury, Phys. Rev. Lett. 95, 118101 (2005)
Low-density limit
ATP(mM)
∞
0.9
0.3375
0.15
Excellent agreement with qualitative trends and quantitative
data obtained from single-molecule experiments.
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 !!
Lane-changing by single-headed kinesin KIF1A motors
Chowdhury, Garai and Wang (2008)
Lane-change allowed from weakly-bound state
W(x,y) → W(x,y+1) with wbl+
W(x,y) → W(x,y-1) with wblW(x,y) → S(x,y+1) with wfl+
W(x,y) → S(x,y-1) with wfl-
Y
X
Lane = Protofilament
Effect of lane changing on the flux of KIF1A motors
Chowdhury, Garai and Wang (2008)
Flux
(per lane)
New prediction:
wfl/wf
Flux can increase or decrease depending on the rate
of fuel consumption.
Theoretical models
of
RNA polymerase
and
Ribosome
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
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
Biochemical cycle of ribosome during polypeptide elongation
E
P A
t-RNA
t-RNA t-RNA
Basu and Chowdhury (2007)
t-RNA t-RNA-EF-Tu (GTP)
t-RNA t-RNA EF-G (GTP)
i
t-RNA t-RNA
i+1
t-RNA
t-RNA t-RNA-EF-Tu (GDP+P)
t-RNA t-RNA-EF-Tu (GDP)
Theoretical model of ribosomes and rates of protein synthesis
A. Basu and D. Chowdhury, Phys. Rev. E 75, 021902 (2007)
Initiation
α
EP A
EPA
EPA
E PA
Codon
(Triplet of nucleotides on mRNA track)
β
Termination
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)
Basu and Chowdhury, Phys. Rev. E 75, 021902 (2007)
Effects of sequence inhomogeneity of real mRNA
Basu and Chowdhury, Phys. Rev. E 75, 021902 (2007)
Genes crr and cysK of E-coli (bacteria) K-12 strain MG1655
Rate of
protein synthesis
Rate of fuel consumption
“Hungry codons” are the bottlenecks
Examples of molecular
motors III:
Membrane-associated
Rotary Motors
Viral DNA packaging machine
Fuel: ATP
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.
Pressure in a Phi-29 viral capsid ~ 60 Atmospheric pressure
~ 10 times the pressure in a champagne bottle
The packaging motor can generate a force large
enough to withstand this pressure!!
Membrane-associated Rotary Motors
Bacterial
Flagellar
motor
ocw.mit.edu
•Produces three ATPs per twelve
protons passing through the it
ATP synthase
10 nm
Movie
www.biologie.uni-osnabrueck.de/biophys/Junge/pictures/ATPaseVideo/Synthase.Mov
Conclusion
Combination of powerful techniques from several disciplines has already
provided some insight into the mechanisms of natural nano-machines.
Physics
Chemistry
Molecular
Machines
Molecular
Cell Biology
Nano-technology
“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).
Thank You
Acknowledgements
Collaborators (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).
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)
Funding: CSIR (India), MPI-PKS (Germany).
Support: IITK-TIFR MoU, IITK-NUS MoU.
* Now at Stanford University