Physics of nano-motors: from cargo transport to gene expression
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Transcript of Physics of nano-motors: from cargo transport to gene expression
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Physics of nano-motors: Physics of nano-motors:
from cargo transport to gene from cargo transport to gene expressionexpression
Debashish Chowdhury
Physics Department,
Indian Institute of Technology,
Kanpur
Home page: http://home.iitk.ac.in/~debch/profile_DC.html
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Motor Transport System = Motor + Track + Fuel
(A) Properties of single-motor:
(i) Composition and structure (inventory of parts and architectural design)
Fundamental questions:
(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) Control systems and regulators of operation.
(ii) Structural/conformational and bio-chemical dynamics (operational mechanism driven by mechano-chemical cycles):
power-stroke or Brownian ratchet?
(iii) Effects of steric interactions on the spatio-temporal organization
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Power-stroke versus Brownian ratchet
Joe Howard, Curr. Biol. 16, R517 (2006).
The operational mechanism of a real molecular motor may involve a combination of power stroke and Brownian ratchet
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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!! Such systems are far from thermodynamic equilibrium and, therefore, do NOT violate second law of thermodynamics.
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Simplest Model of Interacting Self-Driven Particles in 1-d
A particle moves forward, with probability q, iff the target site is empty.
q
Totally Asymmetric Simple Exclusion Process (TASEP)
Discretized position, discrete velocity (0 or 1) and discrete time
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.
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2. Brief overview of the motors of our current interest
4. Ribosome traffic on mRNA track
5. RNA polymerase traffic on DNA
1. Introduction
6. Summary and conclusion
Outline of the talk
3. Single-headed motor traffic on microtubule track
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Brief overview of molecular motors of our
current interest
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Cytoskeletal Molecular Motors: Cargo transport
Porters
Animated cartoon: MCRI, U.K.
Kinesin-1 on Microtubule
Myosin-V on F-actin
Ribbon diagram of the two heads of kinesin-1 (also called conventional kinesin)
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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
Not all kinesins have two-heads.
KIF1A kinesins are single-headed (“lame” porters);
These motors are physical realizations of Brownian ratchets
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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
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
Both +vely charged K-loop of KIF1A and the –vely charged E-hook of MT
are essential for the processive movement of KIF1A.
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(Diffusive)
K KT KDP KD K
ATP P ADP
State 1 State 2
Strongly Attached to MT
Weakly Attached to MT
Brownian ratchet mechanism of movement of single KIF1A
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.
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KIF1A (Red) MT (Green)
10 pM
100 pM
1000pM
2 mM of ATP2 mNishinari, 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)
Many motors are moving simultaneously on the same track;
similarity with traffic
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Model of interacting KIF1A on a single MT protofilament
Current occupation Occupation at next time step
b b
fd a
1 2 2 21 2 21
Greulich, Garai, Nishinari, Okada, Schadschneider, Chowdhury
KIF1A traffic on MT = TASEP for particles with “internal” states
+ Attachments & Detachments
MT track = 1-d lattice; motor-binding site on MT = lattice site
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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 !!
Position
Density
Low-density region High-density region
Chowdhury, Garai and Wang, Phys. Rev. E (Rapid Commun.), 77, 050902(R) (2008)
Non-trivial effects of lane changing on the flux of the KIF1A motors
Mean-field theory versus computer simulations
A new “probe-particle” method developed for locating the domain wall
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MCAK, KLP10A and KLP59C :
members of kinesin-13 family
Kip3p:
a member of kinesin-8 family
SHREDDERS: walk/diffuse and depolymerize the track
www.nature.com/.../v7/n3/thumbs/ncb1222-F7.gifwww.nature.com/.../n9/thumbs/ncb0906-903-f1.jpg
Not all motors are cargo transporters
Govindan, Gopalakrishnan and Chowdhury, Europhys. Lett. 83, 40006 (2008)
Dependence of MT-length distribution on depolymerase concentration
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Not all motors move on tracks made of filamentous proteins
Track
Filamentous Protein Nucleic Acid strand
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).
Microtubule F-actin
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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.
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Motor traffic on Nucleic Acid Tracks
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(RNA polymerase)
Translation
(Ribosome)
DNA
RNA
Protein
Transcription
Central dogma of Molecular Biology and assemblersSimultaneous Transcription and Translation in bacteria
Rob Phillips and Stephen R. Quake, Phys. Today, May 2006.
Many motors move on the same track; similarity with traffic
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Initiation (Start), Elongation, Termination (Stop)
Three Stages of transcription / translation
initiation terminationWe model only elongation stage in detail.
OPEN boundary conditionsAv. 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
RNAP/Ribosome traffic = TASEP for RODS with “internal states”
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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)
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q q
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.
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)
TASEP-like models of ribosome traffic
L = 2
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BUT,
a ribosome is not a “particle”;
it’s mechanical movement
is
coupled to its biochemical cycle
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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/
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The Ribosome
• The ribosome has two subunits: large and small
www.cancerquest.org
B Alberts et al Mol. Biol of the Cell
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
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tRNA, an adapter molecule,
helps in the coordination of the operations of the two subunits
(Monomer of protein)
Correct codon-anticodon matching guarantees correct amino acid species
Codon = Triplet of nucleotides on mRNA
Amino acid
Anti-codon
Interacts with SMALLER s.u.
Interacts with LARGER s.u.
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i - 1 i + 1i
mRNA track
Large subunit
Small subunit
Codon (Triplet of nucleotides) Ribosome
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
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Basu and Chowdhury, Amer. J. Phys. (2007)
A toy model of Ribosome Traffic on a mRNA template during protein synthesis
i - 1 i + 1i
a
mRNA track
Arrival of cognate tRNA
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Basu and Chowdhury, Amer. J. Phys. (2007)
A toy model of Ribosome Traffic on a mRNA template during protein synthesis
i - 1 i + 1i
fl
mRNA track
Peptide bond forms and Larger s.u. moves forward
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Basu and Chowdhury, Amer. J. Phys. (2007)
A toy model of Ribosome Traffic on a mRNA template during protein synthesis
i - 1 i + 1i
fs
mRNA track
Smaller s.u. pulled forward
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Basu and Chowdhury, Amer. J. Phys. (2007)
A toy model of Ribosome Traffic on a mRNA template during protein synthesis
i - 1 i + 1i
a
fl
fs
mRNA track
Large subunit
Small subunit
Peptide bond forms and Larger s.u. moves forward
Smaller s.u. pulled forward
Arrival of cognate tRNA
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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
E P A
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β
Theoretical model of ribosome traffic and protein synthesisA. Basu and D. Chowdhury, Phys. Rev. E 75, 021902 (2007)
Termination
Codon
(Triplet of nucleotides on mRNA track)
αInitiation
E P A E P A E P A
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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)
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Steady-state solution with periodic boundary conditions
J = h2 P5 Q(i|i+l) = h2 P5 Q(1|1+l)
P5 = P/[1 + {h2 keff -1 (L-Nl )/(L+N-Nl -1)}]
Where keff -1 = g-1 + k2
-1 + h1-1 + a
-1 + p a-1 h1
-1
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.
J = {h2 (1-l)}/{(1+-l) + h2(1-l)},
Where h2 = h2/keff.
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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)
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LD: j is independent of HD: j is independent of MC: j is independent of both
q
Phase diag. for q=1 and RSU
Phase diagram of TASEP with Open B. C.
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ribosome conc.
Pa
Using Extremum current principle (Popkov and Schutz, 1999)
Open Boundary Condition and Phase Diagrams
aa-tRNA conc.
Pa
aa-tRNA conc.
Ph GTP conc.
A novel way of creating high-density phase: reduce fuel supply to the motors!!
TASEP
= 1)
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Wen,…, Noller, Bustamante and Tinoco Jr., Nature (March, 2008)
Manipulation of translation by a single ribosome
Dwell Time
Translocation Time
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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 TimeDwell Time
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RNAP traffic on DNA and transcriptional bursts
Tripathi and Chowdhury, Phys. Rev. E, 77, 011921 (2008)
Tripathi and Chowdhury, Europhys. Lett. (in press) (2008)
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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)
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T. Tripathi and D. Chowdhury, Phys. Rev. E 77, 011921 (2008)
Theoretical model of RNAP and RNA synthesis
Transcription-elongation complex (TEC)
= RNAP + DNA template + mRNA transcript
Mechano-chemistry of each RNAP + Steric interactions
RNAP + RNAn → RNAP + RNAn + NTP → RNAP.RNAn+1.PPi → RNAP + RNAn+1
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RNAP traffic and rate of RNA synthesis
Flux= Total rate of RNA synthesis (No./second)
Periodic Boundary conditions Open Boundary conditions
Coverage density NTP (RNA subunit concentration)
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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
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Tripathi and Chowdhury, Europhys. Lett. (in press) (2008)
A Generic model: Transcriptional burst caused by gene switching
“ON”
“OFF”
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 t while the time gap between any pair of successive bursts is at least t. Two choices: t = 0.5 min. and 2.5 min.
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Experiment: Chubb, Trcek, Shenoy and Singer, Curr. Biol. 16, 1018 (2006)
Burst DURATION
Burst INTERVAL
Theory: Tripathi and Chowdhury, EPL (2008)
Burst INTERVAL
Burst DURATION
on exp(- on tdur)
off exp(- off tint)
Distr. Of burst duration and intervals depend only on the rates of switching
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Burst Size
P(n)exp(- off /keff)] exp(-noff/keff)wherekeff = eff/l, and eff = 12 21
f/(12 + 21
f)
Burst-size Distribution
Burst-size distribution depends on the rate constants in the elongation cycle.
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Summary and Conclusion
(1)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.
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Thank You
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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).
Funding: CSIR (India), MPI-PKS (Germany).
Now at Stanford University
Support: IITK-TIFR MoU, IITK-NUS MoU.
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Shaw, Zia, Lee, PRE (2003)
Coverage density = N l/L
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Main steps of ribosome in the mechano-chemical cycle in the elongation stage
tRNA selection
Peptide bond formation
translocation
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Mechano-chemical cycle of ribosome during polypeptide elongation
Basu and Chowdhury, Phys. Rev. E 75, 021902 (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
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i - 1 i + 1i
1
2
3
4
5
1
2
3
4
5 5
4
3
2
1
pa
h1
g
h2
k2
Naturally discretized positions of a ribosome:
separation between successive codons (triplets of nucleotides)
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Steady-state flux with periodic boundary conditions: mean-field theory versus computer simulations
Basu and Chowdhury, Phys. Rev. E 75, 021902 (2007)
Flux = Total rate of protein synthesis
Number density
l = 3
l = 12
Flux of ribosomes = Total rate of protein synthesis (No./second)
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-
+
= -
= 1--
Open Boundary Condition and Phase Diagrams
Imagine that the left and right ends of the system are connected to two reservoirs with appropriate number densities ρ- and ρ+ ,
respectively, so that, assuming the same jumping rates as in the bulk, effects of and can be incorporated
Popkov and Schutz, Europhys. Lett. 48, 257 (1999)
Antal and Schutz, Phys. Rev. E 62, 83 (2000)
Popkov and Peschel, Phys. Rev. E 64, 026126 (2001)
Technique:
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where
Pjump = probability that, given a set of l empty sites, a ribosome jumps onto it in the next time step.
We now identify Pjump as the parameter α.
Evaluation of ρ- and ρ+
i.e.,
+ = 0
and
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Phase diagram of the open system (for = 1, i.e., += 0) in the ribosome conc. – aminoacyl-tRNA conc. plane
The Phase boundary is the solution to:ρ-(α,ωa,ωh1, ωh2) = ρ*(α,ωa,ωh1, ωh2)
PaJ
Extremum principle (Popkov and Schutz, 1999): j = max J() if - > *
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Ph
Pa
Phase diagram of the open system (for = 1, i.e., += 0) in the GTP conc. – aminoacyl-tRNA conc. plane
Extremum principle (Popkov and Schutz, 1999): j = max J() if - > *
The Phase boundary is the solution to:ρ-(α,ωa,ωh1, ωh2) = ρ*(α,ωa,ωh1, ωh2)
h
J
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Effect of sequence-inhomogeneity on translational noise
Garai, Chowdhury and Ramakrishnan (2008)Homogeneous sequence Inhomogeneous sequence
Time Headway Time Headway
Time series of translational events Time series of translational events
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i i+1i-1
22
1
2 2
1 1
bb2222
bb1111
ff2222
ff1111
ff2121
bb1212
2121
1212
Discrete state space of individual RNAP and the transitions
Tripathi and Chowdhury, Phys. Rev. E, 77, 011921 (2008);
adapted from Wang, Elston, Mogilner, Oster (1998)
NO PPi is bound to the RNAP catalytic site
PPi is bound to the RNAP catalytic site
12 Release of PPi (the rate-limiting step)
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Dominant pathway in each cycle of individual RNAP
21 = 021 [PPi]f
21 = f021 [NTP]
i i+1i-1
22
1
2 2
1 1
PPi is bound to the RNAP catalytic site
NO PPi is bound to the RNAP catalytic site
12 Release of PPi
Tripathi and Chowdhury, Phys. Rev. E, 77, 011921 (2008);
adapted from Wang, Elston, Mogilner, Oster (1998)
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= a , 1,2 = d,
1,2 = = 0
Phase-diagram in the h- a plane
Blue = 1,
Red = 2
Very low h: almost all in state 1 and Homogeneously distributed
a
h
Nishinari, Okada, Schadschneider and Chowdhury, Phys. Rev. Lett. 95, 118101 (2005)
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Binding site on MT track
ii-1 i+1
h
s
1 11
2 2 2bb
f
a
d
1,2 Two “chemical” states
Discrete “State-space” of a single KIF1A and the transitions
Spatial position
Chemical state
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Master eqns. for KIF1A traffic in mean-field approximation:
continuous time
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)
Si = Probability of finding a motor in the Strongly-bound state.
Wi = Probability of finding a motor in the Weakly-bound state.
i = 1,2,…,L
GAIN terms LOSS terms
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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
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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, Phys. Rev. E (Rapid Commun.), 77, 050902(R) (2008)
Lane = Protofilament
Lane-change allowed from weakly-bound state
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Discrete State-Space of a KIF1A motor and mechano-chemical transitions (including lane-changing)
Chowdhury, Garai and Wang, Phys. Rev. E (Rapid Commun.), 77, 050902 (R) (2008)
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Master equations in the mean-field approximation
dSi(j,t)/dt = a[1-Si(j,t)-Wi(j,t)] + f Wi-1(j,t)[1-Si(j,t)-Wi(j,t)] + s Wi(j,t) – h Si(j,t) – d Si(j,t)
+ fl+[Wi(j-1,t)][1-Si(j,t)-Wi(j,t)] + fl-[Wi(j+1,t)][1-Si(j,t)-Wi(j,t)]
dWi(t)/dt = h Si (j,t) + b [Wi-1(j,t) + Wi+1(j,t)] [1-Si(j,t)-Wi(j,t)]
- b Wi [2-Si+1(j,t)-Wi+1(j,t) -Si-1(j,t)-Wi-1(j,t)] – s Wi(j,t) – f Wi(j,t)[1-Si+1(j,t)-Wi+1(j,t)]
+ bl[Wi(j-1,t) + Wi(j+1,t)] [1-Si(j,t)-Wi(j,t)]
bl Wi(j,t)[2-Si(j+1,t)-Wi(j+1,t)-Si(j-1,t)-Wi(j-1,t)]
fl+Wi(j,t)[1-Si(j+1,t)-Wi(j+1,t)]
- fl- Wi(j,t)[1-Si(j-1,t)-Wi(j-1,t)]i = 1,2,…,N; j = 1,2,…,13
Si(j,t) = Probability of finding a motor in the Strongly-bound state at site i on the protofilament j.
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Chowdhury, Garai and Wang (2008)
flf
Flux
(per lane)
flf
Density
Non-monotonic variation with frequency of lane-changing!!
New prediction:
Flux can increase or decrease depending on the rate of fuel consumption.