making the analogy between molecular chemical physics and cell biology jianhua xing dept of...
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Making the analogy between molecular chemical physics
and cell biology
Jianhua XingDept of Biological Sciences
Virginia Tech
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a) Design principles of biological networks
b) How a system functions robustly against stochasticity
Some basic questions in systems biology:
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I am a chemist by training!
Berkeley, Fall 2000
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Chemical Physics Cell Biology
Time: fs- msSize: angstrom to nm
Time: ms to weeksSize: microns to mm or larger
I. Differences and Similarities between molecular chemical physics and cell biology
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Strong analogy between molecular dynamics and cell biology
State represented by atomic coordinates
State represented by molecular number of species
Atoms jiggle around due to thermal fluctuations
Species numbers fluctuate due to stochastic processes with low copy numbers
Transition between different stable conformations
Transition between different cell phenotypes
In some sense cellular dynamics resembles macromolecule dynamics
x3
x2x1
N3
N2N1
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II Theoretical basis for the analogy
Thermodynamic equilibrium nonequilibrium steady state
No flux Flux
1) Nonequilibrium theory development is a frontier of theoretical physics
Detailed balance:A
CB
b1a1 a3
a2
b2
b3 a1a2 a3
b1b2 b31
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2. A system described by the general stochastic dynamics (the Langevin equation) with stationary distributions can be rigorously mapped to a Hamiltonian system
d
dtx G(x) g(x) (t)
H lim
m 0
1
2m(%p A)2 (x)
1
2Y a(x) T
K Y a(x)
p: conjugate momenta; A: vector potential due to violation of detailed balance; Φ: scalar potential; Y: auxiliary degrees of freedom; K: constant matrix; a: function determined by the systemThe zero mass limit corresponds to Dirac’s constrained Hamiltonian method.
Equilibrium stateNESS
Noise strength Temperature
Many equilibrium (and close to equilibrium) results can be applied to Nonequilibrium processes (far away from equilibrium)!
Ao, J. Phys A (2004)Xing, J. Phys A: Math Theor Phys (2010)
Gibbs-Boltzman distribution: ss (x) exp( (x))
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III Examples illustrating (power of) the new way of thinking
1. Pheotypic reprogramming as an analogy to thermally activated barrier crossing
2. Some theoretical development: Model reduction and nonlinear time series analysis using Mori-Zwanzig projection
3. Uncovering network motifs leading to endotoxin tolerance and priming in macrophages as a statistical physics problem
4. Existence and consequences of dynamic disorder in molecular and cellular dynamics
1.Pheotypic reprogramming as an analogy to thermally activated barrier crossing
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With the same genome, cells may have different phenotypes
One can view the regulatory network as a high-dimensional potential surface
Muller et al. Nature, 2008 Dellago & Bolhuis, 2007
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Phenotype reprogramming resembles rate processes---what chemists are familiar!
Resonant activation in cell phenotypic transition
Persister cells: Low growth rateHard to kill
antibiotics
Normally growing cells: High growth rateEasy to kill
1111Original Add antibiotics Antibiotics removed
Fu, Zhu, Xing, Phys. Biol. (2010)1212
PersisterNormally growing
Persister
Normally growing cell
Resonant activation in cell phenotypic transition
No perturbation No perturbation
Resonant perturbation Resonant perturbation
Red: persister cell number; Black: normally growing cell numberGray: antibiotics period
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Using resonance to facilitate cell phenotypic transitions in general
Optimal fragmentation of radiotherapy/chemotherapy
Survival Apoptosis
a) Better cancer therapy strategy?
Therapy resembles changing barrier height
b) Synchronizing HIV dormancy-activation transition for treatment?
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2. Some theoretical development: Model reduction and nonlinear time series analysis using Mori-Zwanzig projection
Interconnected systemToo many parameters and variablesIncomplete data
The Mori-Zwanzig projection method widely used for Hamiltonian systems
Projection for general system
Zwanzig (1960), J. Chem. Phys.Mori (1965), Prog. Theor. Phys.Xing, Kim (2011), J. Chem. Phys.
Min et. al (2005), PRLXing & Kim (2006), PRE
0
X
j
W (X) (i S
jiT
ji) &X
i(t)
d
0
t
i s
ji(t s) &X
i(s)
F
j(t)
0 dW (x)
dx d(t )
dx( )
d0
t
F(t)
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Numerical test
Memory kernel
Fitted autocorrelation function
Predicted and simulated autocorrelation function
Xing, Kim (2011), J. Chem. Phys.
lnss
• Immune systemImmune system• Innate immune systemInnate immune system• Adaptive immune Adaptive immune
systemsystem
• Macrophage -- “The big Macrophage -- “The big eaters”eaters”
• Function: Function: • PhagocytosisPhagocytosis• Antigen PresentationAntigen Presentation• Cytokine releaseCytokine release
http://www.youtube.com/watch?v=KiLJl3NwmpU
http://en.wikipedia.org/wiki/Macrophage
3. Uncovering network motifs leading to endotoxin tolerance and priming in macrophages as a statistical physics problem
LPS tolerance or priming:LPS tolerance or priming:a cellular adaptivity/reprogramming processa cellular adaptivity/reprogramming process
in vitro experiments
Immunological and clinical significanceImmunological and clinical significance
Molecular mechanism??Molecular mechanism??
Evaluating volume of the priming (or tolerance) regions in the 14-D parameter space can be mapped into partition function calculation
Problem formulation and computational method
V H (d S)d H (d S)exp( E(S))dS is the scoring function quantifying the system dynamics with a given set of parameters, d is a threshold, H is the Heaviside function, E = H(S - d) is an effective energy term, and is the inverse of an effective temperature.
Fu et al. in preparation
The search is challenging, a brute force sampling with 10^8 steps gives a few to thousands of priming results.We designed a two-stage sampling scheme to overcome the difficulty.
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x2 during the signaling stage
x
1 d
uri
ng
th
e p
rim
ing
sta
ge
0 0.2 0.4 0.6 0.8
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
Su
pp
ressor
deacti
vati
on Pathway synergy
The results can be clearly classified into two groups with experimentally measurable quantities
x1 x2
x3
x1 x2
x3
Suppressor deactivation Pathway synergy?
Two mechanisms for priming
Tolerance only requires slow inhibitor dynamics
Existing experimental evidences support the theoretical results
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The discovered mechanisms are supported by existing experimental results
Hu X, et al. Immunol Rev. 2008Hu X, et al. Immunity. 2008Hu X, et al. Immunity. 2009
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Bigger questions:
1. Design principles of the immune system: multi-task optimization
?
Balance Frustration Principle of minimum frustration
2. Approaches analogous to multi-dimensional spectroscopies and nonlinear response theories
S1, t1
S2, t2R(s1, t1; S2, t2)
Xing et al. (2005), PNAS, 102:16539-16546
Brief history:1. Ligand binding of myoglobin, Austin et al. 19752. Hysteretic and mnemonical enzymes (Frieden 1970, Ricard & Cornish Bowden 1987)3. Recent single enzymology studies further suggest that slow conformational fluctuation is a general phenomenon (Lu et al. 1998, Yang et al. 2003, English et al. 2006) 4. Protein motors are examples of proteins with slow conformational changes
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Native state
4. Existence and consequences of dynamic disorder in molecular and cellular dynamics
F1-ATPase
Single molecule enzymology studies
English et al., (2006), Nat. Chem. Biol. 2:87-94 2727
Low substrate concentration
High substrate concentration
Beta-galactosidase
dc
dtk((t))c
Conformational fluctuations can be very slow
Min et. al (2005), PRLXing & Kim (2006), PREXing(2007), Phys. Rev. LettWu, Xing (2009),J Phy Chem B Wu, Xing, ( (to be submitted)
Elastic network model
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Experimental data
Fluorescein (FL)-antiFL complex
The physiological consequences of molecular dynamic disoder can only be fully understood in the context of network dynamics
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Analogous dynamic disorder in cellular dynamics—nongenetic heterogeneity
dc
dt f (ctotal ,,c)
Ctotal fluctuates slowly, on the time scale of 2 or more cell generations, due to synthesis, degradation, etc
Fluctuating with time Spencer et al,, Nature, 459:428-432 (2009)Sigal et al., Nature, 444: 643-646 (2006)
MacromoleculeSlow conformational fluctuations
CellNongenetic hetereogeneity, slow phenotypic and subphenotipic transitions
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“ If the facts don't fit the theory, change the facts.”“It is the theory that decides what can be observed.” ----- Albert Einstein
“ Biologists can be divided into two classes: experimentalists who observe things that cannot be explained, and theoreticians who explain things that cannot be observed.” -----Aharon Katzir-Katchalsky or George Oster
My dream: Cell biology as a new frontier of (theoretical and experimental) chemical physics and nonequilibirum statistical physics
Summary
AcknowledgementAcknowledgement Xing’s labXing’s lab
Dr. Ping WangDr. Ping Wang Dr. Zhanghan WuDr. Zhanghan Wu Yan FuYan Fu Xiaoshang JiangXiaoshang Jiang Ravi KappiyoorRavi Kappiyoor Philip HochendonerPhilip Hochendoner
CollaboratorsCollaborators Dr. LiwuLi (VT)Dr. LiwuLi (VT) Dr. John Tyson (VT)Dr. John Tyson (VT) Dr. Ken Kim (LLNL)Dr. Ken Kim (LLNL) Dr. Guang Yao (UA)Dr. Guang Yao (UA)
Financial supportFinancial support The Thomas F. Jeffress and Kate Miller Jeffress Memorial The Thomas F. Jeffress and Kate Miller Jeffress Memorial
TrustTrust NSF Emerging Frontier ProgramNSF Emerging Frontier Program NIGMS/DMS Mathematical Biology Program NIGMS/DMS Mathematical Biology Program
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Tolerance Mechanism