Making the analogy between molecular chemical physics and cell biology Jianhua Xing Dept of Biological Sciences Virginia Tech.

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