Making the analogy between
molecular chemical physics and
cell biology
Jianhua Xing
Dept of Biological Sciences
Virginia Tech
Some basic questions in systems biology:
a) Design principles of biological networks
b) How a system functions robustly against stochasticity
2
I am a chemist by training!
Berkeley, Fall 2000
3
I. Differences and Similarities between molecular chemical
physics and cell biology
Chemical Physics
Time: fs- ms
Size: angstrom to nm
Cell Biology
Time: ms to weeks
Size: microns to mm or larger
4
Strong analogy between molecular dynamics and cell biology
N3
x3
x1
N1
x2
N2
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
cell phenotypes
Transition between different
stable conformations
In some sense cellular dynamics resembles
macromolecule dynamics
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II Theoretical basis for the analogy
1) Nonequilibrium theory development is a frontier of theoretical physics
No flux
Thermodynamic equilibrium
Detailed balance:
b1
B
A
a1 a3
a2
b2
b3
C
Flux
nonequilibrium steady state
a1 a2  a3
1
b1 b2  b3
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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
x  G(x)   g(x) (t)
dt
T
 1
 1
2
H  lim 
(p% A)   (x)   Y  a(x) K Y  a(x)
m0  2m
 2
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 system
The zero mass limit corresponds to Dirac’s constrained Hamiltonian method.
Gibbs-Boltzman distribution:
ss (x)  exp( (x))
Many equilibrium (and close to equilibrium) results can be applied to
Nonequilibrium processes (far away from equilibrium)!
NESS
Equilibrium state
Noise strength
Temperature
Ao, J. Phys A (2004)
Xing, J. Phys A: Math Theor Phys (2010)
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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
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1. Pheotypic reprogramming as an analogy to thermally
activated barrier crossing
With the
same
genome,
cells may
have
different
phenotypes
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One can view the regulatory network as a high-dimensional potential
surface
Muller et al. Nature, 2008
Dellago & Bolhuis, 2007
Phenotype
reprogramming
resembles rate
processes---what
chemists are familiar!
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Resonant activation in cell phenotypic transition
antibiotics
Normally growing cells:
High growth rate
Easy to kill
Original
Add antibiotics
Persister cells: Low
growth rate
Hard to kill
Antibiotics removed
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Resonant activation in cell phenotypic transition
Persister
Normally growing
Normally growing cell
Persister
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Fu, Zhu, Xing, Phys. Biol. (2010)
No perturbation
Resonant perturbation
No perturbation
Resonant perturbation
Red: persister cell number; Black: normally growing cell number
Gray: antibiotics period
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Using resonance to facilitate cell phenotypic transitions in general
a) Better cancer therapy strategy?
Optimal
fragmentation of
radiotherapy/chemoth
erapy
Therapy resembles changing barrier height
Survival
Apoptosis
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
The Mori-Zwanzig projection method widely
used for Hamiltonian systems
Min et. al (2005), PRL
Xing & Kim (2006), PRE
t
dW (x)
dx( )
0
   d (t   )
 F(t)
0
dx
d
Interconnected system
Too many parameters and
variables
Incomplete data
Zwanzig (1960), J. Chem. Phys.
Mori (1965), Prog. Theor. Phys.
Xing, Kim (2011), J. Chem. Phys.
Projection for general system
 
 
t

&
0  
W (X)   (S ji  T ji ) X i (t)      ds ji (t  s) X&i (s)   Fj (t)

i
 X j
  i 0
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Numerical test
 ln ss
Predicted and
simulated
auto
correlation
function
Memory
kernel
Fitted auto
correlation
function
Xing, Kim (2011), J. Chem. Phys.
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3. Uncovering network motifs leading to endotoxin tolerance
and priming in macrophages as a statistical physics problem
•
Immune system
•
•
•
Macrophage -- “The big
eaters”
•
Function:
•
•
•
http://en.wikipedia.org/wiki/Macrophage
http://www.youtube.com/watch?v=KiLJl3NwmpU
Innate immune system
Adaptive immune system
Phagocytosis
Antigen Presentation
Cytokine release
LPS tolerance or priming:
a cellular adaptivity/reprogramming process
in vitro experiments
Immunological and clinical significance
Molecular mechanism??
Problem formulation and computational method
Evaluating volume of the priming (or tolerance) regions in the 14-D
parameter space can be mapped into partition function calculation
V   H(d  S)d   H(d  S)exp( E(S))d
S 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.
The results can be clearly classified into two groups with
experimentally measurable quantities
-0.2
-0.4
-0.6
Suppressor deactivation
 x1 during the priming stage
0
Pathway synergy
-0.8
0.8
0.6
0.4
0.2
0
0.2
0.4
0.6
0.8
 x during the signaling stage
2
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Suppressor deactivation
Two
mechanisms
for priming
x1
x2
x3
Pathway synergy?
x1
x2
x3
Tolerance
only requires
slow inhibitor
dynamics
Existing experimental evidences support the theoretical results
The discovered mechanisms are
supported by existing
experimental results
Hu X, et al. Immunol Rev. 2008
Hu X, et al. Immunity. 2008
Hu X, et al. Immunity. 2009
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Bigger questions:
1. Design principles of the immune system: multi-task optimization
?
Frustration
Balance
Principle of minimum frustration
2. Approaches analogous to multi-dimensional spectroscopies and nonlinear response theories
S1, t1
R(s1, t1; S2, t2)
S2, t2
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4. Existence and consequences of dynamic disorder in
molecular and cellular dynamics
Brief history:
1. Ligand binding of myoglobin, Austin et al. 1975
2. 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
F1-ATPase
Native state
Xing et al. (2005), PNAS, 102:16539-16546
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Single molecule enzymology studies
High substrate concentration
Low substrate concentration
Beta-galactosidase
English et al., (2006), Nat. Chem. Biol. 2:87-94
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Conformational fluctuations can be very slow
Experimental data
Elastic network model
dc
 k( (t))c
dt
Fluorescein (FL)-antiFL complex

The physiological consequences of molecular
dynamic disoder can only be fully understood in the
context of network dynamics
Min et. al (2005), PRL
Xing & Kim (2006), PRE
Xing(2007), Phys. Rev. Lett
Wu, Xing (2009),J Phy Chem B
Wu, Xing, ( (to be submitted)
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Analogous dynamic disorder in cellular dynamics—nongenetic
heterogeneity
Macromolecule
Slow conformational fluctuations
Cell
Nongenetic hetereogeneity, slow
phenotypic and subphenotipic transitions
dc
 f (ctotal , , c)
dt
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)
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Summary
“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
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Acknowledgement

Xing’s lab
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Collaborators
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Dr. Ping Wang
Dr. Zhanghan Wu
Yan Fu
Xiaoshang Jiang
Ravi Kappiyoor
Philip Hochendoner
Dr.
Dr.
Dr.
Dr.
LiwuLi (VT)
John Tyson (VT)
Ken Kim (LLNL)
Guang Yao (UA)
Financial support
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The Thomas F. Jeffress and Kate Miller Jeffress Memorial Trust
NSF Emerging Frontier Program
NIGMS/DMS Mathematical Biology Program
Suppressor deactivation
x2
x2
x2
1
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x1
x2 x
1
x3
x3
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x3
x1
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x1
Pathway synergy?
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Tolerance Mechanism