Making the analogy between molecular chemical physics and cell biology

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

2. Some basic questions in systems biology: a) Design principles of biological networks b) How a system functions robustly against stochasticity

3. I am a chemist by training! Berkeley, Fall 2000

4. I. Differences and Similarities between molecular chemical physics and cell biology Chemical Physics Cell Biology Time: fs- ms Size: angstrom to nm Time: ms to weeks Size: microns to mm or larger

5. Strong analogy between molecular dynamics and cell biology N3 x3 N1 x1 N2 x2 State represented by molecular number of species State represented by atomic coordinates 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

6. II Theoretical basis for the analogy 1) Nonequilibrium theory development is a frontier of theoretical physics No flux Flux Detailed balance: Thermodynamic equilibrium nonequilibrium steady state A b3 b1 a1 a3 a2 B C b2

7. 2. A system described by the general stochastic dynamics (the Langevin equation) with stationary distributions can be rigorously mapped to a Hamiltonian system 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: 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)

8. III Examples illustrating (power of) the new way of thinking • Pheotypic reprogramming as an analogy to thermally activated barrier crossing • Some theoretical development: Model reduction and nonlinear time series analysis using Mori-Zwanzig projection • Uncovering network motifs leading to endotoxin tolerance and priming in macrophages as a statistical physics problem • Existence and consequences of dynamic disorder in molecular and cellular dynamics

9. Pheotypic reprogramming as an analogy to thermally activated barrier crossing With the same genome, cells may have different phenotypes

10. 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!

11. Resonant activation in cell phenotypic transition antibiotics Normally growing cells: High growth rate Easy to kill Persister cells: Low growth rate Hard to kill Original Add antibiotics Antibiotics removed

12. Resonant activation in cell phenotypic transition Persister Normally growing Normally growing cell Persister Fu, Zhu, Xing, Phys. Biol. (2010)

13. No perturbation No perturbation Resonant perturbation Resonant perturbation Red: persister cell number; Black: normally growing cell number Gray: antibiotics period

14. Using resonance to facilitate cell phenotypic transitions in general a) Better cancer therapy strategy? Optimal fragmentation of radiotherapy/chemotherapy Therapy resembles changing barrier height Survival Apoptosis b) Synchronizing HIV dormancy-activation transition for treatment?

15. 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 Interconnected system Too many parameters and variables Incomplete data Projection for general system Zwanzig (1960), J. Chem. Phys. Mori (1965), Prog. Theor. Phys. Xing, Kim (2011), J. Chem. Phys.

16. Numerical test Predicted and simulated auto correlation function Memory kernel Fitted auto correlation function Xing, Kim (2011), J. Chem. Phys.

17. 3. Uncovering network motifs leading to endotoxin tolerance and priming in macrophages as a statistical physics problem Immune system Innate immune system Adaptive immune system Macrophage -- “The big eaters” Function: Phagocytosis Antigen Presentation Cytokine release http://en.wikipedia.org/wiki/Macrophage http://www.youtube.com/watch?v=KiLJl3NwmpU

18. LPS tolerance or priming:a cellular adaptivity/reprogramming process in vitro experiments

19. Immunological and clinical significance Molecular mechanism??

20. 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 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

21. 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.

22. The results can be clearly classified into two groups with experimentally measurable quantities Pathway synergy Suppressor deactivation

23. Suppressor deactivation Pathway synergy? Two mechanisms for priming x1 x1 x2 x2 x3 x3 Tolerance only requires slow inhibitor dynamics Existing experimental evidences support the theoretical results

24. 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

25. 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

26. 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 Native state F1-ATPase Xing et al. (2005), PNAS, 102:16539-16546

27. Single molecule enzymology studies High substrate concentration Low substrate concentration Beta-galactosidase English et al., (2006), Nat. Chem. Biol. 2:87-94

28. Elastic network model Conformational fluctuations can be very slow Experimental data Fluorescein (FL)-antiFL complex 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) The physiological consequences of molecular dynamic disoder can only be fully understood in the context of network dynamics

29. Analogous dynamic disorder in cellular dynamics—nongenetic heterogeneity Cell Nongenetic hetereogeneity, slow phenotypic and subphenotipic transitions Macromolecule Slow conformational fluctuations 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)

30. 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

31. Acknowledgement • Xing’s lab • Dr. Ping Wang • Dr. Zhanghan Wu • Yan Fu • Xiaoshang Jiang • Ravi Kappiyoor • Philip Hochendoner • Collaborators • Dr. LiwuLi (VT) • Dr. John Tyson (VT) • Dr. Ken Kim (LLNL) • Dr. Guang Yao (UA) • Financial support • The Thomas F. Jeffress and Kate Miller Jeffress Memorial Trust • NSF Emerging Frontier Program • NIGMS/DMS Mathematical Biology Program

32. Suppressor deactivation Pathway synergy? x1 x1 x2 x2 x3 x3

33. Tolerance Mechanism