arXiv subjects

P. Ao

Publications and source records attributed to P. Ao.

At least 19 recordsLinked to original sources

arXiv2008

Towards Kinetic Modeling of Global Metabolic Networks with Incomplete Experimental Input on Kinetic Parameters

This is the first report, to our knowledge, on a systematic method for constructing a large scale kinetic metabolic model with incomplete information on kinetic parametersr, and its initial application to the modeling of central metabolism of Methylobacterium extorquens AM1, a methylotrophic and environmental important bacterium, with all necessary constraints. Through a systematic and consistent procedure of finding a set of parameters in the physiological range we overcome an outstanding difficulty in large scale kinetic modeling: the requirement for a massive number of enzymatic reaction parameters. We are able to construct the kinetic model based on general biological considerations and incomplete experimental kinetic parameters. The success of our approach with incompletely input information is guaranteed by two known principles in biology, the robustness of the system and the cooperation among its various parts. (Will be pleased to be informed on other methodologies dealing with same type of problems: aoping@u.washington.edu)

q-bio.MN↗

arXiv2008

Stochastic Dynamical Structure (SDS) of Nonequilibrium Processes in the Absence of Detailed Balance. III: potential function in local stochastic dynamics and in steady state of Boltzmann-Gibbs type distribution function

From a logic point of view this is the third in the series to solve the problem of absence of detailed balance. This paper will be denoted as SDS III. The existence of a dynamical potential with both local and global meanings in general nonequilibrium processes has been controversial. Following an earlier explicit construction by one of us (Ao, J. Phys. {\bf A37}, L25 '04, arXiv:0803.4356, referred to as SDS II), in the present paper we show rigorously its existence for a generic class of situations in physical and biological sciences. The local dynamical meaning of this potential function is demonstrated via a special stochastic differential equation and its global steady-state meaning via a novel and explicit form of Fokker-Planck equation, the zero mass limit. We also give a procedure to obtain the special stochastic differential equation for any given Fokker-Planck equation. No detailed balance condition is required in our demonstration. For the first time we obtain here a formula to describe the noise induced shift in drift force comparing to the steady state distribution, a phenomenon extensively observed in numerical studies. The comparison to two well known stochastic integration methods, Ito and Stratonovich, are made ready. Such comparison was made elsewhere (Ao, Phys. Life Rev. {\bf 2} (2005) 117. q-bio/0605020).

q-bio.QM↗

arXiv2008

Stochastic Dynamical Structure (SDS) of Nonequilibrium Processes in the Absence of Detailed Balance. II: construction of SDS with nonlinear force and multiplicative noise

There is a whole range of emergent phenomena in non-equilibrium behaviors can be well described by a set of stochastic differential equations. Inspired by an insight gained during our study of robustness and stability in phage lambda genetic switch in modern biology, we found that there exists a classification of generic nonequilibrium processes: In the continuous description in terms of stochastic differential equations, there exists four dynamical elements: the potential function $ϕ$, the friction matrix $ S$, the anti-symmetric matrix $ T $, and the noise. The generic feature of absence of detailed balance is then precisely represented by $T$. For dynamical near a fixed point, whether or not it is stable or not, the stochastic dynamics is linear. A rather complete analysis has been carried out (Kwon, Ao, Thouless, cond-mat/0506280; PNAS, {\bf 102} (2005) 13029), referred to as SDS I. One important and persistent question is the existence of a potential function with nonlinear force and with multiplicative noise, with both nice local dynamical and global steady state properties. Here we demonstrate that a dynamical structure built into stochastic differential equation allows us to construct such a global optimization potential function. First, we provide the construction. One of most important ingredient is the generalized Einstein relation. We then present an approximation scheme: The gradient expansion which turns every order into linear matrix equations. The consistent of such methodology with other known stochastic treatments will be discussed in next paper, SDS III; and the explicitly connection to statistical mechanics and thermodynamics will be discussed in a forthcoming paper, SDS IV.

cond-mat.other↗

arXiv2007

A Generic Rate Equation for modeling Enzymatic Reactions under Living Conditions

Based on our experience in kinetic modeling of coupled multiple metabolic pathways we propose a generic rate equation for the dynamical modeling of metabolic kinetics. Its symmetric form makes the kinetic parameters (or functions) easy to relate to values in database and to use in computation. In addition, such form is workable to arbitrary number of substrates and products with different stoichiometry. We explicitly show how to obtain such rate equation exactly for various binding mechanisms. Hence the proposed rate equation is formally rigorous. Various features of such a generic rate equation are discussed. For irreversible reactions, the product inhibition which directly arise from enzymatic reaction is eliminated in a natural way. We also discuss how to include the effects of modifiers and cooperativity.

q-bio.MN↗

arXiv2007

Cancer Genesis and Progression as Dynamics in Functional Landscape of Endogenous Molecular-Cellular Network

An endogenous molecular-cellular network for both normal and abnormal functions is assumed to exist. This endogenous network forms a nonlinear stochastic dynamical system, with many stable attractors in its functional landscape. Normal or abnormal robust states can be decided by this network in a manner similar to the neural network. In this context cancer is hypothesized as one of its robust intrinsic states. This hypothesis implies that a nonlinear stochastic mathematical cancer model is constructible based on available experimental data and its quantitative prediction is directly testable. Within such model the genesis and progression of cancer may be viewed as stochastic transitions between different attractors. Thus it further suggests that progressions are not arbitrary. Other important issues on cancer, such as genetic vs epigenetics, double-edge effect, dormancy, are discussed in the light of present hypothesis. A different set of strategies for cancer prevention, cure, and care, is therefore suggested.

q-bio.SC↗

arXiv2007

Quantitative Resolution to some "Absolute Discrepancies" in Cancer Theories: a View from Phage lambda Genetic Switch

Is it possible to understand cancer? Or more specifically, is it possible to understand cancer from genetic side? There already many answers in literature. The most optimistic one has claimed that it is mission-possible. Duesberg and his colleagues reviewed the impressive amount of research results on cancer accumulated over 100 years. It confirms the a general opinion that considering all available experimental results and clinical observations there is no cancer theory without major difficulties, including the prevailing gene-based cancer theories. They have then listed 9 "absolute discrepancies" for such cancer theory. In this letter the quantitative evidence against one of their major reasons for dismissing mutation cancer theory, by both in vivo experiment and a first principle computation, is explicitly pointed out.

q-bio.SC↗

arXiv2007

Is Adaptive Landscape in Biology a Metaphor or a Quantitative Concept? or Both?

Some biologists accept Wright's adaptive landscape idea, believing it is one of most profound concepts in evolutionary dynamics. Some wouldn't, believing that "the idea that there is such a quantity remains one of the most widely held popular misconceptions about evolution." The two groups usually have very limited communication with each other. Sometimes such isolation can be good, because it protects budding ideas in a harsh environment. Thanks to the theoretical and experimental progress during past few years, time may have arrived to consider both sides seriously. Present letter is a small attempt to bridge this gap.

q-bio.PE↗

arXiv2007

On the existence of potential landscape in the evolution of complex systems

A recently developed treatment of stochastic processes leads to the construction of a potential landscape for the dynamical evolution of complex systems. Since the existence of a potential function in generic settings has been frequently questioned in literature,herewe study several related theoretical issues that lie at core of the construction. We showthat the novel treatment,via a transformation,is closely related to the symplectic structure that is central in many branches of theoretical physics. Using this insight, we demonstrate an invariant under the transformation. We further explicitly demonstrate, in one-dimensional case, the contradistinction among the new treatment to those of Ito and Stratonovich, as well as others.Our results strongly suggest that the method from statistical physics can be useful in studying stochastic, complex systems in general.

q-bio.QM↗

arXiv2006

Two years later--lessons from vortex dynamics in super media

Two years ago the reasons for resistance to the fundamental vortex dynamics in super media emerged in 1990's were analyzed (cond-mat/0407007). Five "mistakes" were identified to explain this resistance. Given the current tremendous interest in vortex dynamics, it would be desirable to provide a progress report: A survey of literature reveals that 3 out 5 "mistakes" has in fact been confirmed by other researchers.

cond-mat.supr-con↗

arXiv2006

Efficiency, Robustness and Stochasticity of Gene Regulatory Networks in Systems Biology: lambda Switch as a Working Example

Phage lambda is one of the most studied biological models in modern molecular biology. Over the past 50 years quantitative experimental knowledge on this biological model has been accumulated at all levels: physics, chemistry, genomics, proteomics, functions, and more. All its components have been known to a great detail. The theoretical task has been to integrate its components to make the organism working quantitatively in a harmonic manner. This would test our biological understanding and would lay a solid fundamental for further explorations and applications, an obvious goal of systems biology. One of the outstanding challenges in doing so has been the so-called stability puzzle of lambda switch: the biologically observed robustness and its difficult mathematical reconstruction based on known experimental values. In this chapter we review the recent theoretical and experimental efforts on tackling this problem. An emphasis is put on the minimum quantitative modeling where a successful numerical agreement between experiments and modeling has been achieved. A novel method tentatively named stochastic dynamical structure analysis emerged from such study is also discussed within a broad modeling perspective.

q-bio.SC↗

arXiv2005

Nonequilibrium Statistical Mechanics and Thermodynamics from Darwinian Dynamics: a Primer

We present here an exploration on on the physical implications of the Darwinian dynamics. We first show that how the nonequilibrium statistical mechanics emerges naturally. We then show that the first three laws of the thermodynamics, the Zeroth Law, the First Law and the Second Law can be followed from the Darwinian dynamics, except the Third Law. The inability to derive the Third Law indicates that the Darwinian dynamics belongs to the "classical" domain. Specifically, the Second Law is proved from the dynamical point of view. Two types of current dynamical equalities are explicitly discussed in the paper: one is based on Feynman-Kac formula and one is a generalization of the Einstein relation. Both are directly accessible to experimental tests. Our demonstration indicates that the Darwinian dynamics is logically a simple and straightforward starting point to get into thermodynamics and is complementary to the conservative dynamics dominated in physics.

physics.class-ph↗

arXiv2005

Quantitative Measure of Stability in Gene Regulatory Networks

A quantitative measure of stability in stochastic dynamics starts to emerge in recent experiments on bioswitches. This quantity, similar to the potential function in mathematics, is deeply rooted in biology, dated back at the beginning of quantitative description of biological processes: the adaptive landscape of Wright (1932) and the development landscape of Waddington (1940). Nevertheless, its quantitative implication has been frequently challenged by biologists. Recent progresses in quantitative biology begin to meet those outstanding challenges.

q-bio.QM↗

arXiv2005

Boltzmann-Gibbs Distribution of Fortune and Broken Time-Reversible Symmetry in Econodynamics

Within the description of stochastic differential equations it is argued that the existence of Boltzmann-Gibbs type distribution in economy is independent of the time reversal symmetry in econodynamics. Both power law and exponential distributions can be accommodated by it. The demonstration is based on a mathematical structure discovered during a study in gene regulatory network dynamics. Further possible analogy between equilibrium economy and thermodynamics is explored.

physics.soc-ph↗

arXiv2005

Snapshots on Vortex Dynamics

Salient features of vortex dynamics in super media are summarized. Recent examples are: the demonstration of prominent role of topology in vortex dynamics; the solution to the Hall anomaly which once bothered Bardeen, de Gennes and many others; the unified microscopic treatment of both transverse and frictional forces on moving vortex. The fundamental dynamical equation of vortex matter can now be casted into the elegant form of quantum dissipative dynamics of Leggett. Together with the Kosterlitz-Thouless transition, we have finally reached a coherent picture on both thermodynamic and dynamical roles played by vortices. The key historical progresses are discussed with a broader perspective, to move into the post high $T_c$ superconductor era, the quantum era. References mentioned in the text and given at the end, though very incomplete, along with a list of a few outstanding open problems, may provide a reader a useful guidance and an interesting perspective.

cond-mat.supr-con↗

arXiv2005

Metabolic Network Modelling: Including Stochastic Effects

We propose to model the dynamics of metabolic networks from a systems biology point of view by four dynamical structure elements: potential function, transverse matrix, degradation matrix, and stochastic force. These four elements are balanced to determine the network dynamics, which gives arise to a special stochastic differential equation supplemented by a relationship between the stochastic force and the degradation matrix. Important network behaviors can be obtained from the potential function without explicitly solving for the time-dependent solution. The existence of such a potential function suggests a global optimization principle, and the existence stochastic force corresponds natural to the hierarchical structure in metabolic networks. We provide theoretical evidences to justify our proposal by discussing its connections to others large-scale biochemical systems approaches, such as the network thermodynamics theory, biochemical systems theory, metabolic control analysis, and flux balance analysis. Experimental data displaying stochasticity are also pointed out.

q-bio.MN↗

arXiv2004

Limit Cycle and Conserved Dynamics

We demonstrate that a potential coexists with limit cycle. Here the potential determines the final distribution of population. Our demonstration consists of three steps: We first show the existence of limit from a typical physical sciences setting: the potential is a type of Mexican hat type, with the strength of a magnetic field scale with the strength the potential gradient near the limit cycle, and the friction goes to zero faster than the potential near the limit cycle. Hence the dynamics at the limit cycle is conserved. The diffusion matrix is nevertheless finite at the limit cycle. Secondly, we construct the potential in the dynamics with limit cycle in a typical dynamical systems setting. Thirdly, we argue that such a construction can be carried out in a more general situation based on a method discovered by one of us. This method of dealing with stochastic differential equation is in general different from both Ito and Stratonovich calculus. Our result may be useful in many related applications, such as in the discussion of metastability of limit cycle and in the construction of Hopfield potential in the neural network computation.

nlin.CD↗

arXiv2004

Lessons from vortex dynamics in super media

Some aspects of vortex dynamics theories are critically examined. The discussion is placed in the context of experiments on the Josephson-Anderson effect and on the Hall anomaly in the mixed state.

cond-mat.supr-con↗

arXiv2004

Possible Laws for Artificial Life Evolution

Motivated by a recent article on open problems in artificial life, here I postulate three laws which form a mathematical framework to describe artificial life evolutionary dynamics. They are based on a continuous approximation of population dynamics. Four dynamical elements are required in this formulation: ascendant matrix, transverse matrix, fitness function, and the stochastic drive. The first law states that in the absence of stochastic drive the artificial life always seeks for a local fitness attractor and stay there. It gives the reference point to discuss the general evolutionary dynamics. The second law is explicitly expressed in a unique form of stochastic differential equation with all four dynamical elements. The third law defines the relationship between the focused level of description to its lower and higher ones, and also defines the dichotomy of deterministic and stochastic drives. These laws provide a coherence framework to discuss several current problems, such as emergency and stability. In particular, two quantities are emphasized: the fitness function as the standard for selection and the stochasticity as the source of creativity. Those three laws may appear almost self-evident from a statistical physics point of view. However, their equivalent to a most conventional approach for evolutionary dynamics is shown for the first time by the present author, to the best of his knowledge. The computational advantage of the present formulation in the study of artificial life evolution is also discussed.

nlin.AO↗