Endogenous Network Hypothesis For Cancer And Its Foundation On Nonlinear Stochastic Dynamics

Cancer is a prototypical complex disease whose pathology can neither be properly understood by an individual player — gene,protein as well as molecular pathway,nor the related factors be integrated by linear-additive reasoning,similar to that of a many-body problem in physics.The rapid accumulating large “omics” data in biological sciences provide more information on cancer but also require a new mechanistic underpinning to integrate for rationalizing cancer complexity and to identify collective and individual roles of these players.A unifying and quantitative hypothesis was formulated that cancer is a robust state,or a group of states,of the endogenous molecular-cellular network evolutionarily built for the regulation of the developmental processes and physiological functions.This state may have certain function during the evolution history but is not optimized for the whole organism.The crucial individual players for such a network were found,at least partially,which in turn suggest the existence of a hierarchical structure within biological systems.Such a structure enables a core network to be constructed from currently known experimental knowledge,and to be refined with new discoveries.By examining the nonlinear stochastic dynamics of the core network in the phase space,robust states corresponding to normal physiological and abnormal pathological phenotypes,including cancer,emerge naturally.The dynamical model of the cancer endogenous network is of intrinsic stochasticity,nonlinearity and high-dimensionality,has been a great challenge for traditional theoretical approaches.We thus developed a novel framework originated from Darwin's theory of evolution for handling stochastic processes by solving a series of theoretical and computational problems.To be specific,we proposed a new stochastic integration,A-type.Its relation with the traditional Ito's integration was explicitly obtained.A-type integration has a clear physical meaning and a unique advantage: the steady state distribution of the stochastic process is Boltzmann-Gibbs distribution,we have proved that the potential function(Hamiltonian)therein is a global Lyapunov function of the deterministic counterpart dynamics.The property holds for noise with arbitrary strength.That means the locally most probable states of the steady state distribution correspond to the stable fixed points of the deterministic dynamics.We have also explicitly constructed potential function in a series of typical dynamical systems including fixed points,limit cycles as well as chaotic systems.Therefore,our method establishes a correspondence between stochasticity and determinacy,the problem of solving partial differential equation(e.g.,Fokker-Planck equation)for the crucial positional information(e.g.,stable states and transition states)on the steady state distribution may be largely reduced to solving fixed points of ordinary differential equation(an algebraic equation).In contrast to the expensive stochastic simulation,our method has much less computational cost,which enables the analysis and study of stochastic dynamical model with hundreds of dimensions,and may have wide applications in biology,physics,chemistry,control theory,and economics.Traditional stochastic integrations such as Ito's and Stratonovich's,however,do not possess this advantage,calculation and numerical experiments have verified the point.The nonlinear dynamical model of the network leads to a more encompassing framework synthesizing multiple factors than the currently prevailing linear-additive thinking of the causality in cancer research.We have constructed endogenous network models for prostate cancer and acute promyelocytic leukemia and developed a series of computational tools.The quantitative models so constructed by molecular interactions collected from individual molecular biology and biochemistry experiments recapitulate known clinical observations and predict new phenomena.Endogenous network theory is applicable to other complex diseases,such as the proposed core regulatory network model for osteoporosis caused by the abnormality of osteoblast in this thesis.The framework may serve as a platform of “dry experiments” for seeking new therapies on complex diseases,especially in the challenge of searching drug combinations: our method integrates existing biological knowledge,to find plausible combinations of drug targets by computation,pointing out direction for “wet experiments”.