Ruoshi Yuan

Endogenous molecular-cellular hierarchical modeling of prostate carcinogenesis uncovers robust structure

We explored endogenous molecular-cellular network hypothesis for prostate cancer by constructing relevant endogenous interaction network model and analyzing its dynamical properties. Molecular regulations involved in cell proliferation, apoptosis, differentiation and metabolism are included in a hierarchical mathematical modeling scheme. This dynamical network organizes into multiple robust functional states, including physiological and pathological ones. Some states have characteristics of cancer: elevated metabolic and immune activities, high concentration of growth factors and different proliferative, apoptotic and adhesive behaviors. The molecular profile of calculated cancer state agrees with existing experiments. The modeling results have additional predictions which may be validated by further experiment: 1) Prostate supports both stem cell like and liver style proliferation; 2) While prostate supports multiple cell types, including basal, luminal and endocrine cell type differentiated from its stem cell, luminal cell is most likely to be transformed malignantly into androgen independent type cancer; 3) Retinoic acid pathway and C/EBPα are possible therapeutic targets.

Summing over trajectories of stochastic dynamics with multiplicative noise

We demonstrate that previous path integral formulations for the general stochastic interpretation generate incomplete results exemplified by the geometric Brownian motion. We thus develop a novel path integral formulation for the overdamped Langevin equation with multiplicative noise. The present path integral leads to the corresponding Fokker-Planck equation, and naturally generates a normalized transition probability in examples. Our result solves the inconsistency of the previous path integral formulations for the general stochastic interpretation, and can have wide applications in chemical and physical stochastic processes.

From molecular interaction to acute promyelocytic leukemia: Calculating leukemogenesis and remission from endogenous molecular-cellular network

Acute promyelocytic leukemia (APL) remains the best example of a malignancy that can be cured clinically by differentiation therapy. We demonstrate that APL may emerge from a dynamical endogenous molecular-cellular network obtained from normal, non-cancerous molecular interactions such as signal transduction and translational regulation under physiological conditions. This unifying framework, which reproduces APL, normal progenitor, and differentiated granulocytic phenotypes as different robust states from the network dynamics, has the advantage to study transition between these states, i.e. critical drivers for leukemogenesis and targets for differentiation. The simulation results quantitatively reproduce microarray profiles of NB4 and HL60 cell lines in response to treatment and normal neutrophil differentiation, and lead to new findings such as biomarkers for APL and additional molecular targets for arsenic trioxide therapy. The modeling shows APL and normal states mutually suppress each other, both in “wiring” and in dynamical cooperation. Leukemogenesis and recovery under treatment may be a consequence of spontaneous or induced transitions between robust states, through “passes” or “dragging” by drug effects. Our approach rationalizes leukemic complexity and constructs a platform towards extending differentiation therapy by performing “dry” molecular biology experiments.

Exploring a noisy van der Pol type oscillator with a stochastic approach.

We find exact mappings for a class of limit cycle systems with noise onto quasi-symplectic dynamics, including a van der Pol type oscillator. A dual role potential function is obtained as a component of the quasi-symplectic dynamics. Based on a stochastic interpretation different from the traditional Ito’s and Stratonovich’s, we show the corresponding steady state distribution is the familiar Boltzmann-Gibbs type for arbitrary noise strength. The result provides a new angle for understanding processes without detailed balance and can be verified by experiments.

Dynamical behaviors determined by the Lyapunov function in competitive Lotka-Volterra systems.

Dynamical behaviors of the competitive Lotka-Volterra system even for 3 species are not fully understood. In this paper, we study this problem from the perspective of the Lyapunov function. We construct explicitly the Lyapunov function using three examples of the competitive Lotka-Volterra system for the whole state space: (1) the general 2-species case, (2) a 3-species model, and (3) the model of May-Leonard. The basins of attraction for these examples are demonstrated, including cases with bistability and cyclical behavior. The first two examples are the generalized gradient system, where the energy dissipation may not follow the gradient of the Lyapunov function. In addition, under a new type of stochastic interpretation, the Lyapunov function also leads to the Boltzmann-Gibbs distribution on the final steady state when multiplicative noise is added.

Potential Function in a Continuous Dissipative Chaotic System: Decomposition Scheme and Role of Strange Attractor

In this paper, we demonstrate, first in literature known to us, that potential functions can be constructed in continuous dissipative chaotic systems and can be used to reveal their dynamical properties. To attain this aim, a Lorenz-like system is proposed and rigorously proved chaotic for exemplified analysis. We explicitly construct a potential function monotonically decreasing along the systems dynamics, revealing the structure of the chaotic strange attractor. The potential function can have different forms of construction. We also decompose the dynamical system to explain for the different origins of chaotic attractor and strange attractor. Consequently, reasons for the existence of both chaotic nonstrange attractors and nonchaotic strange attractors are clearly discussed within current decomposition framework.

Endogenous network states predict gain or loss of functions for genetic mutations in hepatocellular carcinoma

Cancers have been typically characterized by genetic mutations. Patterns of such mutations have traditionally been analysed by posteriori statistical association approaches. One may ponder the possibility of a priori determination of any mutation regularity. Here by exploring biological processes implied in a mechanistic theory recently developed (the endogenous molecular–cellular network theory), we found that the features of genetic mutations in cancers may be predicted without any prior knowledge of mutation propensities. With hepatocellular carcinoma (HCC) as an example, we found that the normal hepatocyte and cancerous hepatocyte can be represented by robust stable states of one single endogenous network. These stable states, specified by distinct patterns of expressions or activities of proteins in the network, provide means to directly identify a set of most probable genetic mutations and their effects in HCC. As the key proteins and main interactions in the network are conserved through cell types in an organism, similar mutational features may also be found in other cancers. This analysis yielded straightforward and testable predictions on accumulated and preferred mutation spectra in normal tissue. The validation of predicted cancer state mutation patterns demonstrates the usefulness and potential of a causal dynamical framework to understand and predict genetic mutations in cancer.

Nonequilibrium work relation beyond the Boltzmann-Gibbs distribution

The presence of multiplicative noise can alter measurements of forces acting on nanoscopic objects. Taking into account of multiplicative noise, we derive a series of nonequilibrium thermodynamical equalities as generalization of the Jarzynski equality, the detailed fluctuation theorem and the Hatano-Sasa relation. Our result demonstrates that the Jarzynski equality and the detailed fluctuation theorem remains valid only for systems with the Boltzmann-Gibbs distribution at the equilibrium state, but the Hatano-Sasa relation is robust with respect to different stochastic interpretations of multiplicative noise.

Anomalous free energy changes induced by topology.

We report that nontrivial topology of a driven Brownian particle restricted on a ring leads to anomalous behaviors on free energy change. Starting from steady states with identical distribution and current on the ring, free energy changes are distinct and nonperiodic after the system is driven by the same periodic force protocol. We demonstrate our observation in examples through both exact solutions and numerical simulations. The free energy calculated here can be measured in recent experimental systems.

Exploring a minimal two-component p53 model

The tumor suppressor p53 coordinates many attributes of cellular processes via interlocked feedback loops. To understand the biological implications of feedback loops in a p53 system, a two-component model which encompasses essential feedback loops was constructed and further explored. Diverse bifurcation properties, such as bistability and oscillation, emerge by manipulating the feedback strength. The p53-mediated MDM2 induction dictates the bifurcation patterns. We first identified irradiation dichotomy in p53 models and further proposed that bistability and oscillation can behave in a coordinated manner. Further sensitivity analysis revealed that p53 basal production and MDM2-mediated p53 degradation, which are central to cellular control, are most sensitive processes. Also, we identified that the much more significant variations in amplitude of p53 pulses observed in experiments can be derived from overall amplitude parameter sensitivity. The combined approach with bifurcation analysis, stochastic simulation and sampling-based sensitivity analysis not only gives crucial insights into the dynamics of the p53 system, but also creates a fertile ground for understanding the regulatory patterns of other biological networks.