The effects of reversibility and noise on stochastic phosphorylation cycles and cascades

The phosphorylation-dephosphorylation cycle is a common motif in cellular signaling networks. Previous work has revealed that, when driven by a noisy input signal, these cycles may exhibit bistable behavior. Here, a recently introduced theorem on network bistability is applied to prove that the existence of bistability is dependent on the stochastic nature of the system. Furthermore, the thermodynamics of simple cycles and cascades is investigated in the stochastic setting. Because these cycles are driven by the ATP hydrolysis potential, they may operate far from equilibrium. It is shown that sufficient high ATP hydrolysis potential is necessary for the existence of a bistable steady state. For the single-cycle system, the ensemble average behavior follows the ultrasensitive response expected from analysis of the corresponding deterministic system, but with significant fluctuations. For the two-cycle cascade, the average behavior begins to deviate from the expected response of the deterministic system. Examination of a two-cycle cascade reveals that the bistable steady state may be either propagated or abolished along a cascade, depending on the parameters chosen. Likewise, the variance in the response can be maximized or minimized by tuning the number of enzymes in the second cycle.     

Metabolic control analysis of moiety-conserved cycles

Moiety-conserved cycles are metabolic structures that interconvert different forms of a chemical moiety (such as ATP-ADP-AMP, the different forms of adenylate), while the sum of these forms remains constant. Their metabolic behaviour is treated within the framework of control analysis [Kacser, H. & Burns, J.A. (1973) Symp. Soc. Exp. Biol 27, 65-104]. To explain the importance of the conserved sum of cycle metabolites as a parameter of the system, the cycle is first regarded as a 'black box'. The interactions of the cycle with the rest of the system are expressed in terms of 'cycle elasticities' and 'cycle control coefficients' by the usual connectivity properties. The conserved sum is seen to be an 'external' parameter in the sense that its effect is described by a combined response expression. All cycle coefficients can be written in terms of elasticities and concentrations of cycle metabolites. The treatment shows how connectivity expressions should be modified when moiety-conserved cycles are present and establishes new summation and connectivity properties. The analysis is applied to a two-member moiety-conserved cycle and its general application is discussed.     

Kinetics of bacterial adhesion--a stochastic analysis

In a previous work (Hsu & Wang, 1986), a birth-death type of stochastic model was proposed to analyze bacterial adhesion onto the substrate surface. The model is based upon the assumption that the number of available active sites on the substrate surface is relatively large compared to that of the cells in the system. This assumption is relaxed in the present study, and thus, the problem is considered in a more rigorous manner. The transient behavior of bacterial adhesion is examined through simulation studies. It is found that the present stochastic model should be employed when the number of available active sites is less than or on the same order of magnitude as that of the cells.     

Sensitivity analysis of discrete stochastic systems

Sensitivity analysis quantifies the dependence of system behavior on the parameters that affect the process dynamics. Classical sensitivity analysis, however, does not directly apply to discrete stochastic dynamical systems, which have recently gained popularity because of its relevance in the simulation of biological processes. In this work, sensitivity analysis for discrete stochastic processes is developed based on density function (distribution) sensitivity, using an analog of the classical sensitivity and the Fisher Information Matrix. There exist many circumstances, such as in systems with multistability, in which the stochastic effects become nontrivial and classical sensitivity analysis on the deterministic representation of a system cannot adequately capture the true system behavior. The proposed analysis is applied to a bistable chemical system--the Schl?gl model, and to a synthetic genetic toggle-switch model. Comparisons between the stochastic and deterministic analyses show the significance of explicit consideration of the probabilistic nature in the sensitivity analysis for this class of processes.     

Enzymes as molecular automata: a stochastic model of self-oscillatory glycolytic cycles in cellular metabolism

A stochastic model based on the molecular automata approach was developed to simulate the cyclic dynamics of glycolysis-gluconeogenesis in cell energy metabolism. The stochastic algorithm, based on Gillespie's method, simulates the master equation associated with any network of enzymatically controlled reactions. This model of the glycolytic-gluconeogenetic cycle was developed by assembling the stochastic kinetic reactions controlled by two enzymes: phosphofructokinase (PFKase) and fructose-1, 6-biphosphatase (FBPase). In order to obtain the hysteresis behaviour predicted by classical Sel'kov analysis, a minimum complexity is required in the allosteric regulations. This implies that the FBPase cannot have a single binding site for its transition to the inactive state (a minimum of two or three binding sites is necessary). Given the multimeric structure of this enzyme, this kinetic hypothesis is tenable. Other possible applications of the stochastic automata approach for different cases of channels, receptors and enzymatic control are suggested.