Iterative Approximate Solutions of Kinetic Equations for Reversible Enzyme Reactions

We study kinetic models of reversible enzyme reactions and compare two techniques for analytic approximate solutions of the model. Analytic approximate solutions of non-linear reaction equations for reversible enzyme reactions are calculated using the Homotopy Perturbation Method (HPM) and the Simple Iteration Method (SIM). The results of the approximations are similar. The Matlab programs are included in appendices.Comment: 28 pages, 22 figure

Dynamical fluctuations in biochemical reactions and cycles

We develop theory for the dynamics and fluctuations in some cyclic and linear biochemical reactions. We use the approach of maximum caliber, which computes the ensemble of paths taken by the system, given a few experimental observables. This approach may be useful for interpreting single-molecule or few-particle experiments on molecular motors, enzyme reactions, ion-channels, and phosphorylation-driven biological clocks. We consider cycles where all biochemical states are observable. Our method shows how: (1) the noise in cycles increases with cycle size and decreases with the driving force that spins the cycle and (2) provides a recipe for estimating small-number features, such as probability of backward spin in small cycles, from experimental data. The back-spin probability diminishes exponentially with the deviation from equilibrium. We believe this method may also be useful for other few-particle nonequilibrium biochemical reaction systems

Flow dilution effect on blood coagulation in vivo

Enzyme reaction model of flow dilution effect on blood coagulation in viv

An algebraic method to calculate parameter regions for constrained steady-state distribution in stochastic reaction networks

Steady state is an essential concept in reaction networks. Its stability reflects fundamental characteristics of several biological phenomena such as cellular signal transduction and gene expression. Because biochemical reactions occur at the cellular level, they are affected by unavoidable fluctuations. Although several methods have been proposed to detect and analyze the stability of steady states for deterministic models, these methods cannot be applied to stochastic reaction networks. In this paper, we propose an algorithm based on algebraic computations to calculate parameter regions for constrained steady-state distribution of stochastic reaction networks, in which the means and variances satisfy some given inequality constraints. To evaluate our proposed method, we perform computer simulations for three typical chemical reactions and demonstrate that the results obtained with our method are consistent with the simulation results.Comment: 17 pages, 4 figure

Bistability of an In Vitro Synthetic Autoregulatory Switch

The construction of synthetic biochemical circuits is an essential step for developing quantitative understanding of information processing in natural organisms. Here, we report construction and analysis of an in vitro circuit with positive autoregulation that consists of just four synthetic DNA strands and three enzymes, bacteriophage T7 RNA polymerase, Escherichia coli ribonuclease (RNase) H, and RNase R. The modularity of the DNA switch template allowed a rational design of a synthetic DNA switch regulated by its RNA output acting as a transcription activator. We verified that the thermodynamic and kinetic constraints dictated by the sequence design criteria were enough to experimentally achieve the intended dynamics: a transcription activator configured to regulate its own production. Although only RNase H is necessary to achieve bistability of switch states, RNase R is necessary to maintain stable RNA signal levels and to control incomplete degradation products. A simple mathematical model was used to fit ensemble parameters for the training set of experimental results and was then directly applied to predict time-courses of switch dynamics and sensitivity to parameter variations with reasonable agreement. The positive autoregulation switches can be used to provide constant input signals and store outputs of biochemical networks and are potentially useful for chemical control applications