The eikonal approximation (instanton technique) is applied to the problem of large fluctuations of the number of species in spatially homogeneous chemical reactions with the probability density distribution described by a master equation. For both autocatalytic and nonautocatalytic reactions, the analysis of the distribution about a stable stationary state and of the transitions between coexisting stable states comes, to logarithmic accuracy, to the analysis of Hamiltonian dynamics of an auxiliary dynamical system. The latter can be done explicitly in a few cases, including one-species systems, systems with detailed balance, and systems close to the bifurcation points where the number of the stable states changes. In the last case, the fluctuations display universal features, and, for saddle-node bifurcation points, the logarithm of the probability of escape from the metastable state (per unit time) is proportional to the distance to the bifurcation point (in the parameter space) raised to the power 3/2. We compare the eikonal approximation for the stationary distribution of a master equation to Monte Carlo numerical solutions for two chemical two-variable systems with multiple stationary states, where none of the cited restrictions exists. For one of the systems in the pattern of optimal paths we observe caustics emanating from the saddle point.

book reviews plane stress, impact, loading of plastic structures. Due to the nature of the subject the second part is written at a level considerably more advanced than the first part. It is based on recent research work and should be of great interest to research engineers.The extensive bibliography and abundant problems add to the value of this book.

Fluctuations in rates of gene expression can produce highly erratic time patterns of protein production in individual cells and wide diversity in instantaneous protein concentrations across cell populations. When two independently produced regulatory proteins acting at low cellular concentrations competitively control a switch point in a pathway, stochastic variations in their concentrations can produce probabilistic pathway selection, so that an initially homogeneous cell population partitions into distinct phenotypic subpopulations. Many pathogenic organisms, for example, use this mechanism to randomly switch surface features to evade host responses. This coupling between molecular-level fluctuations and macroscopic phenotype selection is analyzed using the phage λ lysis-lysogeny decision circuit as a model system. The fraction of infected cells selecting the lysogenic pathway at different phage:cell ratios, predicted using a molecular-level stochastic kinetic model of the genetic regulatory circuit, is consistent with experimental observations. The kinetic model of the decision circuit uses the stochastic formulation of chemical kinetics, stochastic mechanisms of gene expression, and a statistical-thermodynamic model of promoter regulation. Conventional deterministic kinetics cannot be used to predict statistics of regulatory systems that produce probabilistic outcomes. Rather, a stochastic kinetic analysis must be used to predict statistics of regulatory outcomes for such stochastically regulated systems.

The theory of Ostwald ripening is extended to include the dependence on the volume fraction of the minority phase. The size distribution function for droplets of the minority phase and the power laws of the time dependences are derived for the late stages of phase separation. The asymptotic distribution function is found to be independent of initial conditions but does depend on the equilibrium volume fraction associated with a given quench. We show that the average radius grows as t1/3 and the density of droplets decays as t−1. The growth law and the amplitudes for these temporal power laws derivate from their value in the limit of zero volume fraction as the square root of the volume fraction. The effect of competition among droplets causes the distribution to broaden and to increase the coarsening rate.

A method for the prediction of the interactions within complex reaction networks from experimentally measured time series of the concentration of the species composing the system has been tested experimentally on the first few steps of the glycolytic pathway. The reconstituted reaction system, containing eight enzymes and 14 metabolic intermediates, was kept away from equilibrium in a continuous-flow, stirred-tank reactor. Input concentrations of adenosine monophosphate and citrate were externally varied overtime, and their concentrations in the reactor and the response of eight other species were measured. Multidimensional scaling analysis and heuristic algorithms applied to two-species time-lagged correlation functions derived from the time series yielded a diagram from which the interactions among all of the species could be deduced. The diagram predicts essential features of the known reaction network in regard to chemical reactions and interactions among the measured species. The approach is applicable to

We propose a reversible reaction mechanism with a single stationary state in which certain concentrations assume either high or low values dependent on the concentration of a catalyst. The properties of this mechanism are those of a McCulloch-Pitts neuron. We suggest a mechanism of interneuronal connections in which the stationary state of a chemical neuron is determined by the state of other neurons in a homogeneous chemical system and is thus a "hardware" chemical implementation of neural networks. Specific connections are determined for the construction of logic gates: AND, NOR, etc. Neural networks may be constructed in which the flow oftime is continuous and computations are achieved by the attainment of a stationary state of the entire chemical reaction system, or in which the flow of time is discretized by an oscillatory reaction. In another article, we will give a chemical implementation of finite state machines and stack memories, with which in principle the construction of a universal Turing machine is possible.Computations may be supported by many different systems (1, 2), including physical systems like the digital computer, Fredkin logic gates (3), billiard-ball collisions (4), enzymes operating on a polymer chain (1, 5), and more abstract systems like cellular automata (6-8), partial differential equations that simulate cellular automata (9), generalized shifts (4), and neural networks (10-13). Some of these systems can be computationally universal and thus are formally equivalent with a universal Turing machine (10,14). We may inquire about whether computationally universal devices may be constructed solely from chemical reaction mechanisms in a homogeneous medium. All living entities process information to varying degrees, and this can occur only by chemical means. It is for this reason alone that the subject is ofinterest. In this article, we discuss the construction of chemical networks where coupled reaction mechanisms implement "programmed" computations as the concentrations evolve in time. It has already been noted that bistable chemical systems are in many ways analogous to a flip-flop circuit, by coupling bistable reactions it is possible to build universal automata (15,16), and that various chemical mechanisms share a formal relationship with electronic devices (17, 18). We address the construction of computational devices from the viewpoint of neural networks. We propose a chemical reaction network, which is a "hardware" implementation of a neural network, and hence the network can in principle be as powerful as a universal Turing machine (10).Neural networks are a versatile basis for computation (19). Any finite state machine, and hence the finite state part of a universal Turing machine, can be simulated by a neural network (10,20). Neural networks also form the basis of many collective computational systems such as feedforward networks or Hopfield's network (11-13). A chemical neural network may serve as the "hardware" for any of the approaches to computation. We present hardw...

In prior work we demonstrated the implementation of logic gates, sequential computers (universal Turing machines), and parallel computers by means of the kinetics of chemical reaction mechanisms. In the present article we develop this subject further by first investigating the computational properties of several enzymatic (single and multiple) reaction mechanisms: we show their steady states are analogous to either Boolean or fuzzy logic gates. Nearly perfect digital function is obtained only in the regime in which the enzymes are saturated with their substrates. With these enzymatic gates, we construct combinational chemical networks that execute a given truth-table. The dynamic range of a network's output is strongly affected by "input/output matching" conditions among the internal gate elements. We find a simple mechanism, similar to the interconversion of fructose-6-phosphate between its two bisphosphate forms (fructose-1,6-bisphosphate and fructose-2,6-bisphosphate), that functions analogously to an AND gate. When the simple model is supplanted with one in which the enzyme rate laws are derived from experimental data, the steady state of the mechanism functions as an asymmetric fuzzy aggregation operator with properties akin to a fuzzy AND gate. The qualitative behavior of the mechanism does not change when situated within a large model of glycolysis/gluconeogenesis and the TCA cycle. The mechanism, in this case, switches the pathway's mode from glycolysis to gluconeogenesis in response to chemical signals of low blood glucose (cAMP) and abundant fuel for the TCA cycle (acetyl coenzyme A).

A new derivation is presented for the last stage of phase separation in the kinetics of a first order phase transition, precipitation, where Ostwald ripening is the dominant mechanism. We use a time scaling technique and derive the power law time dependence and distribution function for the size of the particles of the new phase. Equations are derived for the correction terms to the distribution function and power laws. The derivation clarifies and corrects prior work.