A partial-propensity formulation of the stochastic simulation algorithm for chemical reaction networks with delays

Several real-world systems, such as gene expression networks in biological cells, contain coupled chemical reactions with a time delay between reaction initiation and completion. The non-Markovian kinetics of such reaction networks can be exactly simulated using the delay stochastic simulation algorithm (dSSA). The computational cost of dSSA scales with the total number of reactions in the network. We reduce this cost to scale at most with the smaller number of species by using the concept of partial reaction propensities. The resulting delay partial-propensity direct method (dPDM) is an exact dSSA formulation for well-stirred systems of coupled chemical reactions with delays. We detail dPDM and present a theoretical analysis of its computational cost. Furthermore, we demonstrate the implications of the theoretical cost analysis in two prototypical benchmark applications. The dPDM formulation is shown to be particularly efficient for strongly coupled reaction networks, where the number of reactions is much larger than the number of species.     

Improved delay-leaping simulation algorithm for biochemical reaction systems with delays

In biochemical reaction systems dominated by delays, the simulation speed of the stochastic simulation algorithm depends on the size of the wait queue. As a result, it is important to control the size of the wait queue to improve the efficiency of the simulation. An improved accelerated delay stochastic simulation algorithm for biochemical reaction systems with delays, termed the improved delay-leaping algorithm, is proposed in this paper. The update method for the wait queue is effective in reducing the size of the queue as well as shortening the storage and access time, thereby accelerating the simulation speed. Numerical simulation on two examples indicates that this method not only obtains a more significant efficiency compared with the existing methods, but also can be widely applied in biochemical reaction systems with delays.     

Efficient binomial leap method for simulating chemical kinetics

The binomial tau-leaping method of simulating the stochastic time evolution in a reaction system uses a binomial random number to approximate the number of reaction events. Theory implies that this method can avoid negative molecular numbers in stochastic simulations when a larger time step tau is used. Presented here is a modified binomial leap method for improving the accuracy and application range of the binomial leap method. The maximum existing population is first defined in this approach in order to determine a better bound of the number reactions. To derive a general leap procedure in chemically reacting systems, in this method a new sampling procedure based on the species is also designed for the maximum bound of consumed molecules of a reactant species in reaction channel. Numerical results indicate that the modified binomial leap method can be applied to a wider application range of chemically reacting systems with much better accuracy than the existing binomial leap method.     

A new kinetic approach to flowing chemical systems with linearly dependent reactions

A new kinetic approach to flowing chemical system is introduced, based on the elimination of reaction extents attached to linearly dependent reactions. The method is applied to analyze the propagation of acoustic waves in a reacting chemical mixture.

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A new approximate method for the stochastic simulation of chemical systems: the representative reaction approach

We have developed two new approximate methods for stochastically simulating chemical systems. The methods are based on the idea of representing all the reactions in the chemical system by a single reaction, i.e., by the “representative reaction approach” (RRA). Discussed in the article are the concepts underlying the new methods along with flowchart with all the steps required for their implementation. It is shown that the two RRA methods {with the reaction as the representative reaction (RR)} perform creditably with regard to accuracy and computational efficiency, in comparison to the exact stochastic simulation algorithm (SSA) developed by Gillespie and are able to successfully reproduce at least the first two moments of the probability distribution of each species in the systems studied. As such, the RRA methods represent a promising new approach for stochastically simulating chemical systems. © 2011 Wiley Periodicals, Inc. J Comput Chem, 2012     

Acuchem: A computer program for modeling complex chemical reaction systems

Acuchem is a program for solving the system of differential equations describing the temporal behavior of spatially homogeneous, isothermal, multicomponent chemical reaction systems. It is designed to provide modelers, data evaluators, and laboratory scientists with an easy to use program for modeling complex chemical reactions, and for presenting the results in tabular or graphical form. The program is described and some examples of its application given. Acuchem is designed to operate on the IBM Personal Computer family and other compatible microcomputers, and is available in a compiled version on a floppy disk.     

A reduction method for multiple time scale stochastic reaction networks

In this paper we develop a reduction method for multiple time scale stochastic reaction networks. When the transition-rate matrix between different states of the species is available, we obtain systems of reduced equations, whose solutions can successively approximate, to any degree of accuracy, the exact probability that the reaction system be in any particular state. For the case when the transition-rate matrix is not available, one needs to rely on the chemical master equation. For this case, we obtain a corresponding reduced master equation with first-order accuracy. We illustrate the accuracy and efficiency of both approaches by simulating several motivating examples and comparing the results of our simulations with the results obtained by the exact method. Our examples include both linear and nonlinear reaction networks as well as a three time scale stochastic reaction-diffusion model arising from gene expression.     

A reduction method for multiple time scale stochastic reaction networks with non-unique equilibrium probability

We develop a reduction method for general closed multiple time scale stochastic reaction networks for which the fast subsystem may have non-unique equilibrium probability. We obtain a reduced ODE system with nonhomogeneous terms whose solutions can approximate the solutions of the full system accurately. We then apply this reduction method to general linear network and nonlinear networks for which the state diagram can be constructed. We illustrate the accuracy of the reduction method by comparing computational results of the full systems with the reduced ODE systems for several examples. Finally, we show how the reduction method may be extended to three or more time scale reaction networks.     

A transmission dielectric time domain spectroscopy method for aqueous systems

A transmission method in dielectric time domain spectroscopy, suitable for aqueous systems, is described. It is demonstrated that the method can be applied to aqueous electrolytes. The dielectric spectra of solutions of the non-electrolyte glucose and the electrolytes CuSO₄ and sodium carboxymethyl cellulose are given as illustrative applications.     

On the redistribution of electrons for chemical reaction systems

A regional density-functional theory is formulated and applied to the study of ground-state electron redistributions during the course of a chemical reaction. If for a given increment of the reaction process, accumulation of electrons occurs in a certain region of space, then it is called the dynamic acceptor region, denoted by P. The complement is called the dynamic donor region, denoted by Q. The regional energy itself is determined as a unique functional of the electron density of the total system. The regional transfer potentials are defined in such a way that they add to give the total chemical potential, and their values along the reaction coordinate are found to be different between P and Q. The difference between the regional transfer potentials is shown to provide the driving force for electron transfer from Q to P. A characteristic coordinate for following electron transfer and an associated excitation potential are introduced. The excitation potential is a measure of regional virtual excitation due to regional interactions. The regional transfer potential gives the local character of electron transferability, while the excitation potential gives the global character. The theory encompasses the concepts of regional hardness and softness and sheds light on the HSAB principle.     

Green's-function reaction dynamics: a particle-based approach for simulating biochemical networks in time and space

We have developed a new numerical technique, called Green's-function reaction dynamics (GFRD), that makes it possible to simulate biochemical networks at the particle level and in both time and space. In this scheme, a maximum time step is chosen such that only single particles or pairs of particles have to be considered. For these particles, the Smoluchowski equation can be solved analytically using Green's functions. The main idea of GFRD is to exploit the exact solution of the Smoluchoswki equation to set up an event-driven algorithm, which combines in one step the propagation of the particles in space with the reactions between them. The event-driven nature allows GFRD to make large jumps in time and space when the particles are far apart from each other. Here, we apply the technique to a simple model of gene expression. The simulations reveal that spatial fluctuations can be a major source of noise in biochemical networks. The calculations also show that GFRD is highly efficient. Under biologically relevant conditions, GFRD is up to five orders of magnitude faster than conventional particle-based techniques for simulating biochemical networks in time and space. GFRD is not limited to biochemical networks. It can also be applied to a large number of other reaction-diffusion problems.     

Accurate time dependent wave packet calculations for the N + OH reaction

We present accurate quantum calculations of state-to-state cross sections for the N + OH → NO + H reaction performed on the ground (3)A' global adiabatic potential energy surface of Guadagnini et al. [J. Chem. Phys. 102, 774 (1995)]. The OH reagent is initially considered in the rovibrational state ν = 0, j = 0 and wave packet calculations have been performed for selected total angular momentum, J = 0, 10, 20, 30, 40,...,120. Converged integral state-to-state cross sections are obtained up to a collision energy of 0.5 eV, considering a maximum number of eight helicity components, Ω = 0,...,7. Reaction probabilities for J = 0 obtained as a function of collision energy, using the wave packet method, are compared with the recently published time-independent quantum mechanical one. Total reaction cross sections, state-specific rate constants, opacity functions, and product state-resolved integral cross-sections have been obtained by means of the wave packet method for several collision energies and compared with recent quasi-classical trajectory results obtained with the same potential energy surface. The rate constant for OH(ν = 0, j = 0) is in good agreement with the previous theoretical values, but in disagreement with the experimental data, except at 300 K.     

A new method analyzing large and strongly interacting reaction systems

A new method is presented to analyze the various interactions in reaction systems. The method is especially suited for large and strongly interacting systems where other analyzing methods are not practical. The method could isolate the particular interaction from the whole interaction by a procedure termed the partial diagonalization of the bond order matrix. The usefulness of the method is exemplified by the adsorption of CO on Pt and W surfaces. The interactions on the W surface are much stronger than those on the Pt surface, which is consistent with the experimental data. The role of individual interactions for the weakening of the C-O bond and the formation of the Pt-C and W-C bonds is discussed separately.     

Accelerated stochastic simulation algorithm for coupled chemical reactions with delays

Some biochemical processes do not occur instantaneously but have considerably delays associated with them. In the existed methods which solve these chemically reacting systems with delays, averaging over a great deal of simulations is needed for reliable statistical characters. Here we present an accelerating approach, called the "Delay Final All Possible Steps" (DFAPS) approach, which does not alter the course of stochastic simulation, but reduces the required running times. Numerical simulation results indicate that the proposed method can be applied to a wide range of chemically reacting systems with delays and obtain a significant improvement on efficiency and accuracy over the existed methods.     

A generalized separation reaction scheme for assessment of the radioanalytical method of concentration dependent distribution

For the assessment of the analytical error of concentration dependent distribution (CDD), complex-forming separation reaction was proposed in a generalized form of equilibrium , where n is the effective stoichiometric coefficient, i.e. the difference of mean ligand numbers and <n> of a mixture of complexes of analyte M with reagent L in the respective groups (distinguished by bars above the symbols) of the separation system. Calibration curve is derived from measurement of gross activity of complexes, A=A(ML_<n>) and . Theoretical relative error is expressed as a product of three terms, x/x=f₁f₂f₃. The first term f₁ depends on the degree of isotopic dilution, and the recommended ratio of amounts of nonradioactive (x) and radioactive (y) substance M is x/y(1;4). The second term f₂ depends first of all on the slope of distribution ratio (yield of separation ) vs. the analyte; reagent ratio, n(Z+1)/T. The form of slope is analyzed on the basis of the generalized separation reaction. Optimal conditions were discussed from this point of view and the ideal case is at f₂=1. The third term f₃ depends on the activities A and , i.e. on the distribution ratio, sample volumes, and the manner of counting. The ideal ratio of sample activities is A= and the optimal interval (0.2;0.8) is suggested     

A modified Curtius reaction: an efficient and simple method for direct isolation of free amine

The Curtius rearrangement and related reactions are often used to convert carboxylic acids to the corresponding primary amines. However, this reaction often requires harsh conditions for hydrolysis of the isocyanate intermediates to amines, and can also be contaminated by the formation of corresponding ureas due to the reactive nature of the intermediates. We have discovered that by quenching the isocyanate intermediates with sodium trimethylsilanolate, the free amines can be isolated after aqueous workup. This mild and fast procedure provides free amines in one pot with good yields.     

Automatic method for identifying reaction coordinates in complex systems

To interpret simulations of a complex system to determine the physical mechanism of a dynamical process, it is necessary to identify the small number of coordinates that distinguish the stable states from the transition states. We develop an automatic method for identifying these degrees of freedom from a database of candidate physical variables. In the method neural networks are used to determine the functional dependence of the probability of committing to a stable state (committor) on a set of coordinates, and a genetic algorithm selects the combination of inputs that yields the best fit. The method enables us to obtain the first set of coordinates that is demonstrably sufficient to specify the transition state of the C(7eq)--> alpha(R) isomerization of the alanine dipeptide in the presence of explicit water molecules. It is revealed that the solute-solvent coupling can be described by a solvent-derived electrostatic torque around one of the main-chain bonds, and the collective, long-ranged nature of this interaction accounts for previous failures to characterize this reaction.     

Constant time interval method for analysis of reaction rate data

In the study of chemical kinetics, many integrated reaction rate equations have the form In [f(A) + a] = bt + c, where a, b, and c are constants and f(A) is some function of the concentration of a reactant (or product) which can be calculated from the data. The left-hand side of this equation cannot be graphed versus time if the constant a is unknown. However, it is shown that f(A2) varies linearly with f(A₁) if A₂ is the concentration of reactant measured at a constant time interval later than A₁. The constants a and b can be determined from the linear graph. A number of specific examples are considered.