Stochastic approaches for modelling in vivo reactions

In recent years, stochastic modelling has emerged as a physically more realistic alternative for modelling in vivo reactions. There are numerous stochastic approaches available in the literature; most of these assume that observed random fluctuations are a consequence of the small number of reacting molecules. We review some important developments of the stochastic approach and consider its suitability for modelling intracellular reactions. We then describe recent efforts to include the fluctuation effects caused by the structural organisation of the cytoplasm and the limited diffusion of molecules due to macromolecular crowding.     

Selective chemical treatment of cellular microdomains using multiple laminar streams

There are many experiments in which it would be useful to treat a part of the surface or interior of a cell with a biochemical reagent. It is difficult, however, to achieve subcellular specificity, because small molecules diffuse distances equal to the extent of the cell in seconds. This paper demonstrates experimentally, and analyzes theoretically, the use of multiple laminar fluid streams in microfluidic channels to deliver reagents to, and remove them from, cells with subcellular spatial selectivity. The technique made it possible to label different subpopulations of mitochondria fluorescently, to disrupt selected regions of the cytoskeleton chemically, to dislodge limited areas of cell-substrate adhesions enzymatically, and to observe microcompartmental endocytosis within individual cells. This technique does not require microinjection or immobilization of reagents onto nondiffusive objects; it opens a new window into cell biology.     

Peripheral chemical reactions

Forward scattering of the products of direct exoergic atom transfer reactions is proposed as an indication for a peripheral attraction: a reaction in which an atom at the periphery of the reactants is abstracted. Model computations for the O(¹D) + N₂O reaction are used to illustrate the proposed mechanism. The opacity function has a peak at higher impact parameters which is correlated with the forward scattering. Potential energy surfaces which do not manifest peripheral attraction lead to backwards scattering of the products.     

Valency changes in chemical reactions

An analysis of valence changes in selected organic gas phase reactions, calculated on SINDO1 potential surfaces, is performed. It is shown that transition states and intermediates have diradical character if singlet and triplets states are nearly degenerate. As a consequence, normal valencies are expected in Woodward-Hoffman allowed reactions and reduced valencies in forbidden reactions. The formalism is also applied to cationic reactions, but the effects of valency changes are less pronounced.     

Independence of chemical reactions

Up to this time the existence of physically true dependences between elementary reactions has been a returning question. The goal of this paper is to show that the real elementary reactions of a mechanism are practically independent. Introducing the concept of the space-time volume of a reaction (the reciprocal of the reaction rate) it is shown that, except for extremely fast processes (explosions), the reactions form very dilute systems. This systems must be ideal in the sense that interactions between elementary processes are very rare. The system exhibits some analogies with a dilute gas or solution. The extents of interactions can be calculated and the limits of independence estimated in this way.

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Calculating chemical electron-polarization in triplet-molecule reactions

It is assumed that orientation fluctuations for molecules in a liquid form an uncorrelated Markov process, and an expression is derived in quadratures for the initial chemical polarization of the electrons formed by the triplet mechanism. The expression applies for any magnetic field strength and solvent viscosity. If the molecular rotations are slow and the magnetic field is weak, one can perform numerical calculations on the electron chemical polarization.Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 22, No. 2, pp. 203–206, March–April, 1986.     

Power law behavior in chemical reactions

Reactions between metals and chloride solutions have been shown to exhibit magnetic field fluctuations over a wide range of size and time scales. Power law behavior observed in these reactions is consistent with models said to exhibit self-organized criticality. Voltage fluctuations observed during the dissolution of magnesium and aluminum in copper chloride solution are qualitatively similar to the recorded magnetic signals. In this paper, distributions of voltage and magnetic peak sizes, noise spectra, and return times are compared for both reactions studied.     

Infrared laser induced chemical reactions

It is shown that a high power infrared laser can enhance a chemical reaction (by lowering the activation energy) even if the reactants are infrared inactive.     

Dynamics of nonadiabatic chemical reactions

New methods are proposed to treat nonadiabatic chemical dynamics in realistic large molecular systems by using the Zhu-Nakamura (ZN) theory of curve-crossing problems. They include the incorporation of the ZN formulas into the Herman-Kluk type semiclassical wave packet propagation method and the trajectory surface hopping (TSH) method, formulation of the nonadiabatic transition state theory, and its application to the electron transfer problem. Because the nonadiabatic coupling is a vector in multidimensional space, the one-dimensional ZN theory works all right. Even the classically forbidden transitions can be correctly treated by the ZN formulas. In the case of electron transfer, a new formula that can improve the celebrated Marcus theory in the case of normal regime is obtained so that it can work nicely in the intermediate and strong electronic coupling regimes. All these formulations mentioned above are demonstrated to work well in comparison with the exact quantum mechanical numerical solutions and are expected to be applicable to large systems that cannot be treated quantum mechanically numerically exactly. To take into account another quantum mechanical effect, namely, the tunneling effect, an efficient method to detect caustics from which tunneling trajectories emanate is proposed. All the works reported here are the results of recent activities carried out in the author's research group. Finally, the whole set of ZN formulas is presented in Appendix.     

Geometric description of chemical reactions

We use the formalism of Geometrothermodynamics to describe chemical reactions in the context of equilibrium thermodynamics. Any chemical reaction in a closed system is shown to be described by a geodesic in a 2-dimensional manifold that can be interpreted as the equilibrium space of the reaction. We first show this in the particular cases of a reaction with only two species corresponding to either two ideal gases or two van der Waals gases. We then consider the case of a reaction with an arbitrary number of species. The initial equilibrium state of the geodesic is determined by the initial conditions of the reaction. The final equilibrium state, which follows from a thermodynamic analysis of the reaction, is shown to correspond to a coordinate singularity of the thermodynamic metric which describes the equilibrium manifold.     

Laser control of chemical reactions

Chemical reactions are at the heart of chemistry and the dream of controlling the outcome of these reactions is an old one. Thus, with given reactants, a solvent and perhaps assisted by a catalyst, we would like to 'steer' the reactants into a particular desired product. This review focuses on how to control the dynamics of chemical reactions, beyond traditional temperature control, with the emphasis on unimolecular reactions. The electromagnetic radiation of lasers can induce so-called coherent dynamics. The recent theoretical and experimental results on this coherent control are explained and illustrated with computational and experimental examples.     

Oscillations in Lotka-Volterra systems of chemical reactions

For a chemical reaction system modeled byx =k ₁ Ax –k ₂ x ² –k ₃ xy +k ₄ y ²,y =k ₃ xy –k ₄ y ² –k ₅ y +k ₆ B, it is shown that for each positive choice of parametersk _i A, B there exists a unique stationary state which is globally asymptotically stable in the positive quadrant. A criterion for the non-existence of periodic solutions is given for the generalized Lotka-Volterra system:x = f(x)h(x, y),y.     

Bifurcations of dividing surfaces in chemical reactions

We study the dynamical behavior of the unstable periodic orbit (NHIM) associated to the non-return transition state (TS) of the H(2) + H collinear exchange reaction and their effects on the reaction probability. By means of the normal form of the Hamiltonian in the vicinity of the phase space saddle point, we obtain explicit expressions of the dynamical structures that rule the reaction. Taking advantage of the straightforward identification of the TS in normal form coordinates, we calculate the reaction probability as a function of the system energy in a more efficient way than the standard Monte Carlo method. The reaction probability values computed by both methods are not in agreement for high energies. We study by numerical continuation the bifurcations experienced by the NHIM as the energy increases. We find that the occurrence of new periodic orbits emanated from these bifurcations prevents the existence of a unique non-return TS, so that for high energies, the transition state theory cannot be longer applied to calculate the reaction probability.