Classical Chemical Kinetics Research Articles

Application of Network Dimension Theory to the Kinetics of Nanogel Formation in Miniemulsion Vinyl/Divinyl Copolymerization: Free‐Radical and Living Polymerization

AbstractIn vinyl/divinyl copolymerization, a crosslink is formed by the reaction between an active center and a pendant double bond. When both the active center and the pendant double bond are located within the same polymer molecule, the cyclization occurs, which is ineffective for growth in molecular weight. In the present model, the network dimension theory is applied to estimate the mean‐square radius of gyration for the growing polymer molecule, which is used to account for the enrichment effect of pendant double bonds around the active center for the cyclization reaction. The model is applied to the miniemulsion copolymerization, and both conventional free‐radical polymerization and ideal living polymerization are considered. Some of important characteristics of network architecture formed in these two types of polymerization mechanisms that cannot be predicted based on the classical chemical kinetics can be reproduced by the model, such unique characteristics as the pendant double bonds are consumed from the beginning of polymerization in the conventional free‐radical polymerization but not so in the living polymerization. The present model provides useful insights into the size and structural dependent network formation kinetics without relying on the lattice model.

Enhancement of Prebiotic Peptide Formation in Cyclic Environments.

The dynamic behaviors of prebiotic reaction networks may be critically important to understanding how larger biopolymers could emerge, despite being unfavorable to form in water. We focus on understanding the dynamics of simple systems, prior to the emergence of replication mechanisms, and what role they may have played in biopolymer formation. We specifically consider the dynamics in cyclic environments using both model and experimental data.Cyclic environmental conditions prevent a system from reaching thermodynamic equilibrium, improving the chance of observing interesting kinetic behaviors. We used an approximate kinetic model to simulate the dynamics of trimetaphosphate (TP)-activated peptide formation from glycine in cyclic wet-dry conditions. The model predicts that environmental cycling allows trimer and tetramer peptides to sustain concentrations above the predicted fixed points of the model due to overshoot, a dynamic phenomenon. Our experiments demonstrate that oscillatory environments can shift product distributions in favor of longer peptides. However, experimental validation of certain behaviors in the kinetic model is challenging, considering that open systems with cyclic environmental conditions break many of the common assumptions in classical chemical kinetics. Overall, our results suggest that the dynamics of simple peptide reaction networks in cyclic environments may have been important for the formation of longer polymers on the early Earth. Similar phenomena may have also contributed to the emergence of reaction networks with product distributions determined not by thermodynamics, but rather by kinetics.

Dimensions of Large‐Sized Network Polymers Formed in Miniemulsion Polymerization

AbstractThe mean‐square radius of gyration of network polymers can be correlated with the graph diameter, and the fraction d of segments located in the diameter chain is used to investigate the dimensions of large‐sized network polymers whose cycle rank is over 103. A simplified Monte Carlo simulation model for the miniemulsion vinyl/divinyl copolymerization is used for the generation of large‐sized network polymers, assuming the classical chemical kinetics are valid. Both conventional free‐radical polymerization and living polymerization are considered, and the heterogeneity of network architecture is controlled by changing the reactivity ratio of double bond in divinyl monomer with respect to that in vinyl monomer. The network maturity index (NMI) which is the cycle rank per primary chain is used to represent the degree of development of the network architecture. As the NMI increases to be well‐developed, the calibrated d, defined by dc = d/fd where fd is a calibration constant that shows the degree of network heterogeneity, starts to follow the master curve. This characteristic behavior applies regardless of the polymerization mechanism and the heterogeneity of the formed network architecture. Detailed characteristics of the master curve and prospects for application to gel molecules are also discussed.

Heisenberg Spin Exchange Between Nitroxide Probes Diffusing in a Percolation Network

AbstractHeisenberg spin exchange between nitroxide (Tempone) spin probes has been measured as a function of concentration in the aqueous phase of the hydrated ion exchange membrane Nafion 117. The observed fast-motional electron paramagnetic resonance spectra were analyzed in terms of the stochastic Liouville equation lineshape calculation of Freed and coworkers and the “new paradigm” for interpreting spin exchange effects proposed by Salikhov. Differences between the effective spin exchange measured from the spectrum by these methods are presented and compared, and indicate that dipolar interactions make a significant contribution to spin exchange in this system. In acidic Nafion membranes, the spin probes are deactivated over time, allowing simultaneous measurement of the decay kinetics and spin exchange as a function of paramagnetic probe concentration. Both these processes deviate from the behavior that would be expected from classical chemical kinetics in isotropic media. The results are discussed in terms of currently available models for diffusion and reaction in a percolation network.

The entropy production rate a bridge between thermodynamics and chemical kinetics

It is shown how through the entropy production rate a natural unification between the formalism of classical thermodynamics and chemical kinetics is achieved. It is also shown how the entropy production rate represents an alternative way to the sensitivity analysis method in order to determine the fundamental steps in a reaction mechanism.

Gel Point Properties in Batch Free‐Radical Vinyl/Divinyl Copolymerization

AbstractGelation is a critical phenomenon, and various simple relationships are expected to hold. On the other hand, it is important to clarify the required conditions for the validity of the relationships. In this theoretical study, the effects of the primary chain connection statistics and the primary chain length distribution change during batch free‐radical vinyl/divinyl copolymerization on the gel point properties are investigated systematically. The weight fraction distribution at the gel point always conforms to the power‐law distribution,W(P)∝P−αwith α = 1.5, as long as the classical chemical kinetics is valid in a closed reaction system. When the primary chain connection statistics is independent of chain length, the cross‐linking density, ρg, of the gel molecule right at the gel point is given by , where is the weight‐average chain length of all primary chains. The random cross‐linking is a special case that belongs to this category. The distribution of the pendant double bonds among polymer molecules having different molecular weights is nonrandom, except for the special cases with equal reactivity of all types of double bonds for which the random cross‐linking applies.

A Crowding Barrier to Protein Inhibition in Colloidal Aggregates.

Small molecule colloidal aggregates adsorb and partially denature proteins, inhibiting them artifactually. Oddly, this inhibition is typically time-dependent. Two mechanisms might explain this: low concentrations of the colloid and enzyme might mean low encounter rates, or colloid-based protein denaturation might impose a kinetic barrier. These two mechanisms should have different concentration dependencies. Perplexingly, when enzyme concentration was increased, incubation times actually lengthened, inconsistent with both models and with classical chemical kinetics of solution species. We therefore considered molecular crowding, where colloids with lower protein surface density demand a shorter incubation time than more crowded colloids. To test this, we grew and shrank colloid surface area. As the surface area shrank, the incubation time lengthened, while as it increased, the converse was true. These observations support a crowding effect on protein binding to colloidal aggregates. Implications for drug delivery and for detecting aggregation-based inhibition will be discussed.

Hamiltonian classical thermodynamics and chemical kinetics

Classical thermodynamics have recently been formulated as Hamiltonian systems elevating the theory of heat to the same level of description as analytical mechanics. Particularly, mechanical and thermodynamical systems can merge in a single dynamical theory to describe equilibrium and non-equilibrium processes by constructing homogeneous of first degree in momenta Hamiltonian functions on the extended thermodynamic phase space and in a variety of representations. By employing geometric Hamiltonian theory we show that classical chemical kinetics can also be put in a Hamiltonian framework with Massieu–Gibbs function as the generating Hamiltonian at constant temperature and pressure. A metric in the physical state manifold as well as the entropy production in irreversible chemical reactions are defined. This way we establish a common computational platform for chemical kinetics and chemical dynamics. Numerical results are presented from the study of consecutive first-order elementary reactions and the non-linear kinetic equations of a model for autocatalytic symmetry breaking chiral reactions. For the latter example, we have examined two cases; that of a closed system with fixed initial concentrations and the steady-state case.

Chemical Dynamics in Living Cells

We introduce a new type of kinetic model and theory for biological networks, useful for a quantitative description of chemical dynamics in living cells. One advantage of our approach is its applicability to networks producing biomolecules with arbitrary lifetime distributions to which the conventional approaches, such as the classical chemical kinetics, chemical master equation, and chemical Langevin equation, are not applicable. Our approach also enables quantitative investigation into biological networks composed of multi-step or multi-channel reactions whose rates may fluctuate due to their coupling to cell environments. We demonstrate these advantages by providing an unprecedented quantitative explanation of non-classical chemical dynamics observed in various biological systems including single enzymes, in vivo motor-protein multiplexes, and cell systems with various synthetic gene networks. Time-permitting, we will also introduce a new transport equation governing thermal motion of biomolecules in living cells.

From the Kissinger equation to model-free kinetics: reaction kinetics of thermally initiated solid-state reactions

Recently the term, “model-free kinetics” has increasingly been used in thermoanalytical studies. It is noteworthy that even without knowledge of the concrete reaction mechanism of a material transformation, “model-free kinetics” can be used to determine relevant kinetic parameters such as activation energy ΔEa, preexponential factor A, and reaction rate constant k. An obvious thought that comes to mind is to combine techniques of the thermal analysis with the classical chemical reaction kinetics. Concerning the investigation of classical reaction kinetics, a series of isothermal experiments is necessary to take the time-to-yield ratio of any chemical reaction into account. Based on an introduced mechanism of the chemical reaction, the reaction rate constant k is determined for a series of temperatures T, i.e. k becomes a function of temperature; k = k(T). Generally, the examined substances are solids (e.g. polymers, plastics) and their thermal conversions are heterogeneous reactions at an interface. Would it, therefore, not be simpler to use non-isothermal procedures of thermal analysis for the kinetic analysis of solid state reactions?

Emergent Lévy behavior in single-cell stochastic gene expression.

Single-cell gene expression is inherently stochastic; its emergent behavior can be defined in terms of the chemical master equation describing the evolution of the mRNA and protein copy numbers as the latter tends to infinity. We establish two types of "macroscopic limits": the Kurtz limit is consistent with the classical chemical kinetics, while the Lévy limit provides a theoretical foundation for an empirical equation proposed in N. Friedman etal., Phys. Rev. Lett. 97, 168302 (2006)PRLTAO0031-900710.1103/PhysRevLett.97.168302. Furthermore, we clarify the biochemical implications and ranges of applicability for various macroscopic limits and calculate a comprehensive analytic expression for the protein concentration distribution in autoregulatory gene networks. The relationship between our work and modern population genetics is discussed.

Kaplan-Meier Meets Chemical Kinetics: Intrinsic Rate of SOD1 Amyloidogenesis Decreased by Subset of ALS Mutations and Cannot Fully Explain Age of Disease Onset.

Over 150 mutations in SOD1 (superoxide dismutase-1) cause amyotrophic lateral sclerosis (ALS), presumably by accelerating SOD1 amyloidogenesis. Like many nucleation processes, SOD1 fibrillization is stochastic (in vitro), which inhibits the determination of aggregation rates (and obscures whether rates correlate with patient phenotypes). Here, we diverged from classical chemical kinetics and used Kaplan-Meier estimators to quantify the probability of apo-SOD1 fibrillization (in vitro) from ∼103 replicate amyloid assays of wild-type (WT) SOD1 and nine ALS variants. The probability of apo-SOD1 fibrillization (expressed as a Hazard ratio) is increased by certain ALS-linked SOD1 mutations but is decreased or remains unchanged by other mutations. Despite this diversity, Hazard ratios of fibrillization correlated linearly with (and for three mutants, approximately equaled) Hazard ratios of patient survival (R2 = 0.67; Pearson's r = 0.82). No correlation exists between Hazard ratios of fibrillization and age of initial onset of ALS (R2 = 0.09). Thus, Hazard ratios of fibrillization might explain rates of disease progression but not onset. Classical kinetic metrics of fibrillization, i.e., mean lag time and propagation rate, did not correlate as strongly with phenotype (and ALS mutations did not uniformly accelerate mean rate of nucleation or propagation). A strong correlation was found, however, between mean ThT fluorescence at lag time and patient survival (R2 = 0.93); oligomers of SOD1 with weaker fluorescence correlated with shorter survival. This study suggests that SOD1 mutations trigger ALS by altering a property of SOD1 or its oligomers other than the intrinsic rate of amyloid nucleation (e.g., oligomer stability; rates of intercellular propagation; affinity for membrane surfaces; and maturation rate).

The H-theorem for the chemical kinetic equations with discrete time and for their generalizations

In this paper the generalizations of equations of chemical kinetics, including classical and quantum chemical kinetics, is considered. We make time discrete in these equations and prove the H-theorem.

Coherent chemical kinetics as quantum walks. I. Reaction operators for radical pairs.

Classical chemical kinetics uses rate-equation models to describe how a reaction proceeds in time. Such models are sufficient for describing state transitions in a reaction where coherences between different states do not arise, in other words, a reaction that contains only incoherent transitions. A prominent example of a reaction containing coherent transitions is the radical-pair model. The kinetics of such reactions is defined by the so-called reaction operator that determines the radical-pair state as a function of intermediate transition rates. We argue that the well-known concept of quantum walks from quantum information theory is a natural and apt framework for describing multisite chemical reactions. By composing Kraus maps that act only on two sites at a time, we show how the quantum-walk formalism can be applied to derive a reaction operator for the standard avian radical-pair reaction. Our reaction operator predicts the same recombination dephasing rate as the conventional Haberkorn model, which is consistent with recent experiments [K. Maeda et al., J. Chem. Phys. 139, 234309 (2013)], in contrast to previous work by Jones and Hore [J. A. Jones and P. J. Hore, Chem. Phys. Lett. 488, 90 (2010)]. The standard radical-pair reaction has conventionally been described by either a normalized density operator incorporating both the radical pair and reaction products or a trace-decreasing density operator that considers only the radical pair. We demonstrate a density operator that is both normalized and refers only to radical-pair states. Generalizations to include additional dephasing processes and an arbitrary number of sites are also discussed.

Kinetics of fast reactions in condensed systems: Some recent results (an autoreview)

In 1972, Alexander Merzhanov formulated theoretical backgrounds for a new line of research in chemical physics termed non-isothermal chemical kinetics (NIK) and outlined fundamental advantages of NIK methods in comparison with those of classical chemical kinetics. Since then, the NIK methods and approaches have been widely used in the basic and applied research in the field of chemistry and chemical engineering. We used the NIK methods to study the kinetics of fast reactions in condensed energetic materials (EM). Overviewed are the kinetic data on high-temperature decomposition of some homogeneous and heterogeneous EMs used in modern rocket and aviation engineering. Discussed are some recent data on the kinetics of fast high-temperature reactions taking place during electrothermal explosion under static conditions obtained with an ETA-100 instrument. New kinetic data on the reactions under static conditions and upon high- and low-speed impact are analyzed and compared.

Diffusion Controlled Reactions, Fluctuation Dominated Kinetics, and Living Cell Biochemistry

In recent years considerable portion of the computer science community has focused its attention on understanding living cell biochemistry and efforts to understand such complication reaction environment have spread over wide front, ranging from systems biology approaches, through network analysis (motif identification) towards developing language and simulators for low level biochemical processes. Apart from simulation work, much of the efforts are directed to using mean field equations (equivalent to the equations of classical chemical kinetics) to address various problems (stability, robustness, sensitivity analysis, etc.). Rarely is the use of mean field equations questioned. This review will provide a brief overview of the situations when mean field equations fail and should not be used. These equations can be derived from the theory of diffusion controlled reactions, and emerge when assumption of perfect mixing is used.

STEPS: reaction-diffsion simulation in complex 3D geometries

STEPS (STochastic Engine for Pathway Simulation) wasdeveloped as a tool for simulating reaction-diffusion sys-tems, such as the signaling pathways involved in synapticplasticity. We aim to provide the tools to allow investiga-tion of the effects of morphology and stochastic fluctua-tions in such systems, since it is widely believed suchfeatures may play an important role in biological function[1]. STEPS is written almost entirely in C++ for high per-formance, but maintains a user interface in Python toallow for greater interactivity and control. The softwareruns on various platforms, including Unix, Mac OS X andWindows. By writing relatively straightforward Pythonscripts the modeler can create the molecular species in thesystem, set up the reaction-diffusion kinetics, define thegeometry of the system, set the initial conditions, importa 3D tetrahedral mesh, run and control the simulationand visualize and/or save the simulation results.STEPS currently includes three solvers, allowing the userto choose the most efficient solution that can accuratelydescribe their model:-WmDirect: Stochastic solver, based on the GillespieDirect Method [2].Recommended for systems that can be assumed to bewell-mixed and where any species is in a sufficiently lowconcentration that the probabilistic nature of the systembecomes significant and a stochastic description is neces-sary [1,3]. The modeler can adapt their Python script torun the simulation a number of times to see the stochasticfluctuations in the system.-WmRK4: Deterministic solver, based on the fourth-orderRunge-Kutta method.Recommended for systems that can be assumed to bewell-mixed and where molecular populations are largeenough that system behavior can be approximated bysolving classical chemical kinetics equations. This is usu-ally the quickest solver as the simulation need only be runonce.-TetExact: Stochastic solver extended for simulating diffu-sion by implementing a 3D tetrahedral mesh.Allows for the investigation of the effects of morphologi-cal aspects such as concentration gradients and chemicalcompartmentalization. This solver requires constructionof a high-quality computational tetrahedral mesh that canadequately represent the relevant morphological features.STEPS currently supports meshes generated by TetGenhttp://tetgen.berlios.de, which is freely available forresearch use. In addition, we aim to implement mesh-gen-eration in STEPS in the future based on the algorithm in[4]. These meshes can then be used for simulation byextending Gillespie's Direct Method [2] to deal with spa-tial processes. Each voxel is treated as a well-mixed vol-ume in which reactions can occur and are coupled to theirneighboring voxels by diffusive fluxes and to neighboring

Chapter 5 Discrete Stochastic Simulation Methods for Chemically Reacting Systems

Discrete stochastic chemical kinetics describe the time evolution of a chemically reacting system by taking into account the fact that, in reality, chemical species are present with integer populations and exhibit some degree of randomness in their dynamical behavior. In recent years, with the development of new techniques to study biochemistry dynamics in a single cell, there are increasing studies using this approach to chemical kinetics in cellular systems, where the small copy number of some reactant species in the cell may lead to deviations from the predictions of the deterministic differential equations of classical chemical kinetics. This chapter reviews the fundamental theory related to stochastic chemical kinetics and several simulation methods based on that theory. We focus on nonstiff biochemical systems and the two most important discrete stochastic simulation methods: Gillespie's stochastic simulation algorithm (SSA) and the tau-leaping method. Different implementation strategies of these two methods are discussed. Then we recommend a relatively simple and efficient strategy that combines the strengths of the two methods: the hybrid SSA/tau-leaping method. The implementation details of the hybrid strategy are given here and a related software package is introduced. Finally, the hybrid method is applied to simple biochemical systems as a demonstration of its application.

The stochastic pump current and the non-adiabatic geometrical phase

We calculate a pump current in a classical two-state stochastic chemical kinetics bymeans of the non-adiabatic geometrical phase interpretation. The two-state systemis attached to two particle reservoirs, and under a periodic perturbation of thekinetic rates, it gives rise to a pump current between the two-state system and theabsorbing states. In order to calculate the pump current, the Floquet theoryfor the non-adiabatic geometrical phase is extended from a Hermitian case to anon-Hermitian case. The dependence of the pump current on the frequency of theperturbative kinetic rates is explicitly derived, and a stochastic resonance-like behavior isobtained.

Stochastic Simulation of Chemical Kinetics

Stochastic chemical kinetics describes the time evolution of a well-stirred chemically reacting system in a way that takes into account the fact that molecules come in whole numbers and exhibit some degree of randomness in their dynamical behavior. Researchers are increasingly using this approach to chemical kinetics in the analysis of cellular systems in biology, where the small molecular populations of only a few reactant species can lead to deviations from the predictions of the deterministic differential equations of classical chemical kinetics. After reviewing the supporting theory of stochastic chemical kinetics, I discuss some recent advances in methods for using that theory to make numerical simulations. These include improvements to the exact stochastic simulation algorithm (SSA) and the approximate explicit tau-leaping procedure, as well as the development of two approximate strategies for simulating systems that are dynamically stiff: implicit tau-leaping and the slow-scale SSA.