Chemical master equation

Stochastic models of gene expression are typically formulated using the chemical master equation, which can be solved exactly or approximately using a repertoire of analytical methods. Here, we provide a tutorial review of an alternative approach based on queueing theory that has rarely been used in the literature of gene expression. We discuss the interpretation of six types of infinite server queues from the angle of stochastic single-cell biology and provide analytical expressions for the stationary and non-stationary distributions and/or moments of mRNA/protein numbers, and bounds on the Fano factor...

This paper analyzes the complete synchronization of a three-layer Rulkov neuron network model connected by electrical synapses in the same layers and chemical synapses between adjacent layers. The outer coupling matrix of the network is not Laplacian as in linear coupling networks. We develop the master stability function method, in which the invariant manifold of the master stability equations (MSEs) does not correspond to the zero eigenvalues of the connection matrix. After giving the existence conditions of the synchronization manifold about the nonlinear chemical coupling, we investigate the dynamics of the synchronization manifold, which will be identical to that of a synchronous network by fixing the same parameters and initial values...

Molecular cluster ions, which are stored in an electromagnetic trap under ultra-high vacuum conditions, undergo blackbody infrared radiative dissociation (BIRD). This process can be simulated with master equation modeling (MEM), predicting temperature-dependent dissociation rate constants, which are very sensitive to the dissociation energy. We have recently introduced a multiple-well approach for master equation modeling, where several low-lying isomers are taken into account. Here, we experimentally measure the BIRD of CO4●-(H2O)1,2 and model the results with a slightly modified multiple-well MEM...

Quantum simulation of dynamics in open quantum systems is crucial but poses a significant challenge due to the non-Hermitian nature leading to nonunitary evolution and the limited quantum resources on current quantum computers. Here we introduce a variational hybrid quantum-classical algorithm designed for simulating the time evolution governed by the Lindblad master equation. Our approach involves on a stochastic unveiling of the density matrix, transforming the Lindblad equation into a wave function-based quantum state diffusion (QSD) method with the aim of reducing qubit requirements...

Protein conformational changes play crucial roles in their biological functions. In recent years, the Markov State Model (MSM) constructed from extensive Molecular Dynamics (MD) simulations has emerged as a powerful tool for modeling complex protein conformational changes. In MSMs, dynamics are modeled as a sequence of Markovian transitions among metastable conformational states at discrete time intervals (called lag time). A major challenge for MSMs is that the lag time must be long enough to allow transitions among states to become memoryless (or Markovian)...

Self-assembly of functional branched filaments, such as actin filaments and microtubules, or dysfunctional ones, such as amyloid fibrils, plays important roles in many biological processes. Here, based on the master equation approach, we study the kinetics of the formation of the branched fibrils. In our model, a branched fibril has one mother branch and several daughter branches. A daughter branch grows from the side of a pre-existing mother branch or daughter branch. In our model, we consider five basic processes for the self-assembly of the branched filaments, namely, the nucleation, the dissociation of the primary nucleus of fibrils, the elongation, the fragmentation, and the branching...

Path integrals offer a robust approach for simulating open quantum dynamics with advancements transcending initial system size limitations. However, accurately modeling systems governed by mechanisms that do not conserve the number of quantum particles, such as lossy cavity modes, remains a challenge. We present a method to incorporate such empirical source and drain mechanisms within a path integral framework using quantum master equations. This technique facilitates rigorous inclusion of bath degrees of freedom while accommodating empirical time scales via Lindbladian dynamics...

Entropy scaling is applied to the shear viscosity, self-diffusion coefficient, and thermal conductivity of simple monatomic fluids. An extensive molecular dynamics simulation series is performed to obtain these transport properties and the residual entropy of three potential model classes with variable repulsive exponents: n, 6 Mie (n = 9, 12, 15, and 18), Buckingham's exponential-six (α = 12, 14, 18, and 30), and Tang-Toennies (αT = 4.051, 4.275, and 4.600). A wide range of liquid and supercritical gas- and liquid-like states is covered with a total of 1120 state points...

Criegee intermediates (CIs), the key intermediates in the ozonolysis of olefins in atmosphere, have received much attention due to their high activity. The reaction mechanism of the most simple Criegee intermediate CH2 OO with vinyl alcohol (VA) was investigated by using the HL//M06-2X/def2TZVP method. The temperature and pressure dependent rate constant and product branching ratio were calculated using the master equation method. For CH2 OO + syn -VA, 1,4-insertion is the main reaction channel while for the CH2 OO + anti -VA, cycloaddition and 1,2-insertion into the O-H bond are more favorable than the 1,4-insertion reaction...

Theory of multistep excitation energy migration within the set of chemically identical chromophores distributed on the surface of a spherical nanoparticle is presented. The Green function solution to the master equation is expanded as a diagrammatic series. Topological reduction of the series leads to the expression for emission anisotropy decay. The solution obtained behaves very well over the whole time range and it remains accurate even for a high number of the attached chromophores. Emission anisotropy decay depends strongly not only on the number of fluorophores linked to the spherical nanoparticle but also on the ratio of critical radius to spherical nanoparticle radius, which may be crucial for optimal design of antenna-like fluorescent nanostructures...

We theoretically investigate homogeneous crystal nucleation in a solution containing a solute and a volatile solvent. The solvent evaporates from the solution, thereby continuously increasing the concentration of the solute. We view it as an idealized model for the far-out-of-equilibrium conditions present during the liquid-state manufacturing of organic electronic devices. Our model is based on classical nucleation theory, taking the solvent to be a source of the transient conditions in which the solute drops out of the solution...

Many chemical reactions and molecular processes occur on time scales that are significantly longer than those accessible by direct simulations. One successful approach to estimating dynamical statistics for such processes is to use many short time series of observations of the system to construct a Markov state model, which approximates the dynamics of the system as memoryless transitions between a set of discrete states. The dynamical Galerkin approximation (DGA) is a closely related framework for estimating dynamical statistics, such as committors and mean first passage times, by approximating solutions to their equations with a projection onto a basis...

Activated chemistry in coupled reaction systems has broadened our understanding of the chemical kinetics. In the case of intermediates formed in gas phase abstraction reactions (e.g., OH + HC(O)C(O)H (glyoxal) →HC(O)CO + H2 O), it is particularly crucial to understand how the reaction energy is partitioned between product species as this determines the propensity for a given product to undergo "prompt" dissociation (e.g., HC(O)CO → HCO + CO) before the excess reaction energy is removed. An example of such an activated system is the OH + glyoxal + O2 coupled reaction system...

In this study, we obtain an exact time-dependent solution of the chemical master equation (CME) of an extension of the two-state telegraph model describing bursty or non-bursty protein expression in the presence of positive or negative autoregulation. Using the method of spectral decomposition, we show that the eigenfunctions of the generating function solution of the CME are Heun functions, while the eigenvalues can be determined by solving a continued fraction equation. Our solution generalizes and corrects a previous time-dependent solution for the CME of a gene circuit describing non-bursty protein expression in the presence of negative autoregulation [Ramos et al...

Recombination between resonance-stabilized hydrocarbon radicals is an important class of reactions that contribute to molecular growth chemistry in combustion. In the present study, the ring growth mechanism in the reaction between fulvenallenyl (C7 H5 ) and cyclopentadienyl (C5 H5 ) radicals is investigated computationally. The reaction pathways are explored by quantum chemical calculations, and the phenomenological and steady-state rate constants are determined by solving the multiple-well master equations...

Simulating mixed-state evolution in open quantum systems is crucial for various chemical physics, quantum optics, and computer science applications. These simulations typically follow the Lindblad master equation dynamics. An alternative approach known as quantum state diffusion unraveling is based on the trajectories of pure states generated by random wave functions, which evolve according to a nonlinear Itô-Schrödinger equation (ISE). This study introduces weak first-order and second-order solvers for the ISE based on directly applying the Itô-Taylor expansion with exact derivatives in the interaction picture...

The reactions of the simplest Criegee intermediate (CH2 OO) with n -butyraldehyde ( n BD) and isobutyraldehyde (iBD) were studied at 253-318 K and (50 ± 2) torr, using Cavity Ring-down spectroscopy (CRDS). The rate coefficients obtained at room temperature were (2.63 ± 0.14) × 10-12 and (2.20 ± 0.21) × 10-12 cm3 molecule-1 s-1 for n BD and iBD, respectively. Both the reactions show negative temperature-dependency, following equations, k n BD ( T = 253-318 K) = (11.51 ± 4.33) × 10-14 × exp{(918...

Hydroxyapatite (HAp) [Ca10 (PO4 )6 (OH)2 ] is remarkably similar to the hard tissue of the human body and the uses of this material in various fields in addition to the medical sector are increasing day by day. In this research, mustered oil, soybean oil, as well as coconut oil were employed as liquid media for synthesizing nanocrystalline HAp using a wet chemical precipitation approach. The X-ray diffraction (XRD) study verified the crystalline phase of the HAp in all the indicated media and discovered similarities with the standard database...

Naphthalene, the most abundant polycyclic aromatic hydrocarbon in the atmosphere, significantly influences OH consumption and secondary organic aerosol (SOA) formation. Naphthoquinone (NQ) is a significant contributor to ring-retaining SOA from naphthalene degradation, impacting the redox properties and toxicity of ambient particles. However, inconsistencies persist regarding concentrations of its isomers, 1,2-NQ and 1,4-NQ. In present work, our theoretical investigation into naphthalene's reaction with OH and subsequent oxygenation unveils their role in SOA formation...

We study the applicability of the Liouvillian exceptional points (LEPs) approach to nanoscale open quantum systems. A generic model of the driven two-level system in a thermal environment is analyzed within the nonequilibrium Green's function (NEGF) and Bloch quantum master equation formulations. We derive the latter starting from the exact NEGF Dyson equations and highlight the qualitative limitations of the LEP treatment by examining the approximations employed in its derivation. We find that the non-Markov character of evolution in open quantum systems does not allow for the introduction of the concept of exceptional points for a description of their dynamics...