Graph-theoretic methods for the analysis of chemical and biochemical networks. I. Multistability and oscillations in ordinary differential equation models

A chemical mechanism is a model of a chemical reaction network consisting of a set of elementary reactions that express how molecules react with each other. In classical mass-action kinetics, a mechanism implies a set of ordinary differential equations (ODEs) which govern the time evolution of the concentrations. In this article, ODE models of chemical kinetics that have the potential for multiple positive equilibria or oscillations are studied. We begin by considering some methods of stability analysis based on the digraph of the Jacobian matrix. We then prove two theorems originally given by A. N. Ivanova which correlate the bifurcation structure of a mass-action model to the properties of a bipartite graph with nodes representing chemical species and reactions. We provide several examples of the application of these theorems.     

Enhanced sampling of chemical and biochemical reactions with metadynamics

Metadynamics (MetaD) is a method that augments molecular dynamics (MD) calculations of all types (classical and quantum) to help systems overcome energy barriers and explore regions of phase space that would otherwise not be seen during a simulation. The method has seen wide ranging uses, and it has proven especially useful for the study of reactions in which bonds break and form. In such cases, the timescale challenges of MD are profoundly limiting, and the advent of this new paradigm for biasing simulations has proven to be incredibly useful. In this review, we set out to summarise the large body of work that uses MetaD for studying reactions so that others can more easily implement this method in their own work. After a brief introduction of the method, we provide detailed summaries of the method applied in various contexts including condensed phase and biological reactions.     

Non-destructive methods for demonstrating chemical changes in the rhizosphere II. Application of methods

Chemical changes in the rhizosphere of soil-grown plants are demonstrated by non-destructive techniques based on colour reactions. The following examples are given: FeIII reduction in the rhizosphere of a Hakea species, MnIV reduction in the rhizosphere of chikpea, complexation of Al in the rhizosphere of Norway spruce, and the activity of acid phosphatase in the rhizosphere of maize.     

Dynamics of a biochemical system with multiple oscillatory domains as a clue for multiple modes of neuronal oscillations

We analyze the behavior of a two-variable biochemical model in conditions where it admits multiple oscillatory domains in parameter space. The model represents an autocatalytic enzyme reaction with input of substrate both from a constant source and from non-linear recycling of product into substrate. This system was previously studied for birhythmicity, i.e. the coexistence between two stable periodic regimes (Moran and Goldbeter 1984), and for multithreshold excitability (Moran and Goldbeter 1985). When two distinct oscillatory domains obtain as a function of the substrate injection rate, the system is capable of exhibiting two markedly different modes of oscillations for slightly different values of this control parameter. Phase plane analysis shows how the multiplicity of oscillatory domains depends on the parameters that govern the underlying biochemical mechanism of product recycling. We analyze the response of the model to various kinds of transient perturbations and to periodic changes in the substrate input that bring the system through the two ranges of oscillatory behavior. The results provide a qualitative explanation for experimental observations (Jahnsen and Llinas 1984b) related to the occurrence of two different modes of oscillations in thalamic neurones.     

Nonequilibrium chemical potentials and free energies for enzyme-catalyzed reactions

Using the statistical theory of nonequilibrium thermodynamics we explore the nature of nonequilibrium corrections to chemical potentials in simple enzyme-catalyzed reactions. The statistical definition of the chemical potential, which pertains to systems that are at stable steady states, is applied to the Michaelis-Menten reaction scheme in a cellular-sized compartment that communicates with out-side reservoirs. Calculations based on the kinetic parameters for hexokinase and triose phosphate isomerase show that substantial corrections to the chemical potential of product (the order of 25 mV) are possible if the reaction is sufficiently far from equilibrium. The dependence of the corrections to the chemical potentials on the size of the cellular compartment are explored, and the relevance of the corrections for understanding the thermodynamics of metabolites is discussed.     

Muscle surface membranes. Preparative methods affect apparent chemical properties and neurotoxin binding

Considerable disagreement exists between results reported by various authors for lipid composition and enzyme activity in purified muscle membrane fractions presumed to be sarcolemma, although an explanation for these discrepancies has not been presented. We have prepared muscle light surface membrane fractions of comparable density (1.050–1.120) by a low-salt sucrose method and by an LiBr-KCl extraction procedure and compared them for density profile, total lipid and cholesterol content, protein composition and ATPase activity. In addition, sodium channels characteristic of excitable membranes have been quantitated in each preparation using [³H]saxitoxin binding assays, and the density of acetylcholine receptors determined in fractions from control and denervated muscle using α-[¹²⁵I]bungarotoxin. Although both fractions contain predominantly surface membrane, the LiBr fraction consistently shows the higher specific activity of $\text{p-}\text{nitrophenylphosphatase}$, higher free cholesterol content, and higher density of sodium channels and acetylcholine receptors. The density distribution of sodium channels appears uniform throughout both fractions. Quantitative differences were seen between sodium dodecyl sulfatepolyacrylamide gel electrophoresis patterns of membrane proteins from the two preparations although most bands are represented in both. A majority of the low-salt sucrose light membrane proteins were accessible in varying degrees to labelling with diazotized diiodosulfanylic acid in intact muscle. These results suggest that light surface membrane fractions may be mixtures of sarcolemma and T-tubular membranes. Using our preparative methods, the LiBr fraction may contain predominantly sarcolemma while low-salt sucrose light membranes may be enriched in T-tubular elements.     

Synchronization properties of networks of electrically coupled neurons in the presence of noise and heterogeneities

We investigate how synchrony can be generated or induced in networks of electrically coupled integrate-and-fire neurons subject to noisy and heterogeneous inputs. Using analytical tools, we find that in a network under constant external inputs, synchrony can appear via a Hopf bifurcation from the asynchronous state to an oscillatory state. In a homogeneous net work, in the oscillatory state all neurons fire in synchrony, while in a heterogeneous network synchrony is looser, many neurons skipping cycles of the oscillation. If the transmission of action potentials via the electrical synapses is effectively excitatory, the Hopf bifurcation is supercritical, while effectively inhibitory transmission due to pronounced hyperpolarization leads to a subcritical bifurcation. In the latter case, the network exhibits bistability between an asynchronous state and an oscillatory state where all the neurons fire in synchrony. Finally we show that for time-varying external inputs, electrical coupling enhances the synchronization in an asynchronous network via a resonance at the firing-rate frequency.

Stability and synchronization analysis of inertial memristive neural networks with time delays

This paper is concerned with the problem of stability and pinning synchronization of a class of inertial memristive neural networks with time delay. In contrast to general inertial neural networks, inertial memristive neural networks is applied to exhibit the synchronization and stability behaviors due to the physical properties of memristors and the differential inclusion theory. By choosing an appropriate variable transmission, the original system can be transformed into first order differential equations. Then, several sufficient conditions for the stability of inertial memristive neural networks by using matrix measure and Halanay inequality are derived. These obtained criteria are capable of reducing computational burden in the theoretical part. In addition, the evaluation is done on pinning synchronization for an array of linearly coupled inertial memristive neural networks, to derive the condition using matrix measure strategy. Finally, the two numerical simulations are presented to show the effectiveness of acquired theoretical results.     

Local and global synchronization transitions induced by time delays in small-world neuronal networks with chemical synapses

Effects of time delay on the local and global synchronization in small-world neuronal networks with chemical synapses are investigated in this paper. Numerical results show that, for both excitatory and inhibitory coupling types, the information transmission delay can always induce synchronization transitions of spiking neurons in small-world networks. In particular, regions of in-phase and out-of-phase synchronization of connected neurons emerge intermittently as the synaptic delay increases. For excitatory coupling, all transitions to spiking synchronization occur approximately at integer multiples of the firing period of individual neurons; while for inhibitory coupling, these transitions appear at the odd multiples of the half of the firing period of neurons. More importantly, the local synchronization transition is more profound than the global synchronization transition, depending on the type of coupling synapse. For excitatory synapses, the local in-phase synchronization observed for some values of the delay also occur at a global scale; while for inhibitory ones, this synchronization, observed at the local scale, disappears at a global scale. Furthermore, the small-world structure can also affect the phase synchronization of neuronal networks. It is demonstrated that increasing the rewiring probability can always improve the global synchronization of neuronal activity, but has little effect on the local synchronization of neighboring neurons.     

Study of Oscillations in a Particular Case of Yates-Pardee-Goodwin Metabolic Pathway with Coupling

The aim of this work is to study the effect of coupling on a metabolic pathway. Specifically we assume that metabolites can exchange matter with outside pools via passive diffusion. The existence of periodic solutions in such a system is considered and resolved using the dual input describing function method. In one particular case of coupling for all permissible parameter sets the minimum dimension is given so that it is possible to detect a periodic solution. The results obtained are compared with previously derived results for systems without coupling. It is concluded that coupling with exterior pools of metabolites can give rise to steady state instead of periodic solution.     

Carotenoids of dragonflies,from the perspective of comparative biochemical and chemical ecological studies

Carotenoids of 20 species of dragonflies (including 14 species of Anisoptera and six species of Zygoptera) were investigated from the viewpoints of comparative biochemistry and chemical ecology. In larvae, β-carotene, β-cryptoxanthin, lutein, and fucoxanthin were found to be major carotenoids in both Anisoptera and Zygoptera. These carotenoids were assumed to have originated from aquatic insects, water fleas, tadpoles, and small fish, which dragonfly larvae feed on. Furthermore, β-caroten-2-ol and echinenone were also found in all species of larvae investigated. In adult dragonflies, β-carotene was found to be a major carotenoid along with lutein, zeaxanthin, β-caroten-2-ol, and echinenone in both Anisoptera and Zygoptera. On the other hand, unique carotenoids, β-zeacarotene, β,ψ-carotene (γ-carotene), torulene, β,γ-carotene, and γ,γ-carotene, were present in both Anisoptera and Zygoptera dragonflies. These carotenoids were not found in larvae. Food chain studies of dragonflies suggested that these carotenoids originated from aphids, and/or possibly from aphidophagous ladybird beetles and spiders, which dragonflies feed on. Lutein and zeaxanthin in adult dragonflies were also assumed to have originated from flying insects they feed on, such as flies, mosquitoes, butterflies, moths, and planthoppers, as well as spiders. β-Caroten-2-ol and echinenone were found in both dragonfly adults and larvae. They were assumed to be metabolites of β-carotene in dragonflies themselves. Carotenoids of dragonflies well reflect the food chain during their lifecycle.     

Finite-time and fixed-time synchronization analysis of inertial memristive neural networks with time-varying delays

This paper investigates the finite-time synchronization and fixed-time synchronization problems of inertial memristive neural networks with time-varying delays. By utilizing the Filippov discontinuous theory and Lyapunov stability theory, several sufficient conditions are derived to ensure finite-time synchronization of inertial memristive neural networks. Then, for the purpose of making the setting time independent of initial condition, we consider the fixed-time synchronization. A novel criterion guaranteeing the fixed-time synchronization of inertial memristive neural networks is derived. Finally, three examples are provided to demonstrate the effectiveness of our main results.     

Variability within the chemical analysis of horticultural substrates

Summary The variability within the chemical analysis of a horticultural substrate is described by the variance components, which are isolated in a hierarchical model, consisting of samples, analysts, subsamples and chemical determinations. It is shown that the samples contribute to the larger part of the total variability, although the variance component due to the analysts should not be neglected and differences between analysts are persistent. The increase of precision in function of the number of samples is shown.     

Quasi-multiparameter sensitivity measure for robustness analysis of complex biochemical networks

Robustness is the ability to resume reliable operation in the face of different types of perturbations. Analysis of how network structure achieves robustness enables one to understand and design cellular systems. It is typically true that all parameters simultaneously differ from their nominal values in vivo, but there have been few intelligible measures to estimate the robustness of a system's function to the uncertainty of all parameters.We propose a numerical and fast measure of a robust property to the uncertainty of all kinetic parameters, named quasi-multiparameter sensitivity (QMPS), which is defined as the sum of the squared magnitudes of single-parameter sensitivities. Despite its plain idea, it has hardly been employed in analysis of biological models. While QMPS is theoretically derived as a linear model, QMPS can be consistent with the expected variance simulated by the widely used Monte Carlo method in nonlinear biological models, when relatively small perturbations are given. To demonstrate the feasibility of QMPS, it is employed for numerical comparison to analyze the mechanism of how specific regulations generate robustness in typical biological models.QMPS characterizes the robustness much faster than the Monte Carlo method, thereby enabling the extensive search of a large parameter space to perform the numerical comparison between alternative or competing models. It provides a theoretical or quantitative insight to an understanding of how specific network structures are related to robustness. In circadian oscillators, a negative feedback loop with multiple phosphorylations is demonstrated to play a critical role in generating robust cycles to the uncertainty of multiple parameters.     

Pretreatment of Siam weed stem by several chemical methods for increasing the enzymatic digestibility

Siam weed [Chromolaena odorata (L.) King & Robinson], an invasive exotic weed in China, was proposed as a feedstock for bioethanol production. This would be a promising way of using for an invasive weed that needs management and control. It was found that the glucan content of the weed stem was similar to that of sugarcane bagasse, but higher than those of corn stover and wheat straw. Several chemical pretreatment methods were applied to the weed stem to increase its enzymatic digestibility. Mild sulfuric acid (<120°C) or alkali pretreatment did not markedly increase the enzymatic digestibility. However, peracetic acid (PAA) pretreatment dramatically enhanced the enzymatic hydrolysis of the weed stem. Compared to some other common agricultural residues, the weed stem was more difficult to pretreat and digest by cellulase. Fourier transform infrared (FTIR) spectra analysis indicated that the cellulose-related bands became more intensive after pretreatment, especially for PAA-pretreated samples. According to X-ray diffraction spectra, the biomass solids had higher crystallinity indices after pretreatment, although these indices were similar for all of the pretreated samples.     

Coupling cell growth and biochemical pathway induction in Saccharomyces cerevisiae for production of (+)-valencene and its chemical conversion to (+)-nootkatone

(+)-Nootkatone is a valuable, functional sesquiterpene that is widely used in food, cosmetics, pharmaceutical, agriculture, and other fields. However, only traces of it accumulate in plants, which is insufficient to meet the market demand. Therefore, commercial (+)-nootkatone is currently synthesized from (+)-valencene. Here, we engineered Saccharomyces cerevisiae to achieve high production of (+)-valencene. Employing gene screening, protein engineering and biosynthetic pathway optimization, we achieved 12.4 g/L (+)-valencene production with the mutant strain. This titer was further increased to 16.6 g/L, the highest titer reported to date, by coupling critical factors for cell growth and biochemical pathway induction. Subsequently, (+)-nootkatone was chemically synthesized from bio-fermented (+)-valencene with a yield of 80%. This study achieved efficient microbial synthesis of (+)-valencene, which may be utilized in industrial production and stabilize the supply of (+)-nootkatone.