How to impose microscopic reversibility in complex reaction mechanisms

Most, but not all, ion channels appear to obey the law of microscopic reversibility (or detailed balance). During the fitting of reaction mechanisms it is therefore often required that cycles in the mechanism should obey microscopic reversibility at all times. In complex reaction mechanisms, especially those that contain cubic arrangements of states, it may not be obvious how to achieve this. Three general methods for imposing microscopic reversibility are described. The first method works by setting the 'obvious' four-state cycles in the correct order. The second method, based on the idea of a spanning tree, works by finding independent cycles (which will often have more than four states) such that the order in which they are set does not matter. The third method uses linear algebra to solve for constrained rates.     

Genetic and biochemical mechanisms of rice resistance to planthopper

Key message

This article presents a comprehensive review on the genetic and biochemicalmechanisms governing rice-planthopper interactions, aiming to contribute substantialplanthopper control and facilitate breeding for resistance to planthoppers in rice.

Abstract

The rice planthopper is the most destructive pest of rice and a substantial threat to rice production. The brown planthopper (BPH), white-backed planthopper (WBPH) and small brown planthopper (SBPH) are three species of delphacid planthoppers and important piercing-sucking pests of rice. Host-plant resistance has been recognized as the most practical, economical and environmentally friendly strategy to control planthoppers. Until now, at least 30, 14 and 34 major genes/quantitative trait loci for resistance to BPH, WBPH and SBPH have been identified, respectively. Recent inheritance and molecular mapping of gene analysis showed that some planthopper-resistance genes in rice derived from different donors aggregate in clusters, while resistance to these three species of planthoppers in a single donor is governed not by any one dominant gene but by multiple genes. Notably, Bph14, Bph26, Bph3 and Bph29 were successfully identified as BPH-resistance genes in rice. Biological and chemical studies on the feeding of planthoppers indicate that rice plants have acquired various forms of defence against planthoppers. Between the rice-planthopper interactions, rice plants defend against planthoppers through activation the salicylic acid-dependent systemic acquired resistance but not jasmonate-dependent hormone response pathways. Transgenic rice for the planthopper-resistance mechanism shows that jasmonate and its metabolites function diversely in rice’s resistance to planthopper. Understanding the genetic and biochemical mechanisms underlying resistance in rice will contribute to the substantial control of such pests and facilitate breeding for rice’s resistance to planthopper more efficiently.

     

Structure and reaction mechanisms of multifunctional mitochondrial cytochrome bc1 complex.

The cytochrome bc1 complex from bovine heart mitochondria is a multi-functional enzyme complex. In addition to electron and proton transfer activity, the complex also processes an activatable peptidase activity and a superoxide generating activity. The crystal structure of the complex exists as a closely interacting functional dimer. There are 13 transmembrane helices in each monomer, eight of which belong to cytochrome b, and five of which belong to cytochrome c1, Rieske iron-sulfur protein (ISP), subunits 7, 10 and 11, one each. The distances of 21 A between bL heme and bH heme and of 27 A between bL heme and the iron-sulfur cluster (FeS), accommodate well the observed fast electron transfers between the involved redox centers. However, the distance of 31 A between heme c1 and FeS, makes it difficult to explain the high electron transfer rate between them. 3D structural analyses of the bc1 complexes co-crystallized with the Qu site inhibitors suggest that the extramembrane domain of the ISP may undergo substantial movement during the catalytic cycle of the complex. This suggestion is further supported by the decreased in the cytochrome bc1 complex activity and the increased in activation energy for mutants with increased rigidity in the neck region of ISP.     

Mathematical model to predict drivers' reaction speeds

Mental distractions and physical impairments can increase the risk of accidents by affecting a driver's ability to control the vehicle. In this article, we developed a linear mathematical model that can be used to quantitatively predict drivers' performance over a variety of possible driving conditions. Predictions were not limited only to conditions tested, but also included linear combinations of these tests conditions. Two groups of 12 participants were evaluated using a custom drivers' reaction speed testing device to evaluate the effect of cell phone talking, texting, and a fixed knee brace on the components of drivers' reaction speed. Cognitive reaction time was found to increase by 24% for cell phone talking and 74% for texting. The fixed knee brace increased musculoskeletal reaction time by 24%. These experimental data were used to develop a mathematical model to predict reaction speed for an untested condition, talking on a cell phone with a fixed knee brace. The model was verified by comparing the predicted reaction speed to measured experimental values from an independent test. The model predicted full braking time within 3% of the measured value. Although only a few influential conditions were evaluated, we present a general approach that can be expanded to include other types of distractions, impairments, and environmental conditions.     

A comparison of approximation techniques for variance-based sensitivity analysis of biochemical reaction systems

Background

Sensitivity analysis is an indispensable tool for the analysis of complex systems. In a recent paper, we have introduced a thermodynamically consistent variance-based sensitivity analysis approach for studying the robustness and fragility properties of biochemical reaction systems under uncertainty in the standard chemical potentials of the activated complexes of the reactions and the standard chemical potentials of the molecular species. In that approach, key sensitivity indices were estimated by Monte Carlo sampling, which is computationally very demanding and impractical for large biochemical reaction systems. Computationally efficient algorithms are needed to make variance-based sensitivity analysis applicable to realistic cellular networks, modeled by biochemical reaction systems that consist of a large number of reactions and molecular species.

Results

We present four techniques, derivative approximation (DA), polynomial approximation (PA), Gauss-Hermite integration (GHI), and orthonormal Hermite approximation (OHA), for analytically approximating the variance-based sensitivity indices associated with a biochemical reaction system. By using a well-known model of the mitogen-activated protein kinase signaling cascade as a case study, we numerically compare the approximation quality of these techniques against traditional Monte Carlo sampling. Our results indicate that, although DA is computationally the most attractive technique, special care should be exercised when using it for sensitivity analysis, since it may only be accurate at low levels of uncertainty. On the other hand, PA, GHI, and OHA are computationally more demanding than DA but can work well at high levels of uncertainty. GHI results in a slightly better accuracy than PA, but it is more difficult to implement. OHA produces the most accurate approximation results and can be implemented in a straightforward manner. It turns out that the computational cost of the four approximation techniques considered in this paper is orders of magnitude smaller than traditional Monte Carlo estimation. Software, coded in MATLAB^®, which implements all sensitivity analysis techniques discussed in this paper, is available free of charge.

Conclusions

Estimating variance-based sensitivity indices of a large biochemical reaction system is a computationally challenging task that can only be addressed via approximations. Among the methods presented in this paper, a technique based on orthonormal Hermite polynomials seems to be an acceptable candidate for the job, producing very good approximation results for a wide range of uncertainty levels in a fraction of the time required by traditional Monte Carlo sampling.     

System of Ca2+ transport in spermatozoids and biochemical mechanisms of capacitation and acrosomic reaction

The paper systematizes modern ideas regarding the role of macroelements (including calcium ions) in physico-chemical, biochemical spermatozoid processes, that provides the preservation of their biological completeness and fertility. Information concerning ion content and ion distribution in semen of males of different age groups and in the ejaculate with different quality indicators is presented. The basic ion-transport systems that are identified in spermatozoid membranes of males and their role in sperm activation, cell active movement ability, maintenance of cell homeostasis etc. are discussed. General schemes of biochemical mechanisms of capacitation process and acrosomic reaction are proposed.     

Linking the computational structure of variance adaptation to biophysical mechanisms

In multiple sensory systems, adaptation to the variance of a sensory input changes the sensitivity, kinetics, and average response over timescales ranging from < 100 ms to tens of seconds. Here, we present a simple, biophysically relevant model of retinal contrast adaptation that accurately captures both the membrane potential response and all adaptive properties. The adaptive component of this model is a first-order kinetic process of the type used to describe ion channel gating and synaptic transmission. From the model, we conclude that all adaptive dynamics can be accounted for by depletion of a signaling mechanism, and that variance adaptation can be explained as adaptation to the mean of a rectified signal. The model parameters show strong similarity to known properties of bipolar cell synaptic vesicle pools. Diverse types of adaptive properties that implement theoretical principles of efficient coding can be generated by a single type of molecule or synapse with just a few microscopic states.     

Mathematical and computational modeling in biology at multiple scales

A variety of topics are reviewed in the area of mathematical and computational modeling in biology, covering the range of scales from populations of organisms to electrons in atoms. The use of maximum entropy as an inference tool in the fields of biology and drug discovery is discussed. Mathematical and computational methods and models in the areas of epidemiology, cell physiology and cancer are surveyed. The technique of molecular dynamics is covered, with special attention to force fields for protein simulations and methods for the calculation of solvation free energies. The utility of quantum mechanical methods in biophysical and biochemical modeling is explored. The field of computational enzymology is examined.     

A new computational method to split large biochemical networks into coherent subnets

Background  

Compared to more general networks, biochemical networks have some special features: while generally sparse, there are a small number of highly connected metabolite nodes; and metabolite nodes can also be divided into two classes: internal nodes with associated mass balance constraints and external ones without. Based on these features, reclassifying selected internal nodes (separators) to external ones can be used to divide a large complex metabolic network into simpler subnetworks. Selection of separators based on node connectivity is commonly used but affords little detailed control and tends to produce excessive fragmentation.     

Mathematical and computational modelling of spatio-temporal signalling in rod phototransduction

Rod photoreceptors are activated by light through activation of a cascade that includes the G protein-coupled receptor rhodopsin, the G protein transducin, its effector cyclic guanosine monophosphate (cGMP) phosphodiesterase and the second messengers cGMP and Ca2+. Signalling is localised to the particular rod outer segment disc, which is activated by absorption of a single photon. Modelling of this cascade has previously been performed mostly by assumption of a well-stirred cytoplasm. We recently published the first fully spatially resolved model that captures the local nature of light activation. The model reduces the complex geometry of the cell to a simpler one using the mathematical theories of homogenisation and concentrated capacity. The model shows that, upon activation of a single rhodopsin, changes of the second messengers cGMP and Ca2+ are local about the particular activated disc. In the current work, the homogenised model is computationally compared with the full, non-homogenised one, set in the original geometry of the rod outer segment. It is found to have an accuracy of 0.03% compared with the full model in computing the integral response and a 5200-fold reduction in computation time. The model can reconstruct the radial time-profiles of cGMP and Ca2+ in the interdiscal spaces adjacent to the activated discs. Cellular electrical responses are localised near the activation sites, and multiple photons sufficiently far apart produce essentially independent responses. This leads to a computational analysis of the notion and estimate of 'spread' and the optimum distribution of activated sites that maximises the response. Biological insights arising from the spatio-temporal model include a quantification of how variability in the response to dim light is affected by the distance between the outer segment discs capturing photons. The model is thus a simulation tool for biologists to predict the effect of various factors influencing the timing, spread and control mechanisms of this G protein-coupled, receptor-mediated cascade. It permits ease of simulation experiments across a range of conditions, for example, clamping the concentration of calcium, with results matching analogous experimental results. In addition, the model accommodates differing geometries of rod outer segments from different vertebrate species. Thus it represents a building block towards a predictive model of visual transduction.     

Mathematical multi-locus approaches to localizing complex human trait genes

Statistical analysis methods for gene mapping originated in counting recombinant and non-recombinant offspring, but have now progressed to sophisticated approaches for the mapping of complex trait genes. Here, we outline new statistical methods that capture the simultaneous effects of multiple gene loci and thereby achieve a more global view of gene action and interaction than is possible by traditional gene-by-gene analysis. We aim to show that the work of statisticians goes far beyond the running of computer programs.     

Energy and phase orientation mechanisms: a computational model

A computational model is proposed for spatial orientation processing beyond the initial stage of linear filtering in visual cortex. The model accounts for orientation pop-out, edge location and orientation, and bar location and orientation. It naturally extends to higher order orientation symmetries. The model is consistent with much of the current understanding of early processing in mammalian visual cortex. It builds on the notions of orientation and spatial frequency specific simple cells, any subsequent non-linearity, and orientation 'pooling'. The processing treats simple cell energy, real, and imaginary responses in a unified way to generate 'feature maps'. The 'pooling' operation in each case is a discrete Fourier transform of the simple cell responses over orientation. The suggested processing has implications for psychophysics (e.g. providing an explanation of why orientation discrimination thresholds are more than an order of magnitude less than simple cell orientation bandwidths), provides some understanding of the variety of 'complex-cell' properties found in visual cortex, and provides a plausible starting point for subsequent processing.     

A general pre-steady-state solution to complex kinetic mechanisms

We have developed a general method for solving transient kinetic equations using Laplace transforms. Laplace transforms can be used to transform systems of differential equations that describe pre-steady-state kinetics to systems of linear algebraic equations. The general form of the pre-steady-state solution is (formula; see text) where I(t) is the time dependence of the physically observed property of the system, n is the number of intermediates, lambda i are the observed rate constants (reciprocals of the relaxation times), t is time, and Ii are the amplitude coefficients associated with each observed rate constant. We have written a program in compiled BASIC to run on a personal computer to evaluate Ii and lambda i. The program will evaluate the rate constants and coefficients of a mechanism with eight intermediates and seven relaxation times in 4 s on an 8-MHz PC-XT equipped with a math coprocessor. The most complex mechanism that we have solved, a mechanism containing 20 intermediates and 19 relaxation times, required approximately 5 min. We believe that this method will be useful to evaluate the differences in transient properties of complex biochemical mechanisms.     

Use of primary deuterium and 15N isotope effects to deduce the relative rates of steps in the mechanisms of alanine and glutamate dehydrogenases

We have used deuterium and 15N isotope effects to study the relative rates of the steps in the mechanisms of alanine and glutamate dehydrogenases. The proposed chemical mechanisms for these enzymes involve carbinolamine formation, imine formation, and reduction of the imine to the amino acid [Grimshaw, C.E., Cook, P.F., & Cleland, W.W. (1981) Biochemistry 20, 5655; Rife, J.E., & Cleland, W.W. (1980) Biochemistry 19, 2328]. These steps are almost equally rate limiting for V/Kammonia with alanine dehydrogenase, while with glutamate dehydrogenase carbinolamine formation, imine formation, and release of glutamate after hydride transfer provide most of the rate limitation of V/Kammonia. Release of oxidized nucleotide is largely rate limiting for Vmax for both enzymes. When beta-hydroxypyruvate replaces pyruvate, or 3-acetylpyridine NADH (Acpyr-NADH) or thio-NADH replaces NADH with alanine dehydrogenase, nucleotide release no longer limits Vmax, and hydride transfer becomes more rate limiting. With glutamate dehydrogenase, replacement of alpha-ketoglutarate by alpha-ketovalerate makes hydride transfer more rate limiting. Use of Acpyr-NADPH has a minimal effect with alpha-ketoglutarate but causes an 8-fold decrease in Vmax with alpha-ketovalerate, with hydride transfer the major rate-limiting step. In contrast, thio-NADPH with either alpha-keto acid causes carbinolamide formation to become almost completely rate limiting. These studies show the power of multiple isotope effects in deducing details of the chemistry and changes in rate-limiting step(s) in complicated reaction mechanisms such as those of alanine and glutamate dehydrogenases.