Controllability of non-linear biochemical systems

Mathematical methods of biochemical pathway analysis are rapidly maturing to a point where it is possible to provide objective rationale for the natural design of metabolic systems and where it is becoming feasible to manipulate these systems based on model predictions, for instance, with the goal of optimizing the yield of a desired microbial product. So far, theory-based metabolic optimization techniques have mostly been applied to steady-state conditions or the minimization of transition time, using either linear stoichiometric models or fully kinetic models within biochemical systems theory (BST). This article addresses the related problem of controllability, where the task is to steer a non-linear biochemical system, within a given time period, from an initial state to some target state, which may or may not be a steady state. For this purpose, BST models in S-system form are transformed into affine non-linear control systems, which are subjected to an exact feedback linearization that permits controllability through independent variables. The method is exemplified with a small glycolytic-glycogenolytic pathway that had been analyzed previously by several other authors in different contexts.     

Design of the lac gene circuit revisited

The lactose (lac) operon of Escherichia coli serves as the paradigm for gene regulation, not only for bacteria, but also for all biological systems from simple phage to humans. The details of the systems may differ, but the key conceptual framework remains, and the original system continues to reveal deeper insights with continued experimental and theoretical study. Nearly as long lasting in impact as the pivotal work of Jacob and Monod is the classic experiment of Novick and Weiner in which they demonstrated all-or-none gene expression in response to an artificial inducer. These results are often cited in claims that normal gene expression is in fact a discontinuous bistable phenomenon. In this paper, I review several levels of analysis of the lac system and introduce another perspective based on the construction of the system design space. These represent variations on a theme, based on a simply stated design principle, that captures the key qualitative features of the system in a largely mechanism-independent fashion. Moreover, this principle can be readily interpreted in terms of specific mechanisms to make predictions regarding monostable vs. bistable behavior. The regions of design space representing bifurcations are compared with the corresponding regions identified through bifurcation analysis. I present evidence based on biological considerations as well as modeling and analysis to suggest that induction of the lac system in its natural setting is a monostable continuously graded phenomenon. Nevertheless, it must be acknowledged that the lac stability question remains unsettled, and it undoubtedly will remain so until there are definitive experimental results.     

An efficient method for calculation of dynamic logarithmic gains in biochemical systems theory

Biochemical systems theory (BST) characterizes a given biochemical system based on the logarithmic gains, rate-constant sensitivities and kinetic-order sensitivities defined at a steady state. This paper describes an efficient method for calculation of the time courses of logarithmic gains, i.e. dynamic logarithmic gains L(Xi, Xj; t), which expresses the percentage change in the value of a dependent variable Xi at a time t in response to an infinitesimal percentage change in the value of an independent variable Xj at t=0. In this method, one first recasts the ordinary differential equations for the dependent variables into an exact canonical nonlinear representation (GMA system) through appropriate transformations of variables. Owing to the structured mathematical form of this representation, the recast system can be fully described by a set of numeric parameters, and the differential equations for the dynamic logarithmic gains can be set up automatically without resource to computer algebra. A simple general-purpose computer program can thus be written that requires only the relevant numeric parameters as input to calculate the time courses of the variables and of the dynamic logarithmic gains for both concentrations and fluxes. Unlike other methods, the proposed method does not require to derive any expression for the partial differentiation of flux expressions with respect to each independent variable. The proposed method has been applied to two kinds of reaction models to elucidate its usefulness.     

Stochastic P systems and the simulation of biochemical processes with dynamic compartments

We introduce a sequential rewriting strategy for P systems based on Gillespie's stochastic simulation algorithm, and show that the resulting formalism of stochastic P systems makes it possible to simulate biochemical processes in dynamically changing, nested compartments. Stochastic P systems have been implemented using the spatially explicit programming language MGS. Implementation examples include models of the Lotka-Volterra auto-catalytic system, and the life cycle of the Semliki Forest virus.     

Prospects for advancing the understanding of complex biochemical systems

The application of mathematical theories to understanding the behaviour of complex biochemical systems is reviewed. Key aspects of behaviour are identified as the flux through particular pathways in a steady state, the nature and stability of dynamical states, and the thermodynamic properties of systems. The first of these is dealt primarily in theories of metabolic control, and metabolic control analysis (MCA) is an important example. The valid application of this theory is limited to steady-state systems, and the cases where the essential features of control can be derived from calibration experiments which perturb the state of the system by a sufficiently small amount from its operating point. In practice, time-dependent systems exist, it is not always possible to know a priori whether applied perturbations are sufficiently small, and important features of control may lie farther from the operating point than the application of the theory permits. The nature and stability of dynamical and thermodynamical states is beyond the scope of MCA. To understand the significance of these limitations fully, and to address the dynamical and thermodynamical properties, more complete theories are required. Non-linear systems theory offers the possibility of studying important questions regarding control of steady and dynamical states. It can also link to thermodynamic properties of the system including the energetic efficiency of particular pathways. However, its application requires a more detailed characterisation of the system under study. This extra detail may be an essential feature of the study of non-equilibrium states in general, and non-ideal pathways in particular. Progress requires considerably more widespread integration of theoretical and experimental approaches than currently exists.     

在生理学研究中如何严格遵循试验设计四原则

目的：为从事生理学研究的科研工作者严格遵循试验设计四原则（以下简称四原则）提供一些有效的技术方法。方法：通过简单介绍"四原则的概念"、举例阐述"生理学研究中在落实四原则方面出现的常见错误和案例"和简单介绍"生理学研究中如何遵循四原则"来阐述遵循四原则的具体做法。结果：需要根据实际情况,选择合适的随机化方法,分层随机化是常用的好方法;应力求设置合理的对照组,才能真正体现出对照原则的价值;有根据地给出每个小组合适的样本含量,是试验结果具有重现性的基本保证;严格遵循随机、对照和重复原则,最终才能实现对比组之间达到极好的均衡效果,这说明均衡原则是一个把关的原则。结论：在生理学科研中,严格遵循四原则对保证生理学研究结果准确可靠至关重要。     

Building and deploying a cyberinfrastructure for the data-driven design of chemical systems and the exploration of chemical space

Abstract

The use of modern data science has recently emerged as a promising new path to tackling the complex challenges involved in the creation of next-generation chemistry and materials. However, despite the appeal of this potentially transformative development, the chemistry community has yet to incorporate it as a central tool in every-day work. Our research program is designed to enable and advance this emerging research approach. It is centred around the creation of a software ecosystem that brings together physics-based modelling, high-throughput in silico screening and data analytics (i.e. the use of machine learning and informatics for the validation, mining and modelling of chemical data). This cyberinfrastructure is devised to offer a comprehensive set of data science techniques and tools as well as a general-purpose scope to make it as versatile and widely applicable as possible. It also emphasises user-friendliness to make it accessible to the community at large. It thus provides the means for the large-scale exploration of chemical space and for a better understanding of the hidden mechanisms that determine the properties of complex chemical systems. Such insights can dramatically accelerate, streamline and ultimately transform the way chemical research is conducted. Aside from serving as a production-level tool, our cyberinfrastructure is also designed to facilitate and assess methodological innovation. Both the software and method development work are driven by concrete molecular design problems, which also allow us to assess the efficacy of the overall cyberinfrastructure.     

Biochemical and genomic regulation of the trehalose cycle in yeast: review of observations and canonical model analysis

The physiological hallmark of heat-shock response in yeast is a rapid, enormous increase in the concentration of trehalose. Normally found in growing yeast cells and other organisms only as traces, trehalose becomes a crucial protector of proteins and membranes against a variety of stresses, including heat, cold, starvation, desiccation, osmotic or oxidative stress, and exposure to toxicants. Trehalose is produced from glucose 6-phosphate and uridine diphosphate glucose in a two-step process, and recycled to glucose by trehalases. Even though the trehalose cycle consists of only a few metabolites and enzymatic steps, its regulatory structure and operation are surprisingly complex. The article begins with a review of experimental observations on the regulation of the trehalose cycle in yeast and proposes a canonical model for its analysis. The first part of this analysis demonstrates the benefits of the various regulatory features by means of controlled comparisons with models of otherwise equivalent pathways lacking these features. The second part elucidates the significance of the expression pattern of the trehalose cycle genes in response to heat shock. Interestingly, the genes contributing to trehalose formation are up-regulated to very different degrees, and even the trehalose degrading trehalases show drastically increased activity during heat-shock response. Again using the method of controlled comparisons, the model provides rationale for the observed pattern of gene expression and reveals benefits of the counterintuitive trehalase up-regulation.     

Application of surface response analysis to the optimization of penicillin acylase purification in aqueous two-phase systems

Penicillin acylase purification from an Escherichia coli crude extract using PEG 3350–sodium citrate aqueous two-phase systems (ATPS) was optimized. An experimental design was used to evaluate the influence of PEG, sodium citrate and sodium chloride on the purification parameters. A central composite design was defined centred on the previously found conditions for highest purification from an osmotic shock extract. Mathematical models for the partition coefficient of protein and enzyme, balance of protein and enzyme, yield and purification were calculated and statistically validated. Analysis of the contours of constant response as a function of PEG and sodium citrate concentrations for three different concentrations of NaCl revealed different effects of the three factors on the studied parameters. A maximum purification factor of 6.5 was predicted for PEG 3350, sodium citrate and NaCl concentrations of 15.1, 11.0 and 8.52% respectively. However, under these conditions the predicted yield was 61%. A better compromise between these two parameters can be found by superimposing the contour plots of the purification factor and yield for 10.3% NaCl. A region in the experimental space can be defined where the purification factor is always higher than 5.5 with yields exceeding 80%.     

Review of genes in development: re-reading the molecular paradigm

Genes in Development is a collection of 13 stimulating essays on "post genomic" approaches to the concept of the gene. At the risk of caricaturing some complex balances, the contributors tend to be skeptical about genetic determinism, the central dogma of molecular biology, reductionism, genes as programs and the concept of the gene as a DNA sequence. They tend to like emergent properties, complexity theory, the parity thesis for developmental resources, developmental systems theory, and membranes. But within this broad weltanschauung the essays in Genes in Development vary widely in their interests and emphases––from the history of twentieth century genetics to the social and ethical issues raised by contemporary genetics––which makes for an attractive and valuable collection.     

Gene technology-based antimetabolite design: the use of an in vitro protein expression system to facilitate antimetabolite design for virally-induced human diseases and malignant conditions

A precondition for the chemotherapeutic treatment of a variety of virally-induced human diseases and malignant conditions is a highly selective interaction of the drug molecule to be used with it's biological target. To ensure the development of novel, effective drugs, it is essential that the biological target is well characterised with regard to it's structure and activity. Such characterisation relies upon adequate amounts of pure target being available. One of the most important enzymatic importers for antimetabolites is the enzyme thymidine kinase. In this article an in vitro protein expression system is described which facilitates the production of milligram amounts of pure and biologically active thymidine kinase, from a number of important biological sources. Results have shown that the in vitro produced enzyme has the exact biochemical propeties of the in vivo enzyme. Thus the in vitro protein expression system is an ideal vechicle to facilitate an in depth investigation of the enzyme's biological properties.     

Genetic and biochemical evidence for distinct key functions of two highly divergent GAPDH genes in catabolic and anabolic carbon flow of the cyanobacterium Synechocystis sp. PCC 6803

Cyanobacterial genomes harbour two separate highly divergent glyceraldehyde-3-phosphate dehydrogenase (GAPDH) genes, gap1 and gap2, which are closely related at the sequence level to the nuclear genes encoding cytosolic and chloroplast GAPDH of higher plants, respectively. Genes gap1 and gap2 of the unicellular cyanobacterium Synechocystis sp. PCC 6803 were cloned and sequenced and subsequently inactivated by insertional mutagenesis to understand their metabolic functions. We obtained homozygous gap1^- mutants which have lost the capacity to grow on glucose under dim light while growth on organic acids as well as photosynthetic growth under CO₂ and high light is not impaired. Homozygous gap2^- mutants show the reciprocal phenotype. Under dim light they only grow on glucose but not on organic acids nor do they survive under photosynthetic conditions. Measurements of the anabolic activities (reduction of 1,3-bisphosphoglycerate) in extracts from wild type and mutant cells show that Gap2 is a major enzyme with dual cosubstrate specificity for NAD and NADP, while Gap1 displays a minor NAD-specific GAPDH activity. However, if measured in the catabolic direction (oxidation of glyceraldehyde-3-phosphate) Gap2 activity is very low and increases three- to fivefold after gel filtration of extracts over Sephadex G25. Our results suggest that enzymes Gap1 and Gap2, although coexpressed in cyanobacterial wild-type cells, play distinct key roles in catabolic and anabolic carbon flow, respectively. While Gap2 operates in the photosynthetic Calvin cycle and in non-photosynthetic gluconeogenesis, Gap1 seems to be essential only for glycolytic glucose breakdown, conditions under which the catabolic activity of Gap2 seems to be repressed by a specific low-molecular-weight inhibitor.     

Evaluation of the effects of the parameters involved in the purification of clavulanic acid from fermentation broth by aqueous two-phase systems

The purification of clavulanic acid (CA), which is an important β-lactam antibiotic produced by submerged cultivation of Streptomyces clavuligerus, was studied through the use of phosphate and polyethylene glycol-based aqueous two-phase systems. The parameters’ effect on the yield and purification was evaluated through an experimental design and the preliminary results showed that the polyethylene molecular mass and tie-line length and phase volume ratio exerted the strongest effect on the yield and distribution coefficient in the range tested. In addition, the response surface methodology was used to optimize the distribution coefficient, yield, and purification factor. The optimal conditions of yield and purification factor are in the regions where polyethylene has a low molecular mass, pH close to the isoelectric point, and lower top phase volume. A 100% yield and a 1.5-fold purification factor are obtained when extracting CA by maximizing the conditions of an aqueous two-phase system.     

Application of empirical design methodologies to the study of the influence of reaction conditions and N-alpha-protecting group structure on the enzymatic X-Phe-Leu-NH(2) dipeptide synthesis in buffer/dimethylformamide solvents systems

The influence of five different N-terminal protecting groups (For, Ac, Boc, Z, and Fmoc) and reaction conditions (temperature and dimethylformamide content) on the alpha-chymotrypsin-catalyzed synthesis of the dipeptide derivative X-Phe-Leu-NH(2) was studied. Groups such as For, Ac, Boc, and Z always rendered good peptide yields (82% to 85%) at low reaction temperatures and DMF concentrations, which depended on the N-alpha protection choice. Boc and Z were the most reactive N-alpha groups and, in addition, the most suitable for peptide synthesis. On the other hand, the use of empirical design methodologies allowed, with minimal experimentation and by multiple regression, to deduce an equation, which correlates the logarithm of the first order kinetic constant (log k') with reaction temperature, DMF concentration, and hydrophobicity (log P values) of the different protecting groups. The predictive value of the equation was tested by comparing the performance of another protective group, such as Aloc, with the performance predicted by said equation. Experimental and calculated k' values were found to be in good agreement.     

Physiological,biochemical and molecular evaluation of mungbean genotypes for agronomical yield under drought and salinity stresses in the presence of humic acid

Drought and salinity are potential threats in arid and semi arid regions. The current study was conducted with objective to optimize the production of different exotic genotypes of mungbean (NM-121-25, Chakwal M-6, DM-3 and PRI-Mung-2018) under drought and salinity stresses using humic acid in field experiments. One year tri-replicate field experiment was performed in RCBD using three factorial arrangement and effects of humic acid (60 kg ha^?1) were evaluated at physiological, biochemical, molecular and agronomical level under individual and integrated applications of drought (no irrigation till 15 days) and salinity (EC 6.4 dSM^?1). Data for physiological parameters (total chlorophyll, photosynthesis rate, stomatal conductance, transpiration rate and membrane damage), antioxidant enzymes (superoxide dismutase, catalase, peroxidase) and proline were collected on weekly basis since after the initiation of drought and salinity stresses. However data for agronomic characteristics (plant height, branches plant^?1, LAI, pods plant^?1, pod length and hundred seed weight) and grain carbohydrate content were collected after harvesting, while sampling for drought (VrDREB2A, VrbZIP17 and VrHsfA6a) and salinity (VrWRKY73, VrUBC1 and VrNHX1) related genes expression study was done after plants attained seedling stage. Under both individual and integrated applications of drought and salinity, all genotypes showed significant (p ≤ 0.05) increase in all traits excluding Cell membrane damage and proline during humic acid application. Likewise, genes expression revealed statistically distinct (p ≤ 0.05) up-regulation under humic acid treatment as compared to no humic acid treatment during both individual and integrated applications of drought and salinity. The genotype PRI-Mung-2018 recorded noteworthy performance during study. Moreover correlation and PCA analysis revealed that ultimate agronomical yield due to humic acid is an outcome of interconnection of physiological and biochemical parameters.