Exploration of the spontaneous fluctuating activity of single enzyme molecules

Single enzyme molecules display inevitable, stochastic fluctuations in their catalytic activity. In metabolism, for instance, the stochastic activity of individual enzymes is averaged out due to their high copy numbers per single cell. However, many processes inside cells rely on single enzyme activity, such as transcription, replication, translation, and histone modifications. Here we introduce the main theoretical concepts of stochastic single-enzyme activity starting from the Michaelis–Menten enzyme mechanism. Next, we discuss stochasticity of multi-substrate enzymes, of enzymes and receptors with multiple conformational states and finally, how fluctuations in receptor activity arise from fluctuations in signal concentration. This paper aims to introduce the exciting field of single-molecule enzyme kinetics and stochasticity to a wider audience of biochemists and systems biologists

A second-order, unconditionally positive, mass-conserving integration scheme for biochemical systems.

Biochemical systems are bound by two mathematically-relevant restrictions. First, state variables in such systems represent non-negative quantities, such as concentrations of chemical compounds. Second, biochemical systems conserve mass and energy. Both properties must be reflected in results of an integration scheme applied to biochemical models. This paper first presents a mathematical framework for biochemical problems, which includes an exact definition of biochemical conservation: elements and energy, rather than state variable units, are conserved. We then analyze various fixed-step integration schemes, including traditional Euler-based schemes and the recently published modified Patankar schemes, and conclude that none of these deliver unconditional positivity and biochemical conservation in combination with higher-order accuracy. Finally, we present two new fixed-step integration schemes, one first-order and one second-order accurate, which do guarantee positivity and (biochemical) conservatio

A Data Integration and Visualization Resource for the Metabolic Network of Synechocystis sp. PCC 6803

Data integration is a central activity in systems biology. The integration of genomic, transcript, protein, metabolite, flux, and computational data yields unprecedented information about the system level functioning of organisms. Often, data integration is done purely computationally, leaving the user with little insight besides statistical information. In this article, we present a visualization tool for the metabolic network of Synechocystis PCC6803, an important model cyanobacterium for sustainable biofuel production. We illustrate how this metabolic map can be used to integrate experimental and computational data for Synechocystis systems biology and metabolic engineering studies. Additionally, we discuss how this map, and the software infrastructure that we supply with it, can be used in the development of other organism-specific metabolic network visualizations. Besides a Python console package VoNDA (http://vonda.sf.net), we provide a working demonstration of the interactive metabolic map and the associated Synechocystis genome-scale stoichiometric model, as well as various ready-to-visualize microarray data sets, at http://f-a-m-e.org/synechocystis/

Social system of transition society theoretical scheme: economy, culture and ecology interrelations

Changes in transcription factor levels, epigenetic status, splicing kinetics and mRNA degradation can each contribute to changes in the mRNA dynamics of a gene. We present a novel method to identify which of these processes is changed in cells in response to external signals or as a result of a diseased state. The method employs a mathematical model, for which the kinetics of gene regulation, splicing, elongation and mRNA degradation were estimated from experimental data of transcriptional dynamics. The time-dependent dynamics of several species of adipose differentiation-related protein (ADRP) mRNA were measured in response to ligand activation of the transcription factor peroxisome proliferator-activated receptor δ (PPARδ). We validated the method by monitoring the mRNA dynamics upon gene activation in the presence of a splicing inhibitor. Our mathematical model correctly identifies splicing as the inhibitor target, despite the noise in the data

Whole-cell metabolic control analysis

Since its conception some fifty years ago, metabolic control analysis (MCA) aims to understand how cells control their metabolism by adjusting the activity of their enzymes. Here we extend its scope to a whole-cell context. We consider metabolism in the evolutionary context of growth-rate maximisation by optimisation of protein concentrations. This framework allows for the prediction of flux control coefficients from proteomics data or stoichiometric modelling. Since genes compete for finite biosynthetic resources, we treat all protein concentrations as interdependent. We show that elementary flux modes (EFMs) emerge naturally as the optimal metabolic networks in the whole-cell context and we derive their control properties. In the evolutionary optimum, the number of expressed EFMs is determined by the number of protein-concentration constraints that limit growth rate. We use published glucose-limited chemostat data of S. cerevisiae to illustrate that it uses only two EFMs prior to the onset of fermentation and that it uses four EFMs during fermentation. We discuss published enzyme-titration data to show that S. cerevisiae and E. coli indeed can express proteins at growth-rate maximising concentrations. Accordingly, we extend MCA to elementary flux modes operating at an optimal state. We find that the expression of growth-unassociated proteins changes results from classical metabolic control analysis. Finally, we show how flux control coefficients can be estimated from proteomics and ribosome-profiling data. We analyse published proteomics data of E. coli to provide a whole-cell perspective of the control of metabolic enzymes on growth rate. We hope that this paper stimulates a renewed interest in metabolic control analysis, so that it can serve again the purpose it once had: to identify general principles that emerge from the biochemistry of the cell and are conserved across biological species