Integrating Kinetic Model of E. coli with Genome Scale Metabolic Fluxes Overcomes Its Open System Problem and Reveals Bistability in Central Metabolism

An understanding of the dynamics of the metabolic profile of a bacterial cell is sought from a dynamical systems analysis of kinetic models. This modelling formalism relies on a deterministic mathematical description of enzyme kinetics and their metabolite regulation. However, it is severely impeded by the lack of available kinetic information, limiting the size of the system that can be modelled. Furthermore, the subsystem of the metabolic network whose dynamics can be modelled is faced with three problems: how to parameterize the model with mostly incomplete steady state data, how to close what is now an inherently open system, and how to account for the impact on growth. In this study we address these challenges of kinetic modelling by capitalizing on multi-omics steady state data and a genome-scale metabolic network model. We use these to generate parameters that integrate knowledge embedded in the genome-scale metabolic network model, into the most comprehensive kinetic model of the central carbon metabolism of E. coli realized to date. As an application, we performed a dynamical systems analysis of the resulting enriched model. This revealed bistability of the central carbon metabolism and thus its potential to express two distinct metabolic states. Furthermore, since our model-informing technique ensures both stable states are constrained by the same thermodynamically feasible steady state growth rate, the ensuing bistability represents a temporal coexistence of the two states, and by extension, reveals the emergence of a phenotypically heterogeneous population

Mycobacterium leprae genomes from a British medieval leprosy hospital: towards understanding an ancient epidemic.

BACKGROUND: Leprosy has afflicted humankind throughout history leaving evidence in both early texts and the archaeological record. In Britain, leprosy was widespread throughout the Middle Ages until its gradual and unexplained decline between the 14th and 16th centuries. The nature of this ancient endemic leprosy and its relationship to modern strains is only partly understood. Modern leprosy strains are currently divided into 5 phylogenetic groups, types 0 to 4, each with strong geographical links. Until recently, European strains, both ancient and modern, were thought to be exclusively type 3 strains. However, evidence for type 2 strains, a group normally associated with Central Asia and the Middle East, has recently been found in archaeological samples in Scandinavia and from two skeletons from the medieval leprosy hospital (or leprosarium) of St Mary Magdalen, near Winchester, England. RESULTS: Here we report the genotypic analysis and whole genome sequencing of two further ancient M. leprae genomes extracted from the remains of two individuals, Sk14 and Sk27, that were excavated from 10th-12th century burials at the leprosarium of St Mary Magdalen. DNA was extracted from the surfaces of bones showing osteological signs of leprosy. Known M. leprae polymorphisms were PCR amplified and Sanger sequenced, while draft genomes were generated by enriching for M. leprae DNA, and Illumina sequencing. SNP-typing and phylogenetic analysis of the draft genomes placed both of these ancient strains in the conserved type 2 group, with very few novel SNPs compared to other ancient or modern strains. CONCLUSIONS: The genomes of the two newly sequenced M. leprae strains group firmly with other type 2F strains. Moreover, the M. leprae strain most closely related to one of the strains, Sk14, in the worldwide phylogeny is a contemporaneous ancient St Magdalen skeleton, vividly illustrating the epidemic and clonal nature of leprosy at this site. The prevalence of these type 2 strains indicates that type 2F strains, in contrast to later European and associated North American type 3 isolates, may have been the co-dominant or even the predominant genotype at this location during the 11th century

MultiMetEval: comparative and multi-objective analysis of genome-scale metabolic models

Comparative metabolic modelling is emerging as a novel field, supported by the development of reliable and standardized approaches for constructing genome-scale metabolic models in high throughput. New software solutions are needed to allow efficient comparative analysis of multiple models in the context of multiple cellular objectives. Here, we present the user-friendly software framework Multi-Metabolic Evaluator (MultiMetEval), built upon SurreyFBA, which allows the user to compose collections of metabolic models that together can be subjected to flux balance analysis. Additionally, MultiMetEval implements functionalities for multi-objective analysis by calculating the Pareto front between two cellular objectives. Using a previously generated dataset of 38 actinobacterial genome-scale metabolic models, we show how these approaches can lead to exciting novel insights. Firstly, after incorporating several pathways for the biosynthesis of natural products into each of these models, comparative flux balance analysis predicted that species like Streptomyces that harbour the highest diversity of secondary metabolite biosynthetic gene clusters in their genomes do not necessarily have the metabolic network topology most suitable for compound overproduction. Secondly, multi-objective analysis of biomass production and natural product biosynthesis in these actinobacteria shows that the well-studied occurrence of discrete metabolic switches during the change of cellular objectives is inherent to their metabolic network architecture. Comparative and multi-objective modelling can lead to insights that could not be obtained by normal flux balance analyses. MultiMetEval provides a powerful platform that makes these analyses straightforward for biologists. Sources and binaries of MultiMetEval are freely available from https://github.com/PiotrZakrzewski/MetEv​al/downloads

Nonidentifiability of the Source of Intrinsic Noise in Gene Expression from Single-Burst Data

Over the last few years, experimental data on the fluctuations in gene activity between individual cells and within the same cell over time have confirmed that gene expression is a “noisy” process. This variation is in part due to the small number of molecules taking part in some of the key reactions that are involved in gene expression. One of the consequences of this is that protein production often occurs in bursts, each due to a single promoter or transcription factor binding event. Recently, the distribution of the number of proteins produced in such bursts has been experimentally measured, offering a unique opportunity to study the relative importance of different sources of noise in gene expression. Here, we provide a derivation of the theoretical probability distribution of these bursts for a wide variety of different models of gene expression. We show that there is a good fit between our theoretical distribution and that obtained from two different published experimental datasets. We then prove that, irrespective of the details of the model, the burst size distribution is always geometric and hence determined by a single parameter. Many different combinations of the biochemical rates for the constituent reactions of both transcription and translation will therefore lead to the same experimentally observed burst size distribution. It is thus impossible to identify different sources of fluctuations purely from protein burst size data or to use such data to estimate all of the model parameters. We explore methods of inferring these values when additional types of experimental data are available

Stochastic models for the in silico simulation of synaptic processes

Background: Research in life sciences is benefiting from a large availability of formal description techniques and analysis methodologies. These allow both the phenomena investigated to be precisely modeled and virtual experiments to be performed in silico. Such experiments may result in easier, faster, and satisfying approximations of their in vitro/vivo counterparts. A promising approach is represented by the study of biological phenomena as a collection of interactive entities through process calculi equipped with stochastic semantics. These exploit formal grounds developed in the theory of concurrency in computer science, account for the not continuous, nor discrete, nature of many phenomena, enjoy nice compositional properties and allow for simulations that have been demonstrated to be coherent with data in literature. Results: Motivated by the need to address some aspects of the functioning of neural synapses, we have developed one such model for synaptic processes in the calyx of Held, which is a glutamatergic synapse in the auditory pathway of the mammalia. We have developed such a stochastic model starting from existing kinetic models based on ODEs of some sub-components of the synapse, integrating other data from literature and making some assumptions about non-fully understood processes. Experiments have confirmed the coherence of our model with known biological data, also validating the assumptions made. Our model overcomes some limitations of the kinetic ones and, to our knowledge, represents the first model of synaptic processes based on process calculi. The compositionality of the approach has permitted us to independently focus on tuning the models of the pre- and post- synaptic traits, and then to naturally connect them, by dealing with “interface” issues. Furthermore, we have improved the expressiveness of the model, e.g. by embedding easy control of element concentration time courses. Sensitivity analysis over several parameters of the model has provided results that may help clarify the dynamics of synaptic transmission, while experiments with the model of the complete synapse seem worth explaining short-term plasticity mechanisms. Conclusions: Specific presynaptic and postsynaptic mechanisms can be further analysed under various conditions, for instance by studying the presynaptic behaviour under repeated activations. The level of details of the description can be refined, for instance by further specifying the neurotransmitter generation and release steps. Taking advantage of the compositionality of the approach, an enhanced model could then be composed with other neural models, designed within the same framework, in order to obtain a more detailed and comprehensive model. In the long term, we are interested, in particular, in addressing models of synaptic plasticity, i.e. activity dependent mechanisms, which are the bases of memory and learning processes. More on the computer science side, we plan to follow some directions to improve the underlying computational model and the linguistic primitives it provides as suggested by the experiments carried out, e.g. by introducing a suitable notion of (spatial) locality

Differential Producibility Analysis (DPA) of Transcriptomic Data with Metabolic Networks: Deconstructing the Metabolic Response of M. tuberculosis

A general paucity of knowledge about the metabolic state of Mycobacterium tuberculosis within the host environment is a major factor impeding development of novel drugs against tuberculosis. Current experimental methods do not allow direct determination of the global metabolic state of a bacterial pathogen in vivo, but the transcriptional activity of all encoded genes has been investigated in numerous microarray studies. We describe a novel algorithm, Differential Producibility Analysis (DPA) that uses a metabolic network to extract metabolic signals from transcriptome data. The method utilizes Flux Balance Analysis (FBA) to identify the set of genes that affect the ability to produce each metabolite in the network. Subsequently, Rank Product Analysis is used to identify those metabolites predicted to be most affected by a transcriptional signal. We first apply DPA to investigate the metabolic response of E. coli to both anaerobic growth and inactivation of the FNR global regulator. DPA successfully extracts metabolic signals that correspond to experimental data and provides novel metabolic insights. We next apply DPA to investigate the metabolic response of M. tuberculosis to the macrophage environment, human sputum and a range of in vitro environmental perturbations. The analysis revealed a previously unrecognized feature of the response of M. tuberculosis to the macrophage environment: a down-regulation of genes influencing metabolites in central metabolism and concomitant up-regulation of genes that influence synthesis of cell wall components and virulence factors. DPA suggests that a significant feature of the response of the tubercle bacillus to the intracellular environment is a channeling of resources towards remodeling of its cell envelope, possibly in preparation for attack by host defenses. DPA may be used to unravel the mechanisms of virulence and persistence of M. tuberculosis and other pathogens and may have general application for extracting metabolic signals from other “-omics” data

Probabilistic Model Checking for Continuous-Time Markov Chains via Sequential Bayesian Inference

Probabilistic model checking for systems with large or unbounded state space is a challenging computational problem in formal modelling and its applications. Numerical algorithms require an explicit representation of the state space, while statistical approaches require a large number of samples to estimate the desired properties with high confidence. Here, we show how model checking of time-bounded path properties can be recast exactly as a Bayesian inference problem. In this novel formulation the problem can be efficiently approximated using techniques from machine learning. Our approach is inspired by a recent result in statistical physics which derived closed form differential equations for the first-passage time distribution of stochastic processes. We show on a number of non-trivial case studies that our method achieves both high accuracy and significant computational gains compared to statistical model checking

Metabolic and evolutionary insights into the closely-related species Streptomyces coelicolor and Streptomyces lividans deduced from high-resolution comparative genomic hybridization

Whilst being closely related to the model actinomycete Streptomyces coelicolor A3(2), S. lividans 66 differs from it in several significant and phenotypically observable ways, including antibiotic production. Previous comparative gene hybridization studies investigating such differences have used low-density (one probe per gene) PCR-based spotted arrays. Here we use new experimentally optimised 104,000 × 60-mer probe arrays to characterize in detail the genomic differences between wild-type S. lividans 66, a derivative industrial strain, TK24, and S. coelicolor M145

Mathematical modeling of intracellular signaling pathways

Dynamic modeling and simulation of signal transduction pathways is an important topic in systems biology and is obtaining growing attention from researchers with experimental or theoretical background. Here we review attempts to analyze and model specific signaling systems. We review the structure of recurrent building blocks of signaling pathways and their integration into more comprehensive models, which enables the understanding of complex cellular processes. The variety of mechanisms found and modeling techniques used are illustrated with models of different signaling pathways. Focusing on the close interplay between experimental investigation of pathways and the mathematical representations of cellular dynamics, we discuss challenges and perspectives that emerge in studies of signaling systems