Quantitative Biology

Temporal variations in biological systems and more generally in natural sciences are typically modelled as a set of Ordinary, Partial, or Stochastic Differential or Difference Equations. Algorithms for learning the structure and the parameters of a dynamical system are distinguished based on whether time is discrete or continuous, observations are time-series or time-course, and whether the system is deterministic or stochastic, however, there is no approach able to handle the various types of dynamical systems simultaneously. In this paper, we present a unified approach to infer both the structure and the parameters of nonlinear dynamical systems of any type under the restriction of being linear with respect to the unknown parameters. Our approach, which is named Unified Sparse Dynamics Learning (USDL), constitutes of two steps. First, an atemporal system of equations is derived through the application of the weak formulation. Then, assuming a sparse representation for the dynamical system, we show that the inference problem can be expressed as a sparse signal recovery problem, allowing the application of an extensive body of algorithms and theoretical results. Results on simulated data demonstrate the efficacy and superiority of the USDL algorithm as a function of the experimental setup (sample size, number of time measurements, number of interventions, noise level). Additionally, USDL's accuracy significantly correlates with theoretical metrics such as the exact recovery coefficient. On real single-cell data, the proposed approach is able to induce high-confidence subgraphs of the signaling pathway. USDL algorithm has been integrated in SCENERY (\url{this http URL}); an online tool for single-cell mass cytometry analytics.

In this work maximum entropy distributions in the space of steady states of metabolic networks are defined upon constraining the first and second moment of the growth rate. Inherent bistability of fast and slow phenotypes, akin to a Van-Der Waals picture, emerges upon considering control on the average growth (optimization/repression) and its fluctuations (heterogeneity). This is applied to the carbon catabolic core of E.coli where it agrees with some stylized facts on the persisters phenotype and it provides a quantitative map with metabolic fluxes, opening for the possibility to detect coexistence from flux data. Preliminary analysis on data for E.Coli cultures in standard conditions shows, on the other hand, degeneracy for the inferred parameters that extend in the coexistence region.

Many discrete models of biological networks rely exclusively on Boolean variables and many tools and theorems are available for analysis of strictly Boolean models. However, multilevel variables are often required to account for threshold effects, in which knowledge of the Boolean case does not generalise straightforwardly. This motivated the development of conversion methods for multilevel to Boolean models. In particular, Van Ham's method has been shown to yield a one-to-one, neighbour and regulation preserving dynamics, making it the de facto standard approach to the problem. However, Van Ham's method has several drawbacks: most notably, it introduces vast regions of "non-admissible" states that have no counterpart in the multilevel, original model. This raises special difficulties for the analysis of interaction between variables and circuit functionality, which is believed to be central to the understanding of dynamic properties of logical models. Here, we propose a new multilevel to Boolean conversion method, with software implementation. Contrary to Van Ham's, our method doesn't yield a one-to-one transposition of multilevel trajectories, however, it maps each and every Boolean state to a specific multilevel state, thus getting rid of the non-admissible regions and, at the expense of (apparently) more complicated, "parallel" trajectories. One of the prominent features of our method is that it preserves dynamics and interaction of variables in a certain manner. As a demonstration of the usability of our method, we apply it to construct a new Boolean counter-example to the well-known conjecture that a local negative circuit is necessary to generate sustained oscillations. This result illustrates the general relevance of our method for the study of multilevel logical models.

Understanding the mathematical properties of graphs underling biological systems could give hints on the evolutionary mechanisms behind these structures. In this article we perform a complete statistical analysis over thousands of graphs representing metabolic and protein-protein interaction (PPI) networks. First, we investigate the quality of fits obtained for the nodes degree distributions to power-law functions. This analysis suggests that a power-law distribution poorly describes the data except for the far right tail in the case of PPI networks. Next we obtain descriptive statistics for the main graph parameters and try to identify the properties that deviate from the expected values had the networks been built by randomly linking nodes with the same degree distribution. This survey identifies the properties of biological networks which are not solely the result of their degree distribution, but emerge from yet unidentified mechanisms other than those that drive these distributions. The findings suggest that, while PPI networks have properties that differ from their expected values in their randomized versions with great statistical significance, the differences for metabolic networks have a smaller statistical significance, though it is possible to identify some drift.

Gene regulation is an important fundamental biological process. The regulation of gene expression is managed through a variety of methods including epigenetic processes (e.g., DNA methylation). Understanding the role of epigenetic changes in gene expression is a fundamental question of molecular biology. Predictions of gene expression values from epigenetic data have tremendous research and clinical potential. Despite active research, studies to date have focused on using statistical models to predict gene expression from methylation data. In contrast, dynamical systems can be used to generate a model to predict gene expression using epigenetic data and a gene regulatory network (GRN) which can also serve as a mechanistic hypothesis. Here we present a novel stochastic dynamical systems model that predicts gene expression levels from methylation data of genes in a given GRN. We provide an evaluation of the model using real patient data and a GRN created from robust reference sources. Software for dataset preparation, model parameter fitting and prediction generation, and reporting are available at \verb|this https URL|.

Computation biology helps to understand all processes in organisms from interaction of molecules to complex functions of whole organs. Therefore, there is a need for mathematical methods and models that deliver logical explanations in a reasonable time. For the last few years there has been a growing interest in biological theory connected to finite fields: the algebraic modeling tools used up to now are based on Gröbner bases or Boolean group. Let n variables representing gene products, changing over the time on p values. A Polynomial dynamical system (PDS) is a function which has several components, each one is a polynom with n variables and coefficient in the finite field Z/pZ that model the evolution of gene products. We propose herein a method using algebraic separators, which are special polynomials abundantly studied in effective Galois theory. This approach avoids heavy calculations and provides a first Polynomial model in linear time.

In this work, a machine learning approach for identifying the multi-omics metabolic regulatory control circuits inside the pathways is described. Therefore, the identification of bacterial metabolic pathways that are more regulated than others in term of their multi-omics follows from the analysis of these circuits . This is a consequence of the alternation of the omic values of codon usage and protein abundance along with the circuits. In this work, the E.Coli's Glycolysis and its multi-omic circuit features are shown as an example.

Gene regulatory networks (GRNs) describe how a collection of genes governs the processes within a cell. Understanding how GRNs manage to consistently perform a particular function constitutes a key question in cell biology. GRNs are frequently modeled as Boolean networks, which are intuitive, simple to describe, and can yield qualitative results even when data is sparse. We generate an expandable database of published, expert-curated Boolean GRN models, and extracted the rules governing these networks. A meta-analysis of this diverse set of models enables us to identify fundamental design principles of GRNs. The biological term canalization reflects a cell's ability to maintain a stable phenotype despite ongoing environmental perturbations. Accordingly, Boolean canalizing functions are functions where the output is already determined if a specific variable takes on its canalizing input, regardless of all other inputs. We provide a detailed analysis of the prevalence of canalization and show that most rules describing the regulatory logic are highly canalizing. Independent from this, we also find that most rules exhibit a high level of redundancy. An analysis of the prevalence of small network motifs, e.g. feed-forward loops or feedback loops, in the wiring diagram of the identified models reveals several highly abundant types of motifs, as well as a surprisingly high overabundance of negative regulations in complex feedback loops. Lastly, we provide the strongest evidence thus far in favor of the hypothesis that GRNs operate at the critical edge between order and chaos.

Essential protein plays a crucial role in the process of cell life. The identification of essential proteins can not only promote the development of drug target technology, but also contribute to the mechanism of biological evolution. There are plenty of scholars who pay attention to discovering essential proteins according to the topological structure of protein network and biological information. The accuracy of protein recognition still demands to be improved. In this paper, we propose a method which integrate the clustering coefficient in protein complexes and topological properties to determine the essentiality of proteins. First, we give the definition of In-clustering coefficient (IC) to describe the properties of protein complexes. Then we propose a new method, complex edge and node clustering coefficient (CENC) to identify essential proteins. Different Protein-Protein Interaction (PPI) networks of Saccharomyces cerevisiae, MIPS and DIP are used as experimental materials. Through some experiments of logistic regression model, the results show that the method of CENC can promote the ability of recognizing essential proteins, by comparing with the existing methods DC, BC, EC, SC, LAC, NC and the recent method UC.

Despite their dynamic nature, certain chromatin marks must be maintained over the long term. This is particulary true for histone 3 lysine 9 (H3K9) trimethylation, that is involved in the maintenance of healthy differentiated cellular states by preventing inappropriate gene expression, and has been recently identified as the most efficient barrier to cellular reprogramming in nuclear transfer experiments. We propose that the capacity of the enzymes SUV39H1/2 to rebind to a minor fraction of their products, either directly or via HP1, contributes to the solidity of this mark through (i) a positive feedback involved in its establishment by the mutual enforcement of H3K9me3 and SUV39H1/2 and then (ii) a negative feedback sufficient to strongly stabilize H3K9me3 heterochromatin in post-mitotic cells by generating local enzyme concentrations capable of counteracting transient bursts of demethylation. This model does not require direct molecular interactions with adjacent nucleosomes and is favoured by a series of additional mechanisms including (i) the protection of chromatin-bound SUV39H1/2 from the turnovers of soluble proteins, which can explain the uncoupling between the cellular contents in SUV39H1 mRNA and protein; (ii) the cooperative dependence on the local density of the H3K9me3 of HP1-dependent heterochomatin condensation and, dispensably (iii) restricted enzyme exchanges with chromocenters confining the reactive bursts of SUV39H1/2 in heterochromatin. This mechanism illustrates how seemingly static epigenetic states can be firmly maintained by dynamic and reversible modifications.