Quantitative Biology

Processing time-dependent information requires cells to quantify the duration of past regulatory events and program the time span of future signals. At the single-cell level, timer mechanisms can be implemented with genetic circuits: sets of genes connected to achieve specific tasks. However, such systems are difficult to implement in single cells due to saturation in molecular components and stochasticity in the limited intracellular space. Multicellular implementations, on the other hand, outsource some of the components of information-processing circuits to the extracellular space, and thereby might escape those constraints. Here we develop a theoretical framework, based on a trilinear coordinate representation, to study the collective behavior of a cellular population composed of three cell types under stationary conditions. This framework reveals that distributing different processes (in our case the production, detection and degradation of a time-encoding signal) across distinct cell types enables the robust implementation of a multicellular timer. Our analysis also shows the circuit to be easily tunable by varying the cellular composition of the consortium.

Many microbial systems are known to actively reshape their proteomes in response to changes in growth conditions induced e.g. by nutritional stress or antibiotics. Part of the re-allocation accounts for the fact that, as the growth rate is limited by targeting specific metabolic activities, cells simply respond by fine-tuning their proteome to invest more resources into the limiting activity (i.e. by synthesizing more proteins devoted to it). However, this is often accompanied by an overall re-organization of metabolism, aimed at improving the growth yield under limitation by re-wiring resource through different pathways. While both effects impact proteome composition, the latter underlies a more complex systemic response to stress. By focusing on E. coli's `acetate switch', we use mathematical modeling and a re-analysis of empirical data to show that the transition from a predominantly fermentative to a predominantly respirative metabolism in carbon-limited growth results from the trade-off between maximizing the growth yield and minimizing its costs in terms of required the proteome share. In particular, E. coli's metabolic phenotypes appear to be Pareto-optimal for these objective functions over a broad range of dilutions.

Querying new information from knowledge sources, in general, and published literature, in particular, aims to provide precise and quick answers to questions raised about a system under study. In this paper, we present ACCORDION (Automated Clustering Conditional On Relating Data of Interactions tO a Network), a novel tool and a methodology to enable efficient answering of biological questions by automatically assembling new, or expanding existing models using published literature. Our approach integrates information extraction and clustering with simulation and formal analysis to allow for an automated iterative process that includes assembling, testing and selecting the most relevant models, given a set of desired system properties. We applied our methodology to a model of the circuitry that con-trols T cell differentiation. To evaluate our approach, we compare the model that we obtained, using our automated model extension approach, with the previously published manually extended T cell differentiation model. Besides demonstrating automated and rapid reconstruction of a model that was previously built manually, ACCORDION can assemble multiple models that satisfy desired properties. As such, it replaces large number of tedious or even imprac-tical manual experiments and guides alternative hypotheses and interventions in biological systems.

Some organism-specific databases about regulation in bacteria have become larger, accelerated by high-throughput methodologies, while others are no longer updated or accessible. Each database homogenize its datasets, giving rise to heterogeneity across databases. Such heterogeneity mainly encompasses different names for a gene and different network representations, generating duplicated interactions that could bias network analyses. Abasy (Across-bacteria systems) Atlas consolidates information from different sources into meta-curated regulatory networks in bacteria. The high-quality networks in Abasy Atlas enable cross-organisms analyses, such as benchmarking studies where gold standards are required. Nevertheless, network incompleteness still casts doubts on the conclusions of network analyses, and available sampling methods cannot reflect the curation process. To tackle this problem, the updated version of Abasy Atlas presented in this work provides historical snapshots of regulatory networks. Thus, network analyses can be performed at different completeness levels, making possible to identify potential bias and to predict future results. We leverage the recently found constraint in the complexity of regulatory networks to develop a novel model to quantify the total number of regulatory interactions as a function of the genome size. This completeness estimation is a valuable insight that may aid in the daunting task of network curation, prediction, and validation. The new version of Abasy Atlas provides 76 networks (204,282 regulatory interactions) covering 42 bacteria (64% Gram-positive and 36% Gram-negative) distributed in 9 species, containing 8,459 regulons and 4,335 modules.

In this work, we design a type of controller that consists of adding a specific set of reactions to an existing mass-action chemical reaction network in order to control a target species. This set of reactions is effective for both deterministic and stochastic networks, in the latter case controlling the mean as well as the variance of the target species. We employ a type of network property called absolute concentration robustness (ACR). We provide applications to the control of a multisite phosphorylation model as well as a receptor-ligand signaling system. For this framework, we use the so-called deficiency zero theorem from chemical reaction network theory as well as multiscaling model reduction methods. We show that the target species has approximately Poisson distribution with the desired mean. We further show that ACR controllers can bring robust perfect adaptation to a target species and are complementary to a recently introduced antithetic feedback controller used for stochastic chemical reactions.

Background: Genome-scale metabolic network models and constraint-based modeling techniques have become important tools for analyzing cellular metabolism. Thermodynamically infeasible cy-cles (TICs) causing unbounded metabolic flux ranges are often encountered. TICs satisfy the mass balance and directionality constraints but violate the second law of thermodynamics. Current prac-tices involve implementing additional constraints to ensure not only optimal but also loopless flux distributions. However, the mixed integer linear programming problems required to solve become computationally intractable for genome-scale metabolic models. Results: We aimed to identify the fewest needed constraints sufficient for optimality under the loop-less requirement. We found that loopless constraints are required only for the reactions that share elementary flux modes representing TICs with reactions that are part of the objective function. We put forth the concept of localized loopless constraints (LLCs) to enforce this minimal required set of loopless constraints. By combining with a novel procedure for minimal null-space calculation, the computational time for loopless flux variability analysis is reduced by a factor of 10-150 compared to the original loopless constraints and by 4-20 times compared to the currently fastest method Fast-SNP with the percent improvement increasing with model size. Importantly, LLCs offer a scalable strategy for loopless flux calculations for multi-compartment/multi-organism models of very large sizes (e.g. >104 reactions) not feasible before. Matlab functions are available at this https URL.

We consider the question whether a chemical reaction network preserves the number and stability of its positive steady states upon inclusion of inflow and outflow reactions. Often a model of a reaction network is presented without inflows and outflows, while in fact some of the species might be degraded or leaked to the environment, or be synthesized or transported into the system. We provide a sufficient and easy-to-check criterion based on the stoichiometry of the reaction network alone and discuss examples from systems biology.

Pituitary gonadotropins play an essential and pivotal role in the control of human and animal reproduction within the hypothalamic-pituitary-gonadal (HPG) axis. The computational modeling of pituitary gonadotropin signaling encompasses phenomena of different natures such as the dynamic encoding of gonadotropin secretion, and the intracellular cascades triggered by gonadotropin binding to their cognate receptors, resulting in a variety of biological outcomes. We overview historical and ongoing issues in modeling and data analysis related to gonadotropin secretion in the field of both physiology and neuro-endocrinology. We mention the different mathematical formalisms involved, their interest and limits. We discuss open statistical questions in signal analysis associated with key endocrine issues. We also review recent advances in the modeling of the intracellular pathways activated by gonadotropins, which yields promising development for innovative approaches in drug discovery. The greatest challenge to be tackled in computational modeling of pituitary gonadotropin signaling is the embedding of gonadotropin signaling within its natural multi-scale environment, from the single cell level, to the organic and whole HPG level. The development of modeling approaches of G protein-coupled receptor signaling, together with multicellular systems biology may lead to unexampled mechanistic understanding with critical expected fallouts in the therapeutic management of reproduction.

Biological systems exhibit processes on a wide range of time and length scales. This work demonstrates that models, wherein the interaction between system constituents is captured by algebraic operations, inherently allow for successive coarse-graining operations through quotients of the algebra. Thereby, the class of model is retained and all possible coarse-graining operations are encoded in the lattice of congruences of the model. We analyze a class of algebraic models generated by the subsequent and simultaneous catalytic functions of chemicals within a reaction network. Our ansatz yields coarse-graining operations that cover the network with local functional patches and delete the information about the environment, and complementary operations that resolve only the large-scale functional structure of the network. Finally, we present a geometric interpretation of the algebraic models through an analogy with classical models on vector fields. We then use the geometric framework to show how a coarse-graining of the algebraic model naturally leads to a coarse-graining of the state-space. The framework developed here is aimed at the study of the functional structure of cellular reaction networks spanning a wide range of scales.

Here we address the challenge of profiling causal properties and tracking the transformation of chemical compounds from an algorithmic perspective. We explore the potential of applying a computational interventional calculus based on the principles of algorithmic probability to chemical structure networks. We profile the sensitivity of the elements and covalent bonds in a chemical structure network algorithmically, asking whether reprogrammability affords information about thermodynamic and chemical processes involved in the transformation of different compound classes. We arrive at numerical results suggesting a correspondence between some physical, structural and functional properties. Our methods are capable of separating chemical classes that reflect functional and natural differences without considering any information about atomic and molecular properties. We conclude that these methods, with their links to chemoinformatics via algorithmic, probability hold promise for future research.