Quantitative Biology

We present a symbolic algorithmic approach that allows to compute invariant manifolds and corresponding reduced systems for differential equations modeling biological networks which comprise chemical reaction networks for cellular biochemistry, and compartmental models for pharmacology, epidemiology and ecology. Multiple time scales of a given network are obtained by scaling, based on tropical geometry. Our reduction is mathematically justified within a singular perturbation setting. The existence of invariant manifolds is subject to hyperbolicity conditions, for which we propose an algorithmic test based on Hurwitz criteria. We finally obtain a sequence of nested invariant manifolds and respective reduced systems on those manifolds. Our theoretical results are generally accompanied by rigorous algorithmic descriptions suitable for direct implementation based on existing off-the-shelf software systems, specifically symbolic computation libraries and Satisfiability Modulo Theories solvers. We present computational examples taken from the well-known BioModels database using our own prototypical implementations.

One of the most difficult problems difficult problem in systems biology is to discover protein-protein interactions as well as their associated functions. The analysis and alignment of protein-protein interaction networks (PPIN), which are the standard model to describe protein-protein interactions, has become a key ingredient to obtain functional orthologs as well as evolutionary conserved pathways and protein complexes. Several methods have been proposed to solve the PPIN alignment problem, aimed to match conserved subnetworks or functionally related proteins. However, the right balance between considering network topology and biological information is one of the most difficult and key points in any PPIN alignment algorithm which, unfortunately, remains unsolved. Therefore, in this work, we propose AligNet, a new method and software tool for the pairwise global alignment of PPIN that produces biologically meaningful alignments and more efficient computations than state-of-the-art methods and tools, by achieving a good balance between structural matching and protein function conservation as well as reasonable running times.

Kinetic proofreading is an error correction mechanism present in the processes of the central dogma and beyond, and typically requires the free energy of nucleotide hydrolysis for its operation. Though the molecular players of many biological proofreading schemes are known, our understanding of how energy consumption is managed to promote fidelity remains incomplete. In our work, we introduce an alternative conceptual scheme called 'the piston model of proofreading' where enzyme activation through hydrolysis is replaced with allosteric activation achieved through mechanical work performed by a piston on regulatory ligands. Inspired by Feynman's ratchet and pawl mechanism, we consider a mechanical engine designed to drive the piston actions powered by a lowering weight, whose function is analogous to that of ATP synthase in cells. Thanks to its mechanical design, the piston model allows us to tune the 'knobs' of the driving engine and probe the graded changes and trade-offs between speed, fidelity and energy dissipation. It provides an intuitive explanation of the conditions necessary for optimal proofreading and reveals the unexpected capability of allosteric molecules to beat the Hopfield limit of fidelity by leveraging the diversity of states available to them. The framework that we built for the piston model can also serve as a basis for additional studies of driven biochemical systems.

Computational techniques are required for narrowing down the vast space of possibilities to plausible prebiotic scenarios, since precise information on the molecular composition, the dominant reaction chemistry, and the conditions for that era are scarce. The exploration of large chemical reaction networks is a central aspect in this endeavour. While quantum chemical methods can accurately predict the structures and reactivities of small molecules, they are not efficient enough to cope with large-scale reaction systems. The formalization of chemical reactions as graph grammars provides a generative system, well grounded in category theory, at the right level of abstraction for the analysis of large and complex reaction networks. An extension of the basic formalism into the realm of integer hyperflows allows for the identification of complex reaction patterns, such as auto-catalysis, in large reaction networks using optimization techniques.

Cells process external and internal signals through chemical interactions. Cells that constitute the immune system (e.g., antigen presenting cell, T-cell, B-cell, mast cell) can have different functions (e.g., adaptive memory, inflammatory response) depending on the type and number of receptor molecules on the cell surface and the specific intracellular signaling pathways activated by those receptors. Explicitly modeling and simulating kinetic interactions between molecules allows us to pose questions about the dynamics of a signaling network under various conditions. However, the application of chemical kinetics to biochemical signaling systems has been limited by the complexity of the systems under consideration. Rule-based modeling (BioNetGen, Kappa, Simmune, PySB) is an approach to address this complexity. In this chapter, by application to the Fc ε RI receptor system, we will explore the origins of complexity in macromolecular interactions, show how rule-based modeling can be used to address complexity, and demonstrate how to build a model in the BioNetGen framework. Open source BioNetGen software and documentation are available at this http URL.

Gene regulatory network (GRN) plays a central role in system biology and genomics. It provides a promising way to model and study complex biological processes. Several computational methods have been developed for the construction and analysis of GRN. In particular, Petri net and its variants were introduced for GRN years ago. On the other hand, Petri net theory itself has been rapidly advanced recently. Especially noteworthy is the combination or treatment of Petri net with the mathematical framework of category theory (categorization), which endows Petri net with the power of abstraction and composability. Open Petri net is a state-of-art implementation of such "categorized" Petri nets. Applying open Petri net to GRN may potentially facilitate the modeling of large scale GRNs. In this manuscript, we took a shallow step towards that direction.

Steady state is an essential concept in reaction networks. Its stability reflects fundamental characteristics of several biological phenomena such as cellular signal transduction and gene expression. Because biochemical reactions occur at the cellular level, they are affected by unavoidable fluctuations. Although several methods have been proposed to detect and analyze the stability of steady states for deterministic models, these methods cannot be applied to stochastic reaction networks. In this paper, we propose an algorithm based on algebraic computations to calculate parameter regions for constrained steady-state distribution of stochastic reaction networks, in which the means and variances satisfy some given inequality constraints. To evaluate our proposed method, we perform computer simulations for three typical chemical reactions and demonstrate that the results obtained with our method are consistent with the simulation results.

Discriminating between correct and incorrect substrates is a core process in biology but how is energy apportioned between the conflicting demands of accuracy ( μ ), speed ( σ ) and total entropy production rate ( P )? Previous studies have focussed on biochemical networks with simple structure or relied on simplifying kinetic assumptions. Here, we use the linear framework for timescale separation to analytically examine steady-state probabilities away from thermodynamic equilibrium for networks of arbitrary complexity. We also introduce a method of scaling parameters that is inspired by Hopfield's treatment of kinetic proofreading. Scaling allows asymptotic exploration of high-dimensional parameter spaces. We identify in this way a broad class of complex networks and scalings for which the quantity σln(μ)/P remains asymptotically finite whenever accuracy improves from equilibrium, so that μ eq /μ→0 . Scalings exist, however, even for Hopfield's original network, for which σln(μ)/P is asymptotically infinite, illustrating the parametric complexity. Outside the asymptotic regime, numerical calculations suggest that, under more restrictive parametric assumptions, networks satisfy the bound, σln(μ/ μ eq )/P<1 , and we discuss the biological implications for discrimination by ribosomes and DNA polymerase. The methods introduced here may be more broadly useful for analysing complex networks that implement other forms of cellular information processing.

The art of viticulture and the quest for making wines has a long tradition and it just started recently that mathematicians entered this field with their main contribution of modelling alcoholic fermentation. These models consist of systems of ordinary differential equations that describe the kinetics of the bio-chemical reactions occurring in the fermentation process. The aim of this paper is to present a new model of wine fermentation that accurately describes the yeast dying component, the presence of glucose transporters, and the formation of aromas and acids. Therefore the new model could become a valuable tool to predict the taste of the wine and provide the starting point for an emerging control technology that aims at improving the quality of the wine by steering a well-behaved fermentation process that is also energetically more efficient. Results of numerical simulations are presented that successfully confirm the validity of the proposed model by comparison with real data.

Sequence alignment has had an enormous impact on our understanding of biology, evolution, and disease. The alignment of biological {\em networks} holds similar promise. Biological networks generally model interactions between biomolecules such as proteins, genes, metabolites, or mRNAs. There is strong evidence that the network topology -- the "structure" of the network -- is correlated with the functions performed, so that network topology can be used to help predict or understand function. However, unlike sequence comparison and alignment -- which is an essentially solved problem -- network comparison and alignment is an NP-complete problem for which heuristic algorithms must be used. Here we introduce SANA, the {\it Simulated Annealing Network Aligner}. SANA is one of many algorithms proposed for the arena of biological network alignment. In the context of global network alignment, SANA stands out for its speed, memory efficiency, ease-of-use, and flexibility in the arena of producing alignments between 2 or more networks. SANA produces better alignments in minutes on a laptop than most other algorithms can produce in hours or days of CPU time on large server-class machines. We walk the user through how to use SANA for several types of biomolecular networks. Availability: this https URL