Showing papers presented at "Computational Methods in Systems Biology in 2021"

BioFVM-X: an MPI+OpenMP 3-D simulator for biological systems

Abstract: Multi-scale simulations require parallelization to address large-scale problems, such as real-sized tumor simulations. BioFVM is a software package that solves diffusive transport Partial Differential Equations for 3-D biological simulations successfully applied to tissue and cancer biology problems. Currently, BioFVM is only shared-memory parallelized using OpenMP, greatly limiting the execution of large-scale jobs in HPC clusters. We present BioFVM-X: an enhanced version of BioFVM capable of running on multiple nodes. BioFVM-X uses MPI+OpenMP to parallelize the generic core kernels of BioFVM and shows promising scalability in large 3-D problems with several hundreds diffusible substrates and \(\approx \)0.5 billion voxels. The BioFVM-X source code, examples and documentation, are available under the BSD 3-Clause license at https://gitlab.bsc.es/gsaxena/biofvm_x.

Web-Based Structural Identifiability Analyzer.

Abstract: Parameter identifiability describes whether, for a given differential model, one can determine parameter values from model equations. Knowing global or local identifiability properties allows construction of better practical experiments to identify parameters from experimental data. In this work, we present a web-based software tool that allows to answer specific identifiability queries. Concretely, our toolbox can determine identifiability of individual parameters of the model and also provide all functions of parameters that are identifiable (also called identifiable combinations) from single or multiple experiments. The program is freely available at https://maple.cloud/app/6509768948056064.

A Roadmap of Cancer: From the Historical Evidence to Recent Salivary Metabolites-based Nanobiosensor Diagnostic Devices

Abstract: The etymology of the term cancer for a dysregulated balance of cell proliferation and cell death may be of the recent centenary. But the occurrence of cancer was reported at various periods in the history. Even though research towards a cure for cancer has received higher interest in various scientific domains due to its need for mankind, appropriate therapy for the complete cure of cancer is yet to be resolved by the research community. On this note, this review emphasizes on the brief overview of the historical beliefs on cancer occurrence, scientific mythology, and also discusses the recent scientific advancement in the diagnosis of cancer. The nanotechnological approaches for the diagnosis of cancer in ex-vivo conditions by means of the point of care devices are highly needed in recent years. This is for the reason that they have a high sensitivity to the biochemical interaction of the metabolites, low cost, and could be used for mass screening of the wide rural public, where the advanced imaging modalities are out of reach. Herein, we emphasize the importance of saliva as a mirror to the body’s health and using nanotechnology-based biosensors, various types of cancer could be diagnosed from salivary metabolites.

Compiling Elementary Mathematical Functions into Finite Chemical Reaction Networks via a Polynomialization Algorithm for ODEs

Abstract: The Turing completeness result for continuous chemical reaction networks (CRN) shows that any computable function over the real numbers can be computed by a CRN over a finite set of formal molecular species using at most bimolecular reactions with mass action law kinetics. The proof uses a previous result of Turing completeness for functions defined by polynomial ordinary differential equations (PODE), the dualrail encoding of real variables by the difference of concentration between two molecular species, and a back-end quadratization transformation to restrict to elementary reactions with at most two reactants. In this paper, we present a polynomialization algorithm of quadratic time complexity to transform a system of elementary differential equations in PODE. This algorithm is used as a front-end transformation to compile any elementary mathematical function, either of time or of some input species, into a finite CRN. We illustrate the performance of our compiler on a benchmark of elementary functions relevant to CRN design problems in synthetic biology specified by mathematical functions. In particular, the abstract CRN obtained by compilation of the Hill function of order 5 is compared to the natural CRN structure of MAPK signalling networks.

Reducing Boolean Networks with Backward Boolean Equivalence

Abstract: Boolean Networks (BNs) are established models to qualitatively describe biological systems. The analysis of BNs might be infeasible for medium to large BNs due to the state-space explosion problem. We propose a novel reduction technique called Backward Boolean Equivalence (BBE), which preserves some properties of interest of BNs. In particular, reduced BNs provide a compact representation by grouping variables that, if initialized equally, are always updated equally. The resulting reduced state space is a subset of the original one, restricted to identical initialization of grouped variables. The corresponding trajectories of the original BN can be exactly restored. We show the effectiveness of BBE by performing a large-scale validation on the whole GINsim BN repository. In selected cases, we show how our method enables analyses that would be otherwise intractable. Our method complements, and can be combined with, other reduction methods found in the literature.

Abstraction of Markov Population Dynamics via Generative Adversarial Nets

Abstract: Markov Population Models are a widespread formalism used to model the dynamics of complex systems, with applications in Systems Biology and many other fields. The associated Markov stochastic process in continuous time is often analyzed by simulation, which can be costly for large or stiff systems, particularly when a massive number of simulations has to be performed (e.g. in a multi-scale model). A strategy to reduce computational load is to abstract the population model, replacing it with a simpler stochastic model, faster to simulate. Here we pursue this idea, building on previous works and constructing a generator capable of producing stochastic trajectories in continuous space and discrete time. This generator is learned automatically from simulations of the original model in a Generative Adversarial setting. Compared to previous works, which rely on deep neural networks and Dirichlet processes, we explore the use of state of the art generative models, which are flexible enough to learn a full trajectory rather than a single transition kernel.

Explainable Artificial Neural Network for Recurrent Venous Thromboembolism Based on Plasma Proteomics

Abstract: Venous thromboembolism (VTE) is the third most common cardiovascular disease, affecting \(\sim \)1,000,000 individuals each year in Europe. VTE is characterized by an annual recurrent rate of \(\sim \)6%, and \(\sim \)30% of patients with unprovoked VTE will face a recurrent event after a six-month course of anticoagulant treatment. Even if guidelines recommend life-long treatment for these patients, about \(\sim \)70% of them will never experience a recurrence and will receive unnecessary lifelong anti-coagulation that is associated with increased risk of bleeding and is highly costly for the society. There is then urgent need to identify biomarkers that could distinguish VTE patients with high risk of recurrence from low-risk patients.

Aeon 2021: Bifurcation Decision Trees in Boolean Networks.

Abstract: Aeon is a recent tool which enables efficient analysis of long-term behaviour of asynchronous Boolean networks with unknown parameters. In this tool paper, we present a novel major release of Aeon (Aeon 2021) which introduces substantial new features compared to the original version. These include (i) enhanced static analysis functionality that verifies integrity of the Boolean network with its regulatory graph; (ii) state-space visualisation of individual attractors; (iii) stability analysis of network variables with respect to parameters; and finally, (iv) a novel decision-tree based interactive visualisation module allowing the exploration of complex relationships between parameters and network behaviour. Aeon 2021 is open-source, fully compatible with SBML-qual models, and available as an online application with an independent native compute engine responsible for resource-intensive tasks. The paper artefact is available via https://doi.org/10.5281/zenodo.5008293.

Cell Culture Studies: A Promising Approach to the Metabolomic Study of Human Aging

Abstract: With the increasing aging of the world’s population, a detailed study of the characteristics of aging, and the pathologies related to this process, are crucial to the development of targeted anti-aging therapies. Therefore, there are several study models for the study of aging, from computational models to animals or even to cell cultures. The latter have shown high potential for aging studies as they are easier to handle, cheaper, do not require the same level of ethical consideration required for animal and human studies, and present little biological heterogeneity when grown under the same conditions and in the same context population. For aging studies, these characteristics are a great advantage since cells have a considerable variety of morphologic characteristics and markers that can be studied. Thus, the aim of this review is to offer an overview of the models used in studies of aging, with a focus on cell culture models, presenting the advantages and disadvantages of cell culture in the study of aging, of what information can we extract of these studies and how cell studies can be compared with the other models.

Learning Boolean controls in regulated metabolic networks: a case-study

Abstract: Many techniques have been developed to infer Boolean regulations from a prior knowledge network and experimental data. Existing methods are able to reverse-engineer Boolean regulations for transcriptional and signaling networks, but they fail to infer regulations that control metabolic networks. This paper provides a formalisation of the inference of regulations for metabolic networks as a satisfiability problem with two levels of quantifiers, and introduces a method based on Answer Set Programming to solve this problem on a small-scale example.

Metabolite Profiling of Different Solvent Extracts of the Microalgae Chlorella vulgaris Via 1H NMR-Based Metabolomics

Abstract: In the present study, profiling of the cultured Chlorella vulgaris metabolome was carried out via1H NMR metabolite profiling of 6 different solvent extracts. The results indicated that the six solvent extracts have metabolite profiles that are clearly different from each other. Multivariate data analysis (MVA) reveals that ethyl acetate and ethanol extracts were well separated from the aqueous extract by PC1 while being well separated from each other by PC2. The same observations were seen with chloroform and 50% ethanol extracts. In contrast, the chemical shift signals for hexane extract clusters in-between that of chloroform and 50% ethanol, indicated that they have similar chemical profiles. Using partial least square discriminative analysis (PLS-DA), compounds responsible for the group separation were identified from the loading plot. Detailed examination of the loading plot shows that ethanol and ethyl acetate extracts contain significantly higher amounts of carotenoids, amino acids, vitamins and fatty acids. A total of 35 compounds were detected from the 6 different solvents upon which the ethanolic and ethyl acetate extracts were identified to contain more metabolites and in a wider range than the other organic solvent extracts. Hence, these two extracts would be more appropriate in metabolite extraction for analysis and for medicinal purposes. Therefore, NMR spectroscopy, in compliment with the right choice of solvent for extraction, could be utilized by relevant industries to evaluate and obtain maximum important metabolites in a shorter time. In addition to possession of high diverse metabolites, the microalgae C. vulgaris could serve as an important functional food ingredient in the aquaculture industry and may possibly be considered as a source of biofuel.

Ppsim: A Software Package for Efficiently Simulating and Visualizing Population Protocols.

Abstract: We introduce ppsim [28], a software package for efficiently simulating population protocols, a widely-studied subclass of chemical reaction networks (CRNs) in which all reactions have two reactants and two products. Each step in the dynamics involves picking a uniform random pair from a population of n molecules to collide and have a (potentially null) reaction. In a recent breakthrough, Berenbrink, Hammer, Kaaser, Meyer, Penschuck, and Tran [6] discovered a population protocol simulation algorithm quadratically faster than the naive algorithm, simulating \(\varTheta (\sqrt{n})\) reactions in constant time (independently of n, though the time scales with the number of species), while preserving the exact stochastic dynamics.

Automated Inference of Production Rules for Glycans

Abstract: Glycans are tree-like polymers made up of sugar monomer building blocks. They are found on the surface of all living cells, and distinct glycan trees act as identity markers for distinct cell types. Proteins called GTase enzymes assemble glycans via the successive addition of monomer building blocks. The rules by which the enzymes operate are not fully understood. In this paper, we present the first SMT-solver-based iterative method that infers the assembly process of the glycans by analyzing the set of glycans from a cell. We have built a tool based on the method and applied it to infer rules based on published glycan data.

Protein Noise and Distribution in a Two-Stage Gene-Expression Model Extended by an mRNA Inactivation Loop.

Abstract: Chemical reaction networks involving molecular species at low copy numbers lead to stochasticity in protein levels in gene expression at the single-cell level. Mathematical modelling of this stochastic phenomenon enables us to elucidate the underlying molecular mechanisms quantitatively. Here we present a two-stage stochastic gene expression model that extends the standard model by an mRNA inactivation loop. The extended model exhibits smaller protein noise than the original two-stage model. Interestingly, the fractional reduction of noise is a non-monotonous function of protein stability, and can be substantial especially if the inactivated mRNA is stable. We complement the noise study by an extensive mathematical analysis of the joint steady-state distribution of active and inactive mRNA and protein species. We determine its generating function and derive a recursive formula for the protein distribution. The results of the analytical formula are cross-validated by kinetic Monte-Carlo simulation.

Population Design for Synthetic Gene Circuits.

Abstract: Synthetic biologists use and combine diverse biological parts to build systems such as genetic circuits that perform desirable functions in, for example, biomedical or industrial applications. Computer-aided design methods have been developed to help choose appropriate network structures and biological parts for a given design objective. However, they almost always model the behavior of the network in an average cell, despite pervasive cell-to-cell variability. Here, we present a computational framework to guide the design of synthetic biological circuits while accounting for cell-to-cell variability explicitly. Our design method integrates a NonLinear Mixed-Effect (NLME) framework into an existing algorithm for design based on ordinary differential equation (ODE) models. The analysis of a recently developed transcriptional controller demonstrates first insights into design guidelines when trying to achieve reliable performance under cell-to-cell variability. We anticipate that our method not only facilitates the rational design of synthetic networks under cell-to-cell variability, but also enables novel applications by supporting design objectives that specify the desired behavior of cell populations.

Interpretable Exact Linear Reductions via Positivity.

Abstract: Kinetic models of biochemical systems used in the modern literature often contain hundreds or even thousands of variables. While these models are convenient for detailed simulations, their size is often an obstacle to deriving mechanistic insights. One way to address this issue is to perform an exact model reduction by finding a self-consistent lower-dimensional projection of the corresponding dynamical system.

Microbial Community Decision Making Models in Batch and Chemostat Cultures

Abstract: Microbial community simulations using genome scale metabolic networks (GSMs) are relevant for many application areas, such as the analysis of the human microbiome. Such simulations rely on assumptions about the culturing environment, affecting if the culture may reach a metabolically stationary state with constant microbial concentrations. They also require assumptions on decision making by the microbes: metabolic strategies can be in the interest of individual community members or of the whole community. However, the impact of such common assumptions on community simulation results has not been investigated systematically. Here, we investigate four combinations of assumptions, elucidate how they are applied in literature, provide novel mathematical formulations for their simulation, and show how the resulting predictions differ qualitatively. Crucially, our results stress that different assumption combinations give qualitatively different predictions on microbial coexistence by differential substrate utilization. This fundamental mechanism is critically under explored in the steady state GSM literature with its strong focus on coexistence states due to crossfeeding (division of labor).

Greening R. Thomas’ Framework with Environment Variables: A Divide and Conquer Approach

Abstract: When we model a complex biological system, we try to understand the causality chains that explain the different behaviours observed. However, these observations are often made under experimental conditions which are not necessarily comparable since they depend on the culture medium for example. The construction of a right modelisation therefore depends on our ability to take into account all this information in a single framework.

Neural Networks to Predict Survival from RNA-seq Data in Oncology

Abstract: Survival analysis consists of studying the elapsed time until an event of interest, such as the death or recovery of a patient in medical studies. This work explores the potential of neural networks in survival analysis from clinical and RNA-seq data. If the neural network approach is not recent in survival analysis, methods were classically considered for low-dimensional input data. But with the emergence of high-throughput sequencing data, the number of covariates of interest has become very large, with new statistical issues to consider. We present and test a few recent neural network approaches for survival analysis adapted to high-dimensional inputs.

LNetReduce: Tool for Reducing Linear Dynamic Networks with Separated Timescales.

Abstract: We introduce LNetReduce, a tool that simplifies linear dynamic networks. Dynamic networks are represented as digraphs labeled by integer timescale orders. Such models describe deterministic or stochastic monomolecular chemical reaction networks, but also random walks on weighted protein-protein interaction networks, spreading of infectious diseases and opinion in social networks, communication in computer networks. The reduced network is obtained by graph and label rewriting rules and reproduces the full network dynamics with good approximation at all timescales. The tool is implemented in Python with a graphical user interface. We discuss applications of LNetReduce to network design and to the study of the fundamental relation between timescales and topology in complex dynamic networks.

Nonlinear Pattern Matching in Rule-Based Modeling Languages.

Abstract: Rule-based modeling is an established paradigm for specifying simulation models of biochemical reaction networks. The expressiveness of rule-based modeling languages depends heavily on the expressiveness of the patterns on the left side of rules. Nonlinear patterns allow variables to occur multiple times. Combined with variables used in expressions, they provide great expressive power, in particular to express dynamics in discrete space. This has been exploited in some of the rule-based languages that were proposed in the last years. We focus on precisely defining the operational semantics of matching nonlinear patterns. We first adopt the usual approach to match nonlinear patterns by translating them to a linear pattern. We then introduce an alternative semantics that propagates values from one occurrence of a variable to other ones, and show that this novel approach permits a more efficient pattern matching algorithm. We confirm this theoretical result by benchmarking proof-of-concept implementations of both approaches.