Quantitative Biology

How smart can a micron-sized bag of chemicals be? How can an artificial or real cell make inferences about its environment? From which kinds of probability distributions can chemical reaction networks sample? We begin tackling these questions by showing four ways in which a stochastic chemical reaction network can implement a Boltzmann machine, a stochastic neural network model that can generate a wide range of probability distributions and compute conditional probabilities. The resulting models, and the associated theorems, provide a road map for constructing chemical reaction networks that exploit their native stochasticity as a computational resource. Finally, to show the potential of our models, we simulate a chemical Boltzmann machine to classify and generate MNIST digits in-silico.

We present an elaborate framework for formally modelling pathways in chemical reaction networks on a mechanistic level. Networks are modelled mathematically as directed multi-hypergraphs, with vertices corresponding to molecules and hyperedges to reactions. Pathways are modelled as integer hyperflows and we expand the network model by detailed routing constraints. In contrast to the more traditional approaches like Flux Balance Analysis or Elementary Mode analysis we insist on integer-valued flows. While this choice makes it necessary to solve possibly hard integer linear programs, it has the advantage that more detailed mechanistic questions can be formulated. It is thus possible to query networks for general transformation motifs, and to automatically enumerate optimal and near-optimal pathways. Similarities and differences between our work and traditional approaches in metabolic network analysis are discussed in detail. To demonstrate the applicability of the mathematical framework to real-life problems we first explore the design space of possible non-oxidative glycolysis pathways and show that recent manually designed pathways can be further optimised. We then use a model of sugar chemistry to investigate pathways in the autocatalytic formose process. A graph transformation-based approach is used to automatically generate the reaction networks of interest.

A key step in the origin of life is the emergence of a primitive metabolism. This requires the formation of a subset of chemical reactions that is both self-sustaining and collectively autocatalytic. A generic theory to study such processes (called 'RAF theory') has provided a precise and computationally effective way to address these questions, both on simulated data and in laboratory studies. One of the classic applications of this theory (arising from Stuart Kauffman's pioneering work in the 1980s) involves networks of polymers under cleavage and ligation reactions; in the first part of this paper, we provide the first exact description of the number of such reactions under various model assumptions. Conclusions from earlier studies relied on either approximations or asymptotic counting, and we show that the exact counts lead to similar (though not always identical) asymptotic results. In the second part of the paper, we solve some questions posed in more recent papers concerning the computational complexity of some key questions in RAF theory. In particular, although there is a fast algorithm to determine whether or not a catalytic reaction network contains a subset that is both self-sustaining and autocatalytic (and, if so, find one), determining whether or not sets exist that satisfy certain additional constraints exist turns out to be NP-complete.

Both action potentials and mechanosensitive signalling are an important communication mechanisms in plants. Considering an information theoretic framework, this paper explores the effective range of multiple action potentials for a long chain of cells (i.e., up to 100) in different configurations, and introduces the study of multiple mechanosensitive activation signals (generated due to a mechanical stimulus) in plants. For both these signals, we find that the mutual information per cell and information propagation speed tends to increase up to a certain number of receiver cells. However, as the number of cells increase beyond 10 to 12, the mutual information per cell starts to decrease. To validate our model and results, we include an experimental verification of the theoretical model, using a PhytlSigns biosignal amplifier, allowing us to measure the magnitude of the voltage associated with the multiple AP and mechanosensitive activation signals induced by different stimulus in plants. Experimental data is used to calculate the mutual information and information propagation speed, which is compared with corresponding numerical results. Since these signals are used for a variety of important tasks within the plant, understanding them may lead to new bioengineering methods for plants.

A practical, biologically motivated case of protein complexes (immunoglobulin G and FcRII receptors) moving on the surface of mastcells, that are common parts of an immunological system, is investigated. Proteins are considered as nanomachines creating a nanonetwork. Accurate molecular models of the proteins and the fluorophores which act as their nanoantennas are used to simulate the communication between the nanomachines when they are close to each other. The theory of diffusion-based Brownian motion is applied to model movements of the proteins. It is assumed that fluorophore molecules send and receive signals using the Forster Resonance Energy Transfer. The probability of the efficient signal transfer and the respective bit error rate are calculated and discussed.

COVID-19 is an infection caused by SARS-CoV-2 (Severe Acute Respiratory Syndrome coronavirus 2), which has caused a global outbreak. Current research efforts are focused on the understanding of the molecular mechanisms involved in SARS-CoV-2 infection in order to propose drug-based therapeutic options. Transcriptional changes due to epigenetic regulation are key host cell responses to viral infection and have been studied in SARS-CoV and MERS-CoV; however, such changes are not fully described for SARS-CoV-2. In this study, we analyzed multiple transcriptomes obtained from cell lines infected with MERS-CoV, SARS-CoV and SARS-CoV-2, and from COVID-19 patient-derived samples. Using integrative analyses of gene co-expression networks and de-novo pathway enrichment, we characterize different gene modules and protein pathways enriched with Transcription Factors or Epifactors relevant for SARS-CoV-2 infection. We identified EP300, MOV10, RELA and TRIM25 as top candidates, and more than 60 additional proteins involved in the epigenetic response during viral infection that have therapeutic potential. Our results show that targeting the epigenetic machinery could be a feasible alternative to treat COVID-19.

In the present work, we study the properties of biological networks by applying analogous notions of fundamental concepts in Riemannian geometry and optimal mass transport to discrete networks described by weighted graphs. Specifically, we employ possible generalizations of the notion of Ricci curvature on Riemannian manifold to discrete spaces in order to infer certain robustness properties of the networks of interest. We compare three possible discrete notions of Ricci curvature (Olivier Ricci curvature, Bakry-Émery Ricci curvature, and Forman Ricci curvature) on some model and biological networks. While the exact relationship of each of the three definitions of curvature to one another is still not known, they do yield similar results on our biological networks of interest. These notions are initially defined on positively weighted graphs; however, Forman-Ricci curvature can also be defined on directed positively weighted networks. We will generalize this notion of directed Forman Ricci curvature on the network to a form that also considers the signs of the directions (e. g., activator and repressor in transcription networks). We call this notion the \emph{signed-control Ricci curvature}. Given real biological networks are almost always directed and possess positive and negative controls, the notion of signed-control curvature can elucidate the network-based study of these complex networks. Finally, we compare the results of these notions of Ricci curvature on networks to some known network measures, namely, betweenness centrality and clustering coefficients on graphs.

Causal gene networks model the flow of information within a cell, but reconstructing them from omics data is challenging because correlation does not imply causation. Combining genomics and transcriptomics data from a segregating population allows to orient the direction of causality between gene expression traits using genomic variants. Instrumental-variable methods (IV) use a local expression quantitative trait locus (eQTL) as a randomized instrument for a gene's expression level, and assign target genes based on distal eQTL associations. Mediation-based methods (ME) additionally require that distal eQTL associations are mediated by the source gene. Here we used Findr, a software providing uniform implementations of IV, ME, and coexpression-based methods, a recent dataset of 1,012 segregants from a cross between two budding yeast strains, and the YEASTRACT database of known transcriptional interactions to compare causal gene network inference methods. We found that causal inference methods result in a significant overlap with the ground-truth, whereas coexpression did not perform better than random. A subsampling analysis revealed that the performance of ME decreases at large sample sizes, due to a loss of sensitivity when residual correlations become significant. IV methods contain false positive predictions, due to genomic linkage between eQTL instruments. IV and ME methods also have complementary roles for identifying causal genes underlying transcriptional hotspots. IV methods correctly predicted STB5 targets for a hotspot centred on the transcription factor STB5, whereas ME failed due to Stb5p auto-regulating its own expression. ME suggests a new candidate gene, DNM1, for a hotspot on Chr XII, where IV methods could not distinguish between multiple genes located within the hotspot.

In this paper, we compared cancerous and normal cell according to their protein-protein interaction network. Cancer is one of the complicated diseases and experimental investigations have been showed that protein interactions have an important role in the growth of cancer. We calculated some graph related parameters such as Number of Vertices, Number of Edges, Closeness, Graph Diameter, Graph Radius, Index of Aggregation, Connectivity, Number of Edges divided by the Number of Vertices, Degree, Cluster Coefficient, Subgraph Centrality, and Betweenness. Furthermore, the number of motifs and hubs in these networks have been measured. In this paper bone, breast, colon, kidney and liver benchmark datasets have been used for experiments. The experimental results show that Graph Degree Mean, Subgraph Centrality, Betweenness, and Hubs have higher values in the cancer cells and can be used as a measure to distinguish between normal and cancerous networks. The cancerous tissues of the five studied samples are denser in the interaction networks.

microRNAs (miRNAs) regulate gene expression at post-transcriptional level by repressing target RNA molecules. Competition to bind miRNAs tends in turn to correlate their targets, establishing effective RNA-RNA interactions that can influence expression levels, buffer fluctuations and promote signal propagation. Such a potential has been characterized mathematically for small motifs both at steady state and \red{away from stationarity}. Experimental evidence, on the other hand, suggests that competing endogenous RNA (ceRNA) crosstalk is rather weak. Extended miRNA-RNA networks could however favour the integration of many crosstalk interactions, leading to significant large-scale effects in spite of the weakness of individual links. To clarify the extent to which crosstalk is sustained by the miRNA interactome, we have studied its emergent systemic features in silico in large-scale miRNA-RNA network reconstructions. We show that, although generically weak, system-level crosstalk patterns (i) are enhanced by transcriptional heterogeneities, (ii) can achieve high-intensity even for RNAs that are not co-regulated, (iii) are robust to variability in transcription rates, and (iv) are significantly non-local, i.e. correlate weakly with miRNA-RNA interaction parameters. Furthermore, RNA levels are generically more stable when crosstalk is strongest. As some of these features appear to be encoded in the network's topology, crosstalk may functionally be favoured by natural selection. These results suggest that, besides their repressive role, miRNAs mediate a weak but resilient and context-independent network of cross-regulatory interactions that interconnect the transcriptome, stabilize expression levels and support system-level responses.