Mathematics at the eve of a historic transition in biology

A century ago physicists and mathematicians worked in tandem and established quantum mechanism. Indeed, algebras, partial differential equations, group theory, and functional analysis underpin the foundation of quantum mechanism. Currently, biology is undergoing a historic transition from qualitative, phenomenological and descriptive to quantitative, analytical and predictive. Mathematics, again, becomes a driving force behind this new transition in biology.Comment: 5 pages, 2 figure

Multi-omics integration reveals molecular networks and regulators of psoriasis.

BackgroundPsoriasis is a complex multi-factorial disease, involving both genetic susceptibilities and environmental triggers. Genome-wide association studies (GWAS) and epigenome-wide association studies (EWAS) have been carried out to identify genetic and epigenetic variants that are associated with psoriasis. However, these loci cannot fully explain the disease pathogenesis.MethodsTo achieve a comprehensive mechanistic understanding of psoriasis, we conducted a systems biology study, integrating multi-omics datasets including GWAS, EWAS, tissue-specific transcriptome, expression quantitative trait loci (eQTLs), gene networks, and biological pathways to identify the key genes, processes, and networks that are genetically and epigenetically associated with psoriasis risk.ResultsThis integrative genomics study identified both well-characterized (e.g., the IL17 pathway in both GWAS and EWAS) and novel biological processes (e.g., the branched chain amino acid catabolism process in GWAS and the platelet and coagulation pathway in EWAS) involved in psoriasis. Finally, by utilizing tissue-specific gene regulatory networks, we unraveled the interactions among the psoriasis-associated genes and pathways in a tissue-specific manner and detected potential key regulatory genes in the psoriasis networks.ConclusionsThe integration and convergence of multi-omics signals provide deeper and comprehensive insights into the biological mechanisms associated with psoriasis susceptibility

TopologyNet: Topology based deep convolutional neural networks for biomolecular property predictions

Although deep learning approaches have had tremendous success in image, video and audio processing, computer vision, and speech recognition, their applications to three-dimensional (3D) biomolecular structural data sets have been hindered by the entangled geometric complexity and biological complexity. We introduce topology, i.e., element specific persistent homology (ESPH), to untangle geometric complexity and biological complexity. ESPH represents 3D complex geometry by one-dimensional (1D) topological invariants and retains crucial biological information via a multichannel image representation. It is able to reveal hidden structure-function relationships in biomolecules. We further integrate ESPH and convolutional neural networks to construct a multichannel topological neural network (TopologyNet) for the predictions of protein-ligand binding affinities and protein stability changes upon mutation. To overcome the limitations to deep learning arising from small and noisy training sets, we present a multitask topological convolutional neural network (MT-TCNN). We demonstrate that the present TopologyNet architectures outperform other state-of-the-art methods in the predictions of protein-ligand binding affinities, globular protein mutation impacts, and membrane protein mutation impacts.Comment: 20 pages, 8 figures, 5 table

Sequence-based Multiscale Model (SeqMM) for High-throughput chromosome conformation capture (Hi-C) data analysis

In this paper, I introduce a Sequence-based Multiscale Model (SeqMM) for the biomolecular data analysis. With the combination of spectral graph method, I reveal the essential difference between the global scale models and local scale ones in structure clustering, i.e., different optimization on Euclidean (or spatial) distances and sequential (or genomic) distances. More specifically, clusters from global scale models optimize Euclidean distance relations. Local scale models, on the other hand, result in clusters that optimize the genomic distance relations. For a biomolecular data, Euclidean distances and sequential distances are two independent variables, which can never be optimized simultaneously in data clustering. However, sequence scale in my SeqMM can work as a tuning parameter that balances these two variables and deliver different clusterings based on my purposes. Further, my SeqMM is used to explore the hierarchical structures of chromosomes. I find that in global scale, the Fiedler vector from my SeqMM bears a great similarity with the principal vector from principal component analysis, and can be used to study genomic compartments. In TAD analysis, I find that TADs evaluated from different scales are not consistent and vary a lot. Particularly when the sequence scale is small, the calculated TAD boundaries are dramatically different. Even for regions with high contact frequencies, TAD regions show no obvious consistence. However, when the scale value increases further, although TADs are still quite different, TAD boundaries in these high contact frequency regions become more and more consistent. Finally, I find that for a fixed local scale, my method can deliver very robust TAD boundaries in different cluster numbers.Comment: 22 PAGES, 13 FIGURE

Lost in translation: Toward a formal model of multilevel, multiscale medicine

For a broad spectrum of low level cognitive regulatory and other biological phenomena, isolation from signal crosstalk between them requires more metabolic free energy than permitting correlation. This allows an evolutionary exaptation leading to dynamic global broadcasts of interacting physiological processes at multiple scales. The argument is similar to the well-studied exaptation of noise to trigger stochastic resonance amplification in physiological subsystems. Not only is the living state characterized by cognition at every scale and level of organization, but by multiple, shifting, tunable, cooperative larger scale broadcasts that link selected subsets of functional modules to address problems. This multilevel dynamical viewpoint has implications for initiatives in translational medicine that have followed the implosive collapse of pharmaceutical industry 'magic bullet' research. In short, failure to respond to the inherently multilevel, multiscale nature of human pathophysiology will doom translational medicine to a similar implosion

Mathematical models for somite formation

Somitogenesis is the process of division of the anterior–posterior vertebrate embryonic axis into similar morphological units known as somites. These segments generate the prepattern which guides formation of the vertebrae, ribs and other associated features of the body trunk. In this work, we review and discuss a series of mathematical models which account for different stages of somite formation. We begin by presenting current experimental information and mechanisms explaining somite formation, highlighting features which will be included in the models. For each model we outline the mathematical basis, show results of numerical simulations, discuss their successes and shortcomings and avenues for future exploration. We conclude with a brief discussion of the state of modeling in the field and current challenges which need to be overcome in order to further our understanding in this area

Reduction of dynamical biochemical reaction networks in computational biology

Biochemical networks are used in computational biology, to model the static and dynamical details of systems involved in cell signaling, metabolism, and regulation of gene expression. Parametric and structural uncertainty, as well as combinatorial explosion are strong obstacles against analyzing the dynamics of large models of this type. Multi-scaleness is another property of these networks, that can be used to get past some of these obstacles. Networks with many well separated time scales, can be reduced to simpler networks, in a way that depends only on the orders of magnitude and not on the exact values of the kinetic parameters. The main idea used for such robust simplifications of networks is the concept of dominance among model elements, allowing hierarchical organization of these elements according to their effects on the network dynamics. This concept finds a natural formulation in tropical geometry. We revisit, in the light of these new ideas, the main approaches to model reduction of reaction networks, such as quasi-steady state and quasi-equilibrium approximations, and provide practical recipes for model reduction of linear and nonlinear networks. We also discuss the application of model reduction to backward pruning machine learning techniques

Mathematical models for somite formation

Somitogenesis is the process of division of the anterior–posterior vertebrate embryonic axis into similar morphological units known as somites. These segments generate the prepattern which guides formation of the vertebrae, ribs and other associated features of the body trunk. In this work, we review and discuss a series of mathematical models which account for different stages of somite formation. We begin by presenting current experimental information and mechanisms explaining somite formation, highlighting features which will be included in the models. For each model we outline the mathematical basis, show results of numerical simulations, discuss their successes and shortcomings and avenues for future exploration. We conclude with a brief discussion of the state of modeling in the field and current challenges which need to be overcome in order to further our understanding in this area