Quantitative Biology

Characterization of the differences between biological and random networks can reveal the design principles that enable the robust realization of crucial biological functions including the establishment of different cell types. Previous studies, focusing on identifying topological features that are present in biological networks but not in random networks, have, however, provided few functional insights. We use a Boolean modeling framework and ideas from spin glass literature to identify functional differences between five real biological networks and random networks with similar topological features. We show that minimal frustration is a fundamental property that allows biological networks to robustly establish cell types and regulate cell fate choice, and this property can emerge in complex networks via Darwinian evolution. The study also provides clues regarding how the regulation of cell fate choice can go awry in a disease like cancer and lead to the emergence of aberrant cell types.

In the real world, most objects and data have multiple types of attributes and inter-connections. Such data structures are named "Heterogeneous Information Networks" (HIN) and have been widely researched. Biological systems are also considered to be highly complicated HIN. In this work, we review various applications of HIN methods to biological and chemical data, discuss some advanced topics, and describe some future research directions.

We chemically characterize the symmetries underlying the exact solutions of a stochastic negatively self-regulating gene. The breaking of symmetry at low molecular number causes three effects. Two branches of the solution exist, having high and low switching rates, such that the low switching rate branch approaches deterministic behavior and the high switching rate branch exhibits sub-Fano behavior. Average protein number differs from the deterministically expected value. Bimodal probability distributions appear as the protein number becomes a readout of the ON/OFF state of the gene.

Causal ordering of key events in the cell cycle is essential for proper functioning of an organism. Yet, it remains a mystery how a specific temporal program of events is maintained despite ineluctable stochasticity in the biochemical dynamics which dictate timing of cellular events. We propose that if a change of cell fate is triggered by the {\em time-integral} of the underlying stochastic biochemical signal, rather than the original signal, then a dramatic improvement in temporal specificity results. Exact analytical results for stochastic models of hourglass-timers and pendulum-clocks, two important paradigms for biological timekeeping, elucidate how temporal specificity is achieved through time-integration. En route, we introduce a natural representation for time-integrals of stochastic processes, provide an analytical prescription for evaluating corresponding first-passage-time distributions, and uncover a mechanism by which a population of identical cells can spontaneously bifurcate into subpopulations of early and late responders, depending on hierarchy of timescales in the dynamics. Moreover, our approach reveals how time-integration of stochastic signals may be realized biochemically, through a simple chemical reaction scheme.

Efficient energy transduction is one driver of evolution; and thus understanding biomolecular energy transduction is crucial to understanding living organisms. As an energy-orientated modelling methodology, bond graphs provide a useful approach to describing and modelling the efficiency of living systems. This paper gives some new results on the efficiency of metabolism based on bond graph models of the key metabolic processes: glycolysis.

The adoption of deep learning techniques in genomics has been hindered by the difficulty of mechanistically interpreting the models that these techniques produce. In recent years, a variety of post-hoc attribution methods have been proposed for addressing this neural network interpretability problem in the context of gene regulation. Here we describe a complementary way of approaching this problem. Our strategy is based on the observation that two large classes of biophysical models of cis-regulatory mechanisms can be expressed as deep neural networks in which nodes and weights have explicit physiochemical interpretations. We also demonstrate how such biophysical networks can be rapidly inferred, using modern deep learning frameworks, from the data produced by certain types of massively parallel reporter assays (MPRAs). These results suggest a scalable strategy for using MPRAs to systematically characterize the biophysical basis of gene regulation in a wide range of biological contexts. They also highlight gene regulation as a promising venue for the development of scientifically interpretable approaches to deep learning.

The Bond Graph approach and the Chemical Reaction Network approach to modelling biomolecular systems developed independently. This paper brings together the two approaches by providing a bond graph interpretation of the chemical reaction network concept of complexes. Both closed and open systems are discussed. The method is illustrated using a simple enzyme-catalysed reaction and a trans-membrane transporter.

Whole-cell modelling is constrained by the laws of nature in general and the laws of thermodynamics in particular. This paper shows how one prolific source of information, stoichiometric models of biomolecular systems, can be integrated with thermodynamic principles using the bond graph approach to network thermodynamics.

We present BoolSi, an open-source cross-platform command line tool for distributed simulations of deterministic Boolean networks with synchronous update. It uses MPI standard to support execution on computational clusters, as well as parallel processing on a single computer. BoolSi can be used to model the behavior of complex dynamic networks, such as gene regulatory networks. In particular, it allows for identification and statistical analysis of network attractors. We perform a case study of the activity of a cambium cell to demonstrate the capabilities of the tool.

This Thesis presents research at the boundary between Statistical Physics and Biology. First, we have devised a class of Boolean constraint satisfaction problems (CSP) whose solutions describe the feasible operational states of a chemical reaction network. After developing statistical mechanics techniques to generate solutions and studying the properties of the solution space for both ensembles and individual instances of random reaction networks, we have applied this framework to the metabolic network of the bacterium E.Coli. Results highlight, on one hand, a complex organization of operational states into "modules" involving different biochemically-defined pathways, and, on the other, a high degree of cross-talk between modules. In summary, we propose that this class of CSPs may provide novel and useful quantitative information linking structure to function in cellular reaction networks.