Quantitative Biology

An environment far from equilibrium is thought to be a necessary condition for the origin and persistence of life. In this context we report open-flow simulations of a non-enzymic proto-metabolic system, in which hydrogen peroxide acts both as oxidant and driver of thermochemical cycling. We find that a Gaussian perturbed input produces a non-Boltzmann output fluctuation distribution around the mean oscillation maximum. Our main result is that net biosynthesis can occur under fluctuating cyclical but not steady drive. Consequently we may revise the necessary condition to "dynamically far from equilibrium".

Numerical solution of the chemical master equation for stochastic reaction networks typically suffers from the state space explosion problem due to the curse of dimensionality and from stiffness due to multiple time scales. The dimension of the state space equals the number of molecular species involved in the reaction network and the size of the system of differential equations equals the number of states in the corresponding continuous-time Markov chain, which is usually enormously huge and often even infinite. Thus, efficient numerical solution approaches must be able to handle huge, possibly infinite and stiff systems of differential equations efficiently. We present an approximate numerical integration approach that combines a dynamical state space truncation procedure with efficient numerical integration schemes for systems of ordinary differential equations including adaptive step size selection based on local error estimates. The efficiency and accuracy is demonstrated by numerical examples.

Are "turn-on" and "turn-off" functions in protein-protein interaction networks exact opposites of each other? To answer this question, we implement a minimal model for the evolution of functional protein-interaction networks using a sequence-based mutational algorithm, and apply the model to study neutral drift in networks that yield oscillatory dynamics. We study the roles of activators and deactivators, two core components of oscillatory protein interaction networks, and find a striking asymmetry in the roles of activating and deactivating proteins, where activating proteins tend to be synergistic and deactivating proteins tend to be competitive.

Predicting stochastic cellular dynamics as emerging from the mechanistic models of molecular interactions is a long-standing challenge in systems biology: low-level chemical reaction network (CRN) models give raise to a highly-dimensional continuous-time Markov chain (CTMC) which is computationally demanding and often prohibitive to analyse in practice. A recently proposed abstraction method uses deep learning to replace this CTMC with a discrete-time continuous-space process, by training a mixture density deep neural network with traces sampled at regular time intervals (which can obtained either by simulating a given CRN or as time-series data from experiment). The major advantage of such abstraction is that it produces a computational model that is dramatically cheaper to execute, while preserving the statistical features of the training data. In general, the abstraction accuracy improves with the amount of training data. However, depending on a CRN, the overall quality of the method -- the efficiency gain and abstraction accuracy -- will also depend on the choice of neural network architecture given by hyper-parameters such as the layer types and connections between them. As a consequence, in practice, the modeller would have to take care of finding the suitable architecture manually, for each given CRN, through a tedious and time-consuming trial-and-error cycle. In this paper, we propose to further automatise deep abstractions for stochastic CRNs, through learning the optimal neural network architecture along with learning the transition kernel of the abstract process. Automated search of the architecture makes the method applicable directly to any given CRN, which is time-saving for deep learning experts and crucial for non-specialists. We implement the method and demonstrate its performance on a number of representative CRNs with multi-modal emergent phenotypes.

Chemical reactions occur in energy, environmental, biological, and many other natural systems, and the inference of the reaction networks is essential to understand and design the chemical processes in engineering and life sciences. Yet, revealing the reaction pathways for complex systems and processes is still challenging due to the lack of knowledge of the involved species and reactions. Here, we present a neural network approach that autonomously discovers reaction pathways from the time-resolved species concentration data. The proposed Chemical Reaction Neural Network (CRNN), by design, satisfies the fundamental physics laws, including the Law of Mass Action and the Arrhenius Law. Consequently, the CRNN is physically interpretable such that the reaction pathways can be interpreted, and the kinetic parameters can be quantified simultaneously from the weights of the neural network. The inference of the chemical pathways is accomplished by training the CRNN with species concentration data via stochastic gradient descent. We demonstrate the successful implementations and the robustness of the approach in elucidating the chemical reaction pathways of several chemical engineering and biochemical systems. The autonomous inference by the CRNN approach precludes the need for expert knowledge in proposing candidate networks and addresses the curse of dimensionality in complex systems. The physical interpretability also makes the CRNN capable of not only fitting the data for a given system but also developing knowledge of unknown pathways that could be generalized to similar chemical systems.

Lck (lymphocyte-specific protein tyrosine kinase) is an enzyme which plays a number of important roles in the function of immune cells. It belongs to the Src family of kinases which are known to undergo autophosphorylation. It turns out that this leads to a remarkable variety of dynamical behaviour which can occur during their activation. We prove that in the presence of autophosphorylation one phenomenon, bistability, already occurs in a mathematical model for a protein with a single phosphorylation site. We further show that a certain model of Lck exhibits oscillations. Finally we discuss the relations of these results to models in the literature which involve Lck and describe specific biological processes, such as the early stages of T cell activation and the stimulation of T cell responses resulting from the suppression of PD-1 signalling which is important in immune checkpoint therapy for cancer.

The analysis of the mutational landscape of cancer, including mutual exclusivity and co-occurrence of mutations, has been instrumental in studying the disease. We hypothesized that exploring the interplay between co-occurrence, mutual exclusivity, and functional interactions between genes will further improve our understanding of the disease and help to uncover new relations between cancer driving genes and pathways. To this end, we designed a general framework, BeWith, for identifying modules with different combinations of mutation and interaction patterns. We focused on three different settings of the BeWith schema: (i) BeME-WithFun in which the relations between modules are enriched with mutual exclusivity while genes within each module are functionally related; (ii) BeME-WithCo which combines mutual exclusivity between modules with co-occurrence within modules; and (iii) BeCo-WithMEFun which ensures co-occurrence between modules while the within module relations combine mutual exclusivity and functional interactions. We formulated the BeWith framework using Integer Linear Programming (ILP), enabling us to find optimally scoring sets of modules. Our results demonstrate the utility of BeWith in providing novel information about mutational patterns, driver genes, and pathways. In particular, BeME-WithFun helped identify functionally coherent modules that might be relevant for cancer progression. In addition to finding previously well-known drivers, the identified modules pointed to the importance of the interaction between NCOR and NCOA3 in breast cancer. Additionally, an application of the BeME-WithCo setting revealed that gene groups differ with respect to their vulnerability to different mutagenic processes, and helped us to uncover pairs of genes with potentially synergetic effects, including a potential synergy between mutations in TP53 and metastasis related DCC gene.

The Turing patterning mechanism is believed to underly the formation of repetitive structures in development, such as zebrafish stripes and mammalian digits, but it has proved difficult to isolate the specific biochemical species responsible for pattern formation. Meanwhile, synthetic biologists have designed Turing systems for implementation in cell colonies, but none have yet led to visible patterns in the laboratory. In both cases, the relationship between underlying chemistry and emergent biology remains mysterious. To help resolve the mystery, this article asks the question: what kinds of biochemical systems can generate Turing patterns? We find general conditions for Turing pattern inception -- the ability to generate unstable patterns from random noise -- which may lead to the ultimate formation of stable patterns, depending on biochemical non-linearities. We find that a wide variety of systems can generate stable Turing patterns, including several which are currently unknown, such as two-species systems composed of two self-activators, and systems composed of a short-range inhibitor and a long-range activator. We furthermore find that systems which are widely believed to generate stable patterns may in fact only generate unstable patterns, which ultimately converge to spatially-homogeneous concentrations. Our results suggest that a much wider variety of systems than is commonly believed could be responsible for observed patterns in development, or could be good candidates for synthetic patterning networks.

Bazhin has analyzed ATP coupling in terms of quasiequilibrium states where fast reactions have reached an approximate steady state while slow reactions have not yet reached equilibrium. After an expository introduction to the relevant aspects of reaction network theory, we review his work and explain the role of emergent conserved quantities in coupling. These are quantities, left unchanged by fast reactions, whose conservation forces exergonic processes such as ATP hydrolysis to drive desired endergonic processes.

This work proposes a unified framework to leverage biological information in network propagation-based gene prioritization algorithms. Preliminary results on breast cancer data show significant improvements over state-of-the-art baselines, such as the prioritization of genes that are not identified as potential candidates by interactome-based algorithms, but that appear to be involved in/or potentially related to breast cancer, according to a functional analysis based on recent literature.