Enhanced Operational Semantics in Systems Biology

We are faced with a great challenge: the cross-fertilization between the fields of formal methods for concurrency, in the computer science domain, and systems biology in the biological realm

Review of "Stochastic Modelling for Systems Biology" by Darren Wilkinson

"Stochastic Modelling for Systems Biology" by Darren Wilkinson introduces the peculiarities of stochastic modelling in biology. This book is particularly suited to as a textbook or for self-study, and for readers with a theoretical background

A core genetic module : the Mixed Feedback Loop

The so-called Mixed Feedback Loop (MFL) is a small two-gene network where protein A regulates the transcription of protein B and the two proteins form a heterodimer. It has been found to be statistically over-represented in statistical analyses of gene and protein interaction databases and to lie at the core of several computer-generated genetic networks. Here, we propose and mathematically study a model of the MFL and show that, by itself, it can serve both as a bistable switch and as a clock (an oscillator) depending on kinetic parameters. The MFL phase diagram as well as a detailed description of the nonlinear oscillation regime are presented and some biological examples are discussed. The results emphasize the role of protein interactions in the function of genetic modules and the usefulness of modelling RNA dynamics explicitly.Comment: To be published in Physical Review

The cytoplasm of living cells: A functional mixture of thousands of components

Inside every living cell is the cytoplasm: a fluid mixture of thousands of different macromolecules, predominantly proteins. This mixture is where most of the biochemistry occurs that enables living cells to function, and it is perhaps the most complex liquid on earth. Here we take an inventory of what is actually in this mixture. Recent genome-sequencing work has given us for the first time at least some information on all of these thousands of components. Having done so we consider two physical phenomena in the cytoplasm: diffusion and possible phase separation. Diffusion is slower in the highly crowded cytoplasm than in dilute solution. Reasonable estimates of this slowdown can be obtained and their consequences explored, for example, monomer-dimer equilibria are established approximately twenty times slower than in a dilute solution. Phase separation in all except exceptional cells appears not to be a problem, despite the high density and so strong protein-protein interactions present. We suggest that this may be partially a byproduct of the evolution of other properties, and partially a result of the huge number of components present.Comment: 11 pages, 1 figure, 1 tabl

The evolutionary dynamics of the Saccharomyces cerevisiae protein interaction network after duplication

Gene duplication is an important mechanism in the evolution of protein interaction networks. Duplications are followed by the gain and loss of interactions, rewiring the network at some unknown rate. Because rewiring is likely to change the distribution of network motifs within the duplicated interaction set, it should be possible to study network rewiring by tracking the evolution of these motifs. We have developed a mathematical framework that, together with duplication data from comparative genomic and proteomic studies, allows us to infer the connectivity of the preduplication network and the changes in connectivity over time. We focused on the whole-genome duplication (WGD) event in Saccharomyces cerevisiae. The model allowed us to predict the frequency of intergene interaction before WGD and the post duplication probabilities of interaction gain and loss. We find that the predicted frequency of self-interactions in the preduplication network is significantly higher than that observed in today's network. This could suggest a structural difference between the modern and ancestral networks, preferential addition or retention of interactions between ohnologs, or selective pressure to preserve duplicates of self-interacting proteins

A Phase 1 trial of intravenous boronophenylalanine-fructose complex in patients with glioblastoma multiforme

Boron neutron capture therapy (BNCT) of glioblastoma multiforme was initially performed at the Brookhaven National Laboratory in the early 1950`s While this treatment for malignant brain tumors has continued in Japan, new worldwide interest has been stimulated by the development of new and more selective boron compounds. Boronophenylalanine (BPA) is a blood-brain barrier penetrating compound that has been used in BNCT of malignant melanomas. SPA has been employed experimentally in BNCT of rat gliosarcoma and has potential use in the treatment of human glioblastoma. As a preface to clinical BNCT trials, we studied the biodistribution of SPA in patients with glioblastoma

A variational approach to the stochastic aspects of cellular signal transduction

Cellular signaling networks have evolved to cope with intrinsic fluctuations, coming from the small numbers of constituents, and the environmental noise. Stochastic chemical kinetics equations govern the way biochemical networks process noisy signals. The essential difficulty associated with the master equation approach to solving the stochastic chemical kinetics problem is the enormous number of ordinary differential equations involved. In this work, we show how to achieve tremendous reduction in the dimensionality of specific reaction cascade dynamics by solving variationally an equivalent quantum field theoretic formulation of stochastic chemical kinetics. The present formulation avoids cumbersome commutator computations in the derivation of evolution equations, making more transparent the physical significance of the variational method. We propose novel time-dependent basis functions which work well over a wide range of rate parameters. We apply the new basis functions to describe stochastic signaling in several enzymatic cascades and compare the results so obtained with those from alternative solution techniques. The variational ansatz gives probability distributions that agree well with the exact ones, even when fluctuations are large and discreteness and nonlinearity are important. A numerical implementation of our technique is many orders of magnitude more efficient computationally compared with the traditional Monte Carlo simulation algorithms or the Langevin simulations.Comment: 15 pages, 11 figure

Pulsed Feedback Defers Cellular Differentiation

Environmental signals induce diverse cellular differentiation programs. In certain systems, cells defer differentiation for extended time periods after the signal appears, proliferating through multiple rounds of cell division before committing to a new fate. How can cells set a deferral time much longer than the cell cycle? Here we study Bacillus subtilis cells that respond to sudden nutrient limitation with multiple rounds of growth and division before differentiating into spores. A well-characterized genetic circuit controls the concentration and phosphorylation of the master regulator Spo0A, which rises to a critical concentration to initiate sporulation. However, it remains unclear how this circuit enables cells to defer sporulation for multiple cell cycles. Using quantitative time-lapse fluorescence microscopy of Spo0A dynamics in individual cells, we observed pulses of Spo0A phosphorylation at a characteristic cell cycle phase. Pulse amplitudes grew systematically and cell-autonomously over multiple cell cycles leading up to sporulation. This pulse growth required a key positive feedback loop involving the sporulation kinases, without which the deferral of sporulation became ultrasensitive to kinase expression. Thus, deferral is controlled by a pulsed positive feedback loop in which kinase expression is activated by pulses of Spo0A phosphorylation. This pulsed positive feedback architecture provides a more robust mechanism for setting deferral times than constitutive kinase expression. Finally, using mathematical modeling, we show how pulsing and time delays together enable “polyphasic” positive feedback, in which different parts of a feedback loop are active at different times. Polyphasic feedback can enable more accurate tuning of long deferral times. Together, these results suggest that Bacillus subtilis uses a pulsed positive feedback loop to implement a “timer” that operates over timescales much longer than a cell cycle

Mathematical Biology at an Undergraduate Liberal Arts College

Since 2002 we have offered an undergraduate major in Mathematical Biology at Harvey Mudd College. The major was developed and is administered jointly by the mathematics and biology faculty. In this paper we describe the major, courses, and faculty and student research and discuss some of the challenges and opportunities we have experienced