Quantitative Biology

Active ion transport is very critical for living cells to maintain and regular internal and external environment. It is known that adenosine 5'-triphosphate (ATP) is a general energy source that applies bond energy for pumps to overcome ion concentration gradient. In this study, we introduce a novel thermodynamic model for active ion transport, which allows the pump to act as a 'Maxwell's demon', and also conforms to the second law of thermodynamics. Transport against the gradient is caused by the thermodynamic fluctuation with information recording in ATP stream. Besides, exhaustive experiments about Na-K ATPase performed in the red cell ghost system are reviewed to verify this model, and all the results can support the solvable theory about the working mechanism of demon pumps. Our findings indicate the possible role of ATP as an information carrier but not energy currency. The high-energy phosphate bonds can improve the efficiency of information recording in relevance to ion transport and may mainly convert to heat.

We introduce a two-species exclusion model to describe the key features of the conflict between the RNA polymerase (RNAP) motor traffic, engaged in the transcription of a segment of DNA, concomitant with the progress of two DNA replication forks on the same DNA segment. One of the species of particles ( P ) represents RNAP motors while the other ( R ) represents replication forks. Motivated by the biological phenomena that this model is intended to capture, a maximum of only two R particles are allowed to enter the lattice from two opposite ends whereas the unrestricted number of P particles constitute a totally asymmetric simple exclusion process (TASEP) in a segment in the middle of the lattice. Consequently, the lattice consists of three segments; the encounters of the P particles with the R particles are confined within the middle segment (segment 2 ) whereas only the R particles can occupy the sites in the segments 1 and 3 . The model captures three distinct pathways for resolving the co-directional as well as head-collision between the P and R particles. Using Monte Carlo simulations and heuristic analytical arguments that combine exact results for the TASEP with mean-field approximations, we predict the possible outcomes of the conflict between the traffic of RNAP motors ( P particles engaged in transcription) and the replication forks ( R particles). The outcomes, of course, depend on the dynamical phase of the TASEP of P particles. In principle, the model can be adapted to the experimental conditions to account for the data quantitatively.

The metazoan genome is replicated in precise cell lineage specific temporal order. However, the mechanism controlling this orchestrated process is poorly understood as no molecular mechanisms have been identified that actively regulate the firing sequence of genome replication. Here we develop a mechanistic model of genome replication capable of predicting, with accuracy rivaling experimental repeats, observed empirical replication timing program in humans. In our model, replication is initiated in an uncoordinated (time-stochastic) manner at well-defined sites. The model contains, in addition to the choice of the genomic landmark that localizes initiation, only a single adjustable parameter of direct biological relevance: the number of replication forks. We find that DNase hypersensitive sites are optimal and independent determinants of DNA replication initiation. We demonstrate that the DNA replication timing program in human cells is a robust emergent phenomenon that, by its very nature, does not require a regulatory mechanism determining a proper replication initiation firing sequence.

We apply a recently developed model of cytoskeletal force generation to study a cell intrinsic contractility, as well as its response to external loading. The model is based on a non-equilibrium thermodynamic treatment of the mechano-chemistry governing force in the stress fiber-focal adhesion system. Our computational study suggests that the mechanical coupling between the stress fibers and focal adhesions leads to a complex, dynamic, mechano-chemical response. We collect the results in response maps whose regimes are distinguished by the initial geometry of the stress fiber-focal adhesion system, and by the external load on the cell. The results from our model connect qualitatively with recent studies on the force response of smooth muscle cells on arrays of polymeric microposts (Mann et al., Lab. on a Chip, 12, 731-740, 2012).

A simple kinematic model for the trajectories of Listeria monocytogenes is generalized to a dynamical system rich enough to exhibit the resonant Hopf bifurcation structure of excitable media and simple enough to be studied geometrically. It is shown how L. monocytogenes trajectories and meandering spiral waves are organized by the same type of attracting set.

The mitotic spindle is an important intermediate structure in eukaryotic cell division, in which each of a pair of duplicated chromosomes is attached through microtubules to centrosomal bodies located close to the two poles of the dividing cell. Several mechanisms are at work towards the formation of the spindle, one of which is the `capture' of chromosome pairs, held together by kinetochores, by randomly searching microtubules. Although the entire cell cycle can be up to 24 hours long, the mitotic phase typically takes only less than an hour. How does the cell keep the duration of mitosis within this limit? Previous theoretical studies have suggested that the chromosome search and capture is optimized by tuning the microtubule dynamic parameters to minimize the search time. In this paper, we examine this conjecture. We compute the mean search time for a single target by microtubules from a single nucleating site, using a systematic and rigorous theoretical approach, for arbitrary kinetic parameters. The result is extended to multiple targets and nucleating sites by physical arguments. Estimates of mitotic time scales are then obtained for different cells using experimental data. In yeast and mammalian cells, the observed changes in microtubule kinetics between interphase and mitosis are beneficial in reducing the search time. In {\it Xenopus} extracts, by contrast, the opposite effect is observed, in agreement with the current understanding that large cells use additional mechanisms to regulate the duration of the mitotic phase.

Planar curves with periodically varying curvature arise in the natural sciences as the result of a wide variety of periodic processes. The total curvature of a periodic arc in such curves constrains their symmetry. It is shown how the total curvature can be computed without reparameterizing the curve to unit speed. The use of the total curvature of the periodic arcs is demonstrated through a series of four examples from various branches of science. Insights gained from these examples are applied to improve the modeling of spiral wave meander.

Biochemical systems that express certain chemical species of interest at the same level at any positive equilibrium are called "absolute concentration robust" (ACR). These species behave in a stable, predictable way, in the sense that their expression is robust with respect to sudden changes in the species concentration, regardless the new positive equilibrium reached by the system. Such a property has been proven to be fundamentally important in certain gene regulatory networks and signaling systems. In the present paper, we mathematically prove that a well-known class of ACR systems studied by Shinar and Feinberg in 2010 hides an internal integral structure. This structure confers these systems with a higher degree of robustness that what was previously unknown. In particular, disturbances much more general than sudden changes in the species concentrations can be rejected, and robust perfect adaptation is achieved. Significantly, we show that these properties are maintained when the system is interconnected with other chemical reaction networks. This key feature enables design of insulator devices that are able to buffer the loading effect from downstream systems - a crucial requirement for modular circuit design in synthetic biology.

Human pluripotent stem cells (hPSCs) have promising clinical applications in regenerative medicine, drug-discovery and personalised medicine due to their potential to differentiate into all cell types, a property know as pluripotency. A deeper understanding of how pluripotency is regulated is required to assist in controlling pluripotency and differentiation trajectories experimentally. Mathematical modelling provides a non-invasive tool through which to explore, characterise and replicate the regulation of pluripotency and the consequences on cell fate. Here we use experimental data of the expression of the pluripotency transcription factor OCT4 in a growing hPSC colony to develop and evaluate mathematical models for temporal pluripotency regulation. We consider fractional Brownian motion and the stochastic logistic equation and explore the effects of both additive and multiplicative noise. We illustrate the use of time-dependent carrying capacities and the introduction of Allee effects to the stochastic logistic equation to describe cell differentiation. This mathematical framework for describing intra-cellular OCT4 regulation can be extended to other transcription factors and developed into sophisticated predictive models.

Eukaryotic transcription generally occurs in bursts of activity lasting minutes to hours; however, state-of-the-art measurements have revealed that many of the molecular processes that underlie bursting, such as transcription factor binding to DNA, unfold on timescales of seconds. This temporal disconnect lies at the heart of a broader challenge in physical biology of predicting transcriptional outcomes and cellular decision-making from the dynamics of underlying molecular processes. Here, we review how new dynamical information about the processes underlying transcriptional control can be combined with theoretical models that predict not only averaged transcriptional dynamics, but also their variability, to formulate testable hypotheses about the molecular mechanisms underlying transcriptional bursting and control.