Quantitative Biology

While ordinary differential equations (ODEs) form the conceptual framework for modelling many cellular processes, specific situations demand stochastic models to capture the influence of noise. The most common formulation of stochastic models for biochemical networks is the chemical master equation (CME). While stochastic simulations are a practical way to realise the CME, analytical approximations offer more insight into the influence of noise. Towards that end, the two-moment approximation (2MA) is a promising addition to the established analytical approaches including the chemical Langevin equation (CLE) and the related linear noise approximation (LNA). The 2MA approach directly tracks the mean and (co)variance which are coupled in general. This coupling is not obvious in CME and CLE and ignored by LNA and conventional ODE models. We extend previous derivations of 2MA by allowing a) non-elementary reactions and b) relative concentrations. Often, several elementary reactions are approximated by a single step. Furthermore, practical situations often require the use relative concentrations. We investigate the applicability of the 2MA approach to the well established fission yeast cell cycle model. Our analytical model reproduces the clustering of cycle times observed in experiments. This is explained through multiple resettings of MPF, caused by the coupling between mean and (co)variance, near the G2/M transition.

We report an experimental study of the influences of the fixed charge and bulk ionic concentrations on the conduction of biological ion channels, and we consider the results within the framework of the ionic Coulomb blockade model of permeation and selectivity. Voltage clamp recordings were used to investigate the Na + /Ca 2+ anomalous mole fraction effect (AMFE) exhibited by the bacterial sodium channel NaChBac and its mutants. Site-directed mutagenesis was used to study the effect of either increasing or decreasing the fixed charge in their selectivity filters for comparison with the predictions of the Coulomb blockade model. The model was found to describe well some aspects of the experimental (divalent blockade and AMFE) and simulated (discrete multi-ion conduction and occupancy band) phenomena, including a concentration-dependent shift of the Coulomb staircase. These results substantially extend the understanding of ion channel selectivity and may also be applicable to biomimetic nanopores with charged walls.

The SARS-CoV-2 virus has resulted in a devastating pandemic of COVID-19. Exploring compounds that could offer a breakthrough in treatment is the need of the hour. Re-positioning cheap, freely available and safe drugs is a priority. The paper proposes evidence for the potential use of diethylcarbamazine (DEC) in the treatment of COVID-19. DEC has inhibitory effects on arachidonic acid metabolism to prostaglandins, little known anti-viral effects on animal retroviruses and demonstrated anti-inflammatory actions in animal models of lung inflammation indicating the need to explore this hypothesis further. We believe this is the first time DEC is being proposed to treat COVID-19.

The hopping model for cargo transport by molecular motors introduced in Refs. goldman1, goldman2, is extended here in order to incorporate the movement of cargo-motor complexes. In this context, hopping process expresses the possibility for cargo to be exchanged between neighbor motors at a microtubule where the transport takes place. Jamming of motors is essential for cargos to execute long-range movement in this way. Results from computer simulations performed using the extended model indicate that cargo may execute bidirectional movement in the presence of motors of a single polarity, confirming previous analytical results. Moreover, these results suggest the existence of a balance between cargo hopping and the movement of the complex that may control the efficiency of cargo transfer and cargo delivering. Considerations about the energy involved in the transport process show that the model presented here offers a considerable advantage over other models in the literature for which cargo movement is restricted to the movement of cargo-motor complexes.

Keratin are among the most abundant proteins in epithelial cells. Functions of the keratin network in cells are shaped by their dynamical organization. Using a collection of experimentally-driven mathematical models, different hypotheses for the turnover and transport of the keratin material in epithelial cells are tested. The interplay between turnover and transport and their effects on the keratin organization in cells are hence investigated by combining mathematical modeling and experimental data. Amongst the collection of mathematical models considered, a best model strongly supported by experimental data is identified. Fundamental to this approach is the fact that optimal parameter values associated with the best fit for each model are established. The best candidate among the best fits is characterized by the disassembly of the assembled keratin material in the perinuclear region and an active transport of the assembled keratin. Our study shows that an active transport of the assembled keratin is required to explain the experimentally observed keratin organization.

Kinesin-8 motor proteins destabilize microtubules. Their absence during cell division is associated with disorganized mitotic chromosome movements and chromosome loss. Despite recent work studying effects of kinesin 8s on microtubule dynamics, it remains unclear whether the kinesin-8 mitotic phenotypes are consequences of their effect on microtubule dynamics, their well-established motor activity, or additional unknown functions. To better understand the role of kinesin-8 proteins in mitosis, we have studied the effects of deletion of the fission-yeast kinesin-8 proteins Klp5 and Klp6 on chromosome movements and spindle length dynamics. Aberrant microtubule-driven kinetochore pushing movements and tripolar mitotic spindles occurred in cells lacking Klp5 but not Klp6. Kinesin-8 deletion strains showed large fluctuations in metaphase spindle length, suggesting a disruption of spindle length stabilization. Comparison of our results from light microscopy with a mathematical model suggests that kinesin-8 induced effects on microtubule dynamics, kinetochore attachment stability, and sliding force in the spindle can explain the aberrant chromosome movements and spindle length fluctuations seen.

Protein assembly plays an important role in the regulation of biological systems. The cytoskeleton assembly activity is provided by the binding cofactors GTP (guanidine triphosphate) or ATP(adenosine triphosphate) to monomeric protein, and is initiated by assembling the monomeric proteins. The binding GTP or ATP is hydrolyzed to GDP (guanidine diphosphate) or ADP (adenosine diphosphate) by the monomeric enzymatic activity. This self-limited assembly is characteristic of the cytoskeleton. To quantitatively evaluate the assembly kinetics, we propose a nonlinear and non-equilibrium kinetic model, with the nonlinearity provided by the fluctuation in monomer concentrations during the diffusion. Numerical simulations suggest that the assembly and disassembly oscillates in a chaos-like manner. We use a kinetic analysis of the center manifold around the critical point to show that minimal increases in ATP/GTP concentrations may lead to some attenuation in the amplification of these fluctuations. The present model and our application of center manifold theory illustrate a unique feature of protein assemblies, and our stability analysis provides an analytical methodology for the biological reaction system.

One of the causes of high fidelity of copying in biological systems is kinetic discrimination. In this mechanism larger dissipation and copying velocity result in improved copying accuracy. We consider a model of a polymerase which simultaneously copies a single stranded RNA and opens a single- to double-stranded junction serving as an obstacle. The presence of the obstacle slows down the motor, resulting in a change of its fidelity, which can be used to gain information about the motor and junction dynamics. We find that the motor's fidelity does not depend on details of the motor-junction interaction, such as whether the interaction is passive or active. Analysis of the copying fidelity can still be used as a tool for investigating the junction kinetics.

The secretion of vesicles for intracellular transport often rely on the aggregation of specialized membrane-bound proteins into a coat able to curve cell membranes. The nucleation and growth of a protein coat is a kinetic process that competes with the energy-consuming turnover of coat components between the membrane and the cytosol. We propose a generic kinetic description of coat assembly and the formation of coated vesicles, and discuss its implication to the dynamics of COP vesicles that traffic within the Golgi and with the Endoplasmic Reticulum. We show that stationary coats of fixed area emerge from the competition between coat growth and the recycling of coat components, in a fashion resembling the treadmilling of cytoskeletal filaments. We further show that the turnover of coat components allows for a highly sensitive switching mechanism between a quiescent and a vesicle producing membrane, upon a slowing down of the exchange kinetics. We claim that the existence of this switching behaviour, also triggered by factors such as the presence of cargo and variation of the membrane mechanical tension, allows for efficient regulation of vesicle secretion. We propose a model, supported by different experimental observations, in which vesiculation of secretory membranes is impaired by the energy consuming desorption of coat proteins, until the presence of cargo or other factors triggers a dynamical switch into a vesicle producing state.

Kinetic theory and thermodynamics are applied to DNA polymerases with exonuclease activity, taking into account the dependence of the rates on the previously incorportated nucleotide. The replication fidelity is shown to increase significantly thanks to this dependence at the basis of the mechanism of exonuclease proofreading. In particular, this dependence can provide up to a hundred-fold lowering of the error probability under physiological conditions. Theory is compared with numerical simulations for the DNA polymerases of T7 viruses and human mitochondria.