Quantitative Biology

Astrocytes express a large variety of G~protein-coupled receptors (GPCRs) which mediate the transduction of extracellular signals into intracellular calcium responses. This transduction is provided by a complex network of biochemical reactions which mobilizes a wealth of possible calcium-mobilizing second messenger molecules. Inositol 1,4,5-trisphosphate is probably the best known of these molecules whose enzymes for its production and degradation are nonetheless calcium-dependent. We present a biophysical modeling approach based on the assumption of Michaelis-Menten enzyme kinetics, to effectively describe GPCR-mediated astrocytic calcium signals. Our model is then used to study different mechanisms at play in stimulus encoding by shape and frequency of calcium oscillations in astrocytes.

Protein synthesis rates are determined, at the translational level, by properties of the transcript's sequence. The efficiency of an mRNA can be tuned by varying the ribosome binding sites controlling the recruitment of the ribosomes, or the codon usage establishing the speed of protein elongation. In this work we propose transcript length as a further key determinant of translation efficiency. Based on a physical model that considers the kinetics of ribosomes advancing on the mRNA and diffusing in its surrounding, as well as mRNA circularisation and ribosome drop-off, we explain how the transcript length may play a central role in establishing ribosome recruitment and the overall translation rate of an mRNA. According to our results, the proximity of the 3' end to the ribosomal recruitment site of the mRNA could induce a feedback in the translation process that would favour the recycling of ribosomes. We also demonstrate how this process may be involved in shaping the experimental ribosome density-gene length dependence. Finally, we argue that cells could exploit this mechanism to adjust and balance the usage of its ribosomal resources.

Ion channels are specific proteins present in the membranes of living cells. They control the flow of specific ions through a cell, initiated by an ion channel's electrochemical gradient. In doing so, they control important physiological processes such as muscle contraction and neuronal connectivity, which cannot be properly activated if these channels go haywire, leading to life-threatening diseases and psychological disorders. Here, we will develop a generalized microscopic theory of ion selectivity applicable to KcsA, Na v Rh and Ca v (L-type) ion channels. We unambiguously expose why and how a given ion-channel can be highly selective, and yet has a conductance of the order of one million ions per second, or higher. We will identify and prove the correct physico-biochemical mechanisms that are responsible for the high selectivity of a particular ion in a given ion channel. The above mechanisms consist of five conditions, which can be directly associated to these parameters - (i) dehydration energy, (ii) concentration of the "correct" ions (iii) Coulomb-van-der-Waals attraction, (iv) pore and ionic sizes, and indirectly to (v) the thermodynamic stability and (vi) the "knock-on" assisted permeation.

This paper proposes that eukaryotic cells, under severe genotoxic stress, can commit genoautotomy (genome 'self-injury') that involves cutting and releasing single-stranded DNA (ssDNA) fragments from double-stranded DNA and leaving ssDNA gaps in the genome. The ssDNA gaps could be easily and precisely repaired later. The released ssDNA fragments may play some role in the regulation of cell cycle progression. Taken together, genoautotomy causes limited nonlethal DNA damage, but prevents the whole genome from lethal damage, and thus should be deemed as a eukaryotic cellular defence response to genotoxic stress.

In order to better understand the process of gene translation, the ribosome flow model (RFM) with pool was introduced recently. This model describes the movement of several ribosomes along an mRNA template and simultaneously captures the dynamics of the finite pool of ribosomes. Studying this system with respect to the number and stability of its equilibria was so far based on monotone systems theory (Margaliot and Tuller, 2012). We extend the results obtained therein by using a geometric approach, showing that the equilibria of the system constitute a normally hyperbolic invariant submanifold. Subsequently, we analyze the Jacobi linearization of the system evaluated at the equilibria in order to show that the equilibria are asymptotically stable relative to certain affine subspaces. As this approach does not require any monotonicity features of the system, it may also be applied for more complex systems of the same kind such as bi-directional ribosome flows or time-varying template numbers.

We report here new electrical laws, derived from nonlinear electro-diffusion theory, about the effect of the local geometrical structure, such as curvature, on the electrical properties of a cell. We adopt the Poisson-Nernst-Planck (PNP) equations for charge concentration and electric potential as a model of electro-diffusion. In the case at hand, the entire boundary is impermeable to ions and the electric field satisfies the compatibility condition of Poisson's equation. We construct an asymptotic approximation for certain singular limits to the steady-state solution in a ball with an attached cusp-shaped funnel on its surface. As the number of charge increases, they concentrate at the end of cusp-shaped funnel. These results can be used in the design of nano-pipettes and help to understand the local voltage changes inside dendrites and axons with heterogenous local geometry.

Rod-like bacteria maintain their cylindrical shapes with remarkable precision during growth. However, they are also capable to adapt their shapes to external forces and constraints, for example by growing into narrow or curved confinements. Despite being one of the simplest morphologies, we are still far from a full understanding of how shape is robustly regulated, and how bacteria obtain their near-perfect cylindrical shapes with excellent precision. However, recent experimental and theoretical findings suggest that cell-wall geometry and mechanical stress play important roles in regulating cell shape in rod-like bacteria. We review our current understanding of the cell wall architecture and the growth dynamics, and discuss possible candidates for regulatory cues of shape regulation in the absence or presence of external constraints. Finally, we suggest further future experimental and theoretical directions, which may help to shed light on this fundamental problem.

Ammonium assimilation in E. coli is regulated by two paralogous proteins (GlnB and GlnK), which orchestrate interactions with regulators of gene expression, transport proteins and metabolic pathways. Yet how they conjointly modulate the activity of glutamine synthetase (GS), the key enzyme for nitrogen assimilation, is poorly understood. We combine experiments and theory to study the dynamic roles of GlnB and GlnK during nitrogen starvation and upshift. We measure time-resolved in vivo concentrations of metabolites, total and post-translationally modified proteins, and develop a concise biochemical model of GlnB and GlnK that incorporates competition for active and allosteric sites, as well as functional sequestration of GlnK. The model predicts the responses of GS, GlnB and GlnK under time-varying external ammonium level in the wild type and two genetic knock-outs. Our results show that GlnK is tightly regulated under nitrogen-rich conditions, yet it is expressed during ammonium run-out and starvation. This suggests a role for GlnK as a buffer of nitrogen shock after starvation, and provides a further functional link between nitrogen and carbon metabolisms.

Many proteins that undergo sequential enzymatic modification in the Golgi cisternae are displayed at the plasma membrane as cell identity markers. The modified proteins, called glycans, represent a molecular code. The fidelity of this glycan code is measured by how accurately the glycan synthesis machinery realises the desired target glycan distribution for a particular cell type and niche. In this paper, we quantitatively analyse the tradeoffs between the number of cisternae and the number and specificity of enzymes, in order to synthesize a prescribed target glycan distribution of a certain complexity. We find that to synthesize complex distributions, such as those observed in real cells, one needs to have multiple cisternae and precise enzyme partitioning in the Golgi. Additionally, for fixed number of enzymes and cisternae, there is an optimal level of specificity of enzymes that achieves the target distribution with high fidelity. Our results show how the complexity of the target glycan distribution places functional constraints on the Golgi cisternal number and enzyme specificity.

During M phase, Endosulfine (Endos) family proteins are phosphorylated by Greatwall kinase (Gwl), and the resultant pEndos inhibits the phosphatase PP2A-B55, which would otherwise prematurely reverse many CDK-driven phosphorylations. We show here that PP2A-B55 is the enzyme responsible for dephosphorylating pEndos during M phase exit. The kinetic parameters for PP2A-B55's action on pEndos are orders of magnitude lower than those for CDK-phosphorylated substrates, suggesting a simple model for PP2A-B55 regulation that we call inhibition by unfair competition. As the name suggests, during M phase PP2A-B55's attention is diverted to pEndos, which binds much more avidly and is dephosphorylated more slowly than other substrates. When Gwl is inactivated during the M phase-to-interphase transition, the dynamic balance changes: pEndos dephosphorylated by PP2A-B55 cannot be replaced, so the phosphatase can refocus its attention on CDK-phosphorylated substrates. This mechanism explains simultaneously how PP2A-B55 and Gwl together regulate pEndos, and how pEndos controls PP2A-B55.