Geometry Selects Highly Designable Structures

By enumerating all sequences of length 20, we study the designability of structures in a two-dimensional Hydrophobic-Polar (HP) lattice model in a wide range of inter-monomer interaction parameters. We find that although the histogram of designability depends on interaction parameters, the set of highly designable structures is invariant. So in the HP lattice model the High Designability should be a purely geometrical feature. Our results suggest two geometrical properties for highly designable structures, they have maximum number of contacts and unique neighborhood vector representation. Also we show that contribution of perfectly stable sequences in designability of structures plays a major role to make them highly designable.Comment: 6 figure, To be appear in JC

Connecting growth with gene expression: of noise and numbers.

Growth is a dynamic process whereby cells accumulate mass. Growth rates of single cells are connected to RNA and protein synthesis rates, and therefore with biomolecule numbers. Noise in gene expression depends on these numbers, and is thus linked with cellular growth. Whether these global attributes of the cell participate in gene regulation is still largely unexplored. New experimental and modelling studies suggest that systemic variations in biomolecule numbers can coordinate cellular processes, including growth itself, through global regulatory feedback that acts in addition to genetic regulatory networks. Here, we review these findings and speculate on possible implications of this less appreciated layer of gene regulation for cellular physiology and adaptation to changing environments

Analytical distributions for stochastic gene expression

Gene expression is significantly stochastic making modeling of genetic networks challenging. We present an approximation that allows the calculation of not only the mean and variance but also the distribution of protein numbers. We assume that proteins decay substantially slower than their mRNA and confirm that many genes satisfy this relation using high-throughput data from budding yeast. For a two-stage model of gene expression, with transcription and translation as first-order reactions, we calculate the protein distribution for all times greater than several mRNA lifetimes and thus qualitatively predict the distribution of times for protein levels to first cross an arbitrary threshold. If in addition the promoter fluctuates between inactive and active states, we can find the steady-state protein distribution, which can be bimodal if promoter fluctuations are slow. We show that our assumptions imply that protein synthesis occurs in geometrically distributed bursts and allows mRNA to be eliminated from a master equation description. In general, we find that protein distributions are asymmetric and may be poorly characterized by their mean and variance. Through maximum likelihood methods, our expressions should therefore allow more quantitative comparisons with experimental data. More generally, we introduce a technique to derive a simpler, effective dynamics for a stochastic system by eliminating a fast variable.Comment: Supplementary information can be found on PNAS websit

Estimating the Non-Existent Mean and Variance of the F-Distribution by Simulation

In theory, all moments of some probability distributions do not necessarily exist. In the other words, they may be infinite or undefined. One of these distributions is the F-distribution whose mean and variance have not been defined for the second degree of freedom less than 3 and 5, respectively. In some cases, a large statistical population having an F-distribution may exist and the aim is to obtain its mean and variance which are an estimation of the non-existent mean and variance of F-distribution. This article considers a large sample F-distribution to estimate its non-existent mean and variance using Simul8 simulation software

A coarse-grained resource allocation model of carbon and nitrogen metabolism in unicellular microbes

Coarse-grained resource allocation models (C-GRAMs) are simple mathematical models of cell physiology, where large components of the macromolecular composition are abstracted into single entities. The dynamics and steady-state behaviour of such models provides insights on optimal allocation of cellular resources and have explained experimentally observed cellular growth laws, but current models do not account for the uptake of compound sources of carbon and nitrogen. Here, we formulate a C-GRAM with nitrogen and carbon pathways converging on biomass production, with parametrizations accounting for respirofermentative and purely respiratory growth. The model describes the effects of the uptake of sugars, ammonium and/or compound nutrients such as amino acids on the translational resource allocation towards proteome sectors that maximized the growth rate. It robustly recovers cellular growth laws including the Monod law and the ribosomal growth law. Furthermore, we show how the growth-maximizing balance between carbon uptake, recycling, and excretion depends on the nutrient environment. Lastly, we find a robust linear correlation between the ribosome fraction and the abundance of amino acid equivalents in the optimal cell, which supports the view that simple regulation of translational gene expression can enable cells to achieve an approximately optimal growth state

Semi-supervised classification and visualisation of multi-view data

An increasing number of multi-view data are being published by studies in several fields. This type of data corresponds to multiple data-views, each representing a different aspect of the same set of samples. We have recently proposed multi-SNE, an extension of t-SNE, that produces a single visualisation of multi-view data. The multi-SNE approach provides low-dimensional embeddings of the samples, produced by being updated iteratively through the different data-views. Here, we further extend multi-SNE to a semi-supervised approach, that classifies unlabelled samples by regarding the labelling information as an extra data-view. We look deeper into the performance, limitations and strengths of multi-SNE and its extension, S-multi-SNE, by applying the two methods on various multi-view datasets with different challenges. We show that by including the labelling information, the projection of the samples improves drastically and it is accompanied by a strong classification performance