A Novel Approach for Calculating Exact Forms of mRNA Distribution in Single-Cell Measurements

Gene transcription is a stochastic process manifested by fluctuations in mRNA copy numbers in individual isogenic cells. Together with mathematical models of stochastic transcription, the massive mRNA distribution data that can be used to quantify fluctuations in mRNA levels can be fitted by Pm(t), which is the probability of producing m mRNA molecules at time t in a single cell. Tremendous efforts have been made to derive analytical forms of Pm(t), which rely on solving infinite arrays of the master equations of models. However, current approaches focus on the steady-state (t→∞) or require several parameters to be zero or infinity. Here, we present an approach for calculating Pm(t) with time, where all parameters are positive and finite. Our approach was successfully implemented for the classical two-state model and the widely used three-state model and may be further developed for different models with constant kinetic rates of transcription. Furthermore, the direct computations of Pm(t) for the two-state model and three-state model showed that the different regulations of gene activation can generate discriminated dynamical bimodal features of mRNA distribution under the same kinetic rates and similar steady-state mRNA distribution.

Origins and breadth of pairwise epistasis in an α-helix of β-lactamase TEM-1

Epistasis affects genome evolution together with our ability to predict individual mutation effects. The mechanistic basis of epistasis remains, however, largely unknown. To quantify and better understand interactions between fitness-affecting mutations, we focus on a 11 amino-acid α-helix of the protein β-lactamase TEM-1, and build a comprehensive library of more than 15,000 double mutants. Analysis of the growth rates of these mutants shows pervasive epistasis, which can be largely explained by a non-linear two-state model, where inactivating, destabilizing, neutral, or stabilizing mutations additively contribute to the phenotype. Hence, most epistatic interactions can be predicted by a non-linear model informed by single-point mutational measurements only. Deviations from the two-state model are consistently found for few pairs of residues, in particular when they are in contact. This result, as well as single-point mutation parameters can be quantitatively found back through direct-coupling-analysis-based statistical models inferred from homologous sequence data. Our results thus shed light on the existence and the origins of the multiple determinants of the epistatic landscape, even at the level of small structural components of a protein, and suggest that the corresponding constraints shape the entire β-lactamase family.

Optimal Effort on Self-Insurance-Cum-Protection: A New Analysis Using Yaari’s Dual Theory

People take different measures to control risks. The measures that can simultaneously reduce loss probability and loss size are called self-insurance-cum-protection. This paper studies self-insurance-cum-protection using Yaari’s dual theory. We analyze the comparative statics of increased risk aversion. Two different sufficient conditions are found in the two-state model, from which an increase in the level of risk aversion will lead to an increase in the level of self-insurance-cum-protection. The first condition is a new result under Yaari’s dual theory and its implication is that the more risk-averse individual is willing to exert greater effort on self-insurance-cum-protection if the probability of loss can be reduced to very small by a less risk-averse individual with optimal effort. The second condition depends on the forms of the self-insurance-cum protection cost and the loss. This condition is the same as that obtained under expected utility in existing literature. Our study therefore assures the robustness this result. We also study comparative statics in the continuous model and find out that the results are analogous to that in the two-state model. In addition, we consider how the availability of market insurance affects the self-insurance-cum-protection level. When the probability of loss is small, the self-insurance-cum-protection and market insurance are substitutes. This means when market insurance is available, people tend to exert less effort on self-insurance-cum-protection.

Worklife and Unemployment: A New Consideration

Do traditional two-state worklife estimates need adjustment for unemployment? To answer, an augmented three-state model classifies individuals as either 1) employed; 2) unemployed; or 3) inactive but not marginally attached. Periods of unemployment may reduce worklives; however, removal of those marginally attached or discouraged from the inactive state raises worklives. The three-state model results are compared to worklife estimates from the same initial data using the traditional two-state model. Results show that in many cases, the two-state model results are a good proxy for the three-state results that control for unemployment.

Distinguishing between models of mammalian gene expression: telegraph-like models versus mechanistic models

Two-state models (telegraph-like models) have a successful history of predicting distributions of cellular and nascent mRNA numbers that can well fit experimental data. These models exclude key rate limiting steps, and hence it is unclear why they are able to accurately predict the number distributions. To answer this question, here we compare these models to a novel stochastic mechanistic model of transcription in mammalian cells that presents a unified description of transcriptional factor, polymerase and mature mRNA dynamics. We show that there is a large region of parameter space where the first, second and third moments of the distributions of the waiting times between two consecutively produced transcripts (nascent or mature) of two-state and mechanistic models exactly match. In this region: (i) one can uniquely express the two-state model parameters in terms of those of the mechanistic model, (ii) the models are practically indistinguishable by comparison of their transcript numbers distributions, and (iii) they are distinguishable from the shape of their waiting time distributions. Our results clarify the relationship between different gene expression models and identify a means to select between them from experimental data.

Coarse snapshots of oxygen-dissociation intermediates of a giant hemoglobin elucidated by determining the oxygen saturation in individual subunits in the crystalline state

Cooperative oxygen binding of hemoglobin (Hb) has been studied for over half a century as a representative example of the allostericity of proteins. The most important problem remaining to be solved is the lack of structural information on the intermediates between the oxygenated and deoxygenated forms. In order to characterize the intermediate structures, it is necessary to obtain intermediate-state crystals, determine their oxygen saturations and then determine the oxygen saturations of each of their constituent subunits, all of which are challenging issues even now. Here, intermediate forms of the 400 kDa giant Hb from the tubeworm Oligobrachia mashikoi are reported. To overcome the above problems without any artificial modifications to the protein or prosthetic groups, intermediate crystals of the giant Hb were prepared from fully oxygenated crystals by a soaking method. The oxygen saturation of the crystals was measured by in situ observation with a microspectrophotometer using thin plate crystals processed by an ultraviolet laser to avoid saturation of absorption. The oxygen saturation of each subunit was determined by occupancy refinement of the bound oxygen based on ambient temperature factors. The obtained structures reveal the detailed relationship between the structural transition and oxygen dissociation. The dimer subassembly of the giant Hb shows strong correlation with the local structural changes at the heme pockets. Although some local ternary-structural changes occur in the early stages of the structural transition, the associated global ternary-structural and quaternary-structural changes might arise at about 50% oxygen saturation. The models based on coarse snapshots of the allosteric transition support the conventional two-state model of Hbs and provide the missing pieces of the intermediate structures that are required for full understanding of the allosteric nature of Hbs in detail.

Superlubric polycrystalline graphene interfaces

The effects of corrugated grain boundaries on the frictional properties of extended planar graphitic contacts incorporating a polycrystalline surface are investigated via molecular dynamics simulations. The kinetic friction is found to be dominated by shear induced buckling and unbuckling of corrugated grain boundary dislocations, leading to a nonmonotonic behavior of the friction with normal load and temperature. The underlying mechanism involves two effects, where an increase of dislocation buckling probability competes with a decrease of the dissipated energy per buckling event. These effects are well captured by a phenomenological two-state model, that allows for characterizing the tribological properties of any large-scale polycrystalline layered interface, while circumventing the need for demanding atomistic simulations. The resulting negative differential friction coefficients obtained in the high-load regime can reduce the expected linear scaling of grain-boundary friction with surface area and restore structural superlubricity at increasing length-scales.