Two-Dimensional Interfacial Exchange Diffusion Has the Potential to Augment Spatiotemporal Precision of Ca2+ Signaling

Nano-junctions between the endoplasmic reticulum and cytoplasmic surfaces of the plasma membrane and other organelles shape the spatiotemporal features of biological Ca2+ signals. Herein, we propose that 2D Ca2+ exchange diffusion on the negatively charged phospholipid surface lining nano-junctions participates in guiding Ca2+ from its source (channel or carrier) to its target (transport protein or enzyme). Evidence provided by in vitro Ca2+ flux experiments using an artificial phospholipid membrane is presented in support of the above proposed concept, and results from stochastic simulations of Ca2+ trajectories within nano-junctions are discussed in order to substantiate its possible requirements. Finally, we analyze recent literature on Ca2+ lipid interactions, which suggests that 2D interfacial Ca2+ diffusion may represent an important mechanism of signal transduction in biological systems characterized by high phospholipid surface to aqueous volume ratios.

Mean exit time in irregularly-shaped annular and composite disc domains

Calculating the mean exit time (MET) for models of diffusion is a classical problem in statistical physics, with various applications in biophysics, economics and heat and mass transfer. While many exact results for MET are known for diffusion in simple geometries involving homogeneous materials, calculating MET for diffusion in realistic geometries involving heterogeneous materials is typically limited to repeated stochastic simulations or numerical solutions of the associated boundary value problem (BVP). In this work we derive exact solutions for the MET in irregular annular domains, including some applications where diffusion occurs in heterogenous media. These solutions are obtained by taking the exact results for MET in an annulus, and then constructing various perturbation solutions to account for the irregular geometries involved. These solutions, with a range of boundary conditions, are implemented symbolically and compare very well with averaged data from repeated stochastic simulations and with numerical solutions of the associated BVP. Software to implement the exact solutions is available on \href{https://github.com/ProfMJSimpson/Exit_time}{GitHub}.

Calculating the force-dependent unbinding rate of biological macromolecular bonds from force-ramp optical trapping assays

The non-covalent biological bonds that constitute protein–protein or protein–ligand interactions play crucial roles in many cellular functions, including mitosis, motility, and cell–cell adhesion. The effect of external force ($$F$$ F ) on the unbinding rate ($${k}_{\text{off}}\left(F\right)$$ k off F ) of macromolecular interactions is a crucial parameter to understanding the mechanisms behind these functions. Optical tweezer-based single-molecule force spectroscopy is frequently used to obtain quantitative force-dependent dissociation data on slip, catch, and ideal bonds. However, analyses of this data using dissociation time or dissociation force histograms often quantitatively compare bonds without fully characterizing their underlying biophysical properties. Additionally, the results of histogram-based analyses can depend on the rate at which force was applied during the experiment and the experiment’s sensitivity. Here, we present an analytically derived cumulative distribution function-like approach to analyzing force-dependent dissociation force spectroscopy data. We demonstrate the benefits and limitations of the technique using stochastic simulations of various bond types. We show that it can be used to obtain the detachment rate and force sensitivity of biological macromolecular bonds from force spectroscopy experiments by explicitly accounting for loading rate and noisy data. We also discuss the implications of our results on using optical tweezers to collect force-dependent dissociation data.

Deterministic approximation for population dynamics in the presence of advantageous mutants

Spatial stochastic simulations of evolutionary processes are computationally expensive. Here, based on spatially explicit decoupling approximations (SEDA) introduced by us earlier, we derive a deterministic approximation to a spatial stochastic birth-death process in the presence of two types: the less advantageous resident type and a more advantageous mutant. At the core of this technique are two essential steps: (1) a system of ODEs that approximate spatial interactions among neighboring individuals must be solved; (2) the time-variable has to be rescaled with a factor (called "alpha") that depends on the kinetic parameters of the wild type and mutant individuals. An explicit formula for alpha is derived, which is a power law of division and death rates of the two types. The method is relatively fast and provides excellent time-series agreement with the stochastic simulation results for the spatial agent-based model. The methodology can be used to describe hard selective sweep events, including the expansion of driver mutations in carcinogenesis, bacterial evolution, and aspects of resistance dynamics.

Smart Design of Green Hydrogen Facilities: A Digital Twin-driven approach

This work studies the potentials of Digital Twin solutions for the design of competitive and reliable green hydrogen facilities. A digital twin based on stochastic simulations is proposed to address the uncertainties associated with investment and operating costs, to increase confidence and stimulate investments. Several input assumptions are involved (i.e., capital and operational costs, energy consumption, available energy, among others) to analyse their influence on financial indicators. A set of facility designs with equipment redundancy, and thus different system availabilities, was proposed. Monte Carlo simulation method is chosen to propagate uncertainties onto the project bankability assessment. By applying the proposed methodology, the opportunity index and internal rate of return (IRR) are calculated. A sensibility analysis is also carried out. The simulations illustrate that the design of a facility can be optimized to achieve higher profits, based on a trade-off between investment and availability. This study concludes that digital twin solutions are an opportunity for reducing the uncertainties associated with green hydrogen facility design. Improvements to the proposed model can be achieved by performing a refined simulation, in relation to the calculation of system availability and maintenance costs.

Robustness of DNA Looping Across Multiple Divisions in Individual Bacteria

DNA looping has emerged as a central paradigm of transcriptional regulation as it is shared across many living systems. One core property of DNA looping-based regulation is its ability to greatly enhance repression or activation of genes with only a few copies of transcriptional regulators. However, this property based on small number of proteins raises the question of the robustness of such a mechanism with respect to the large intracellular perturbations taking place during growth and division of the cell. Here we address the issue of sensitivity to variations of intracellular parameters of gene regulation by DNA looping. We use the lac system as a prototype to experimentally identify the key features of the robustness of DNA looping in growing E. coli cells. Surprisingly, we observe time intervals of tight repression spanning across division events, which can sometimes exceed ten generations. Remarkably, the distribution of such long time intervals exhibits memoryless statistics that is mostly insensitive to repressor concentration, cell division events, and the number of distinct loops accessible to the system. By contrast, gene regulation becomes highly sensitive to these perturbations when DNA looping is absent. Using stochastic simulations, we propose that the robustness to division events of memoryless distributions emerges from the competition between fast, multiple re-binding events of repressors and slow initiation rate of the RNA-polymerase. We argue that fast re-binding events are a direct consequence of DNA looping that ensures robust gene repression across a range of intracellular perturbations.

Time-resolved analysis of transcription kinetics in single live mammalian cells

In eukaryotic cells, RNA polymerase II synthesizes mRNA in three stages, initiation, elongation, and termination, and numerous factors determine how quickly a gene is transcribed to produce mRNA molecules through these steps. However, there are few techniques available to measure the rate of each step in living cells, which prevents a better understanding of transcriptional regulation. Here, we present a quantitative analysis method to extract kinetic rates of transcription from time-lapse imaging data of fluorescently labeled mRNA in live cells. Using embryonic fibroblasts cultured from two knock-in mouse models, we monitored transcription of β-actin and Arc mRNA labeled with MS2 and PP7 stem-loop systems, respectively. After inhibiting transcription initiation, we measured the elongation rate and the termination time by fitting the time trace of transcription intensity with a mathematical model function. We validated our results by comparing them with steady-state fluctuation analysis and stochastic simulations. This live-cell transcription analysis method will be useful for studying the regulation of elongation and termination steps and may provide insight into the diverse mechanisms of transcriptional processes.

Weakly deleterious natural genetic variation amplifies probability of resistance in multiplexed gene drive systems

Evolution of resistance is a major barrier to successful deployment of gene drive systems to suppress natural populations. Multiplexed guide RNAs that require resistance mutations in all target cut sites is a promising strategy to overcome resistance. Using novel stochastic simulations that accurately model evolution at very large population sizes, we explore the probability of resistance due to three important mechanisms: 1) non-homologous end-joining mutations, 2) single nucleotide mutants arising de novo or, 3) single nucleotide polymorphisms pre-existing as standing variation. If the fraction of functional end-joining mutants is rare, we show that standing variation dominates, via a qualitatively new phenomenon where weakly deleterious variants significantly amplify the probability of multi-site resistance. This means resistance can be probable even with many target sites in not very large populations. This result has broad application to resistance arising in multi-site evolutionary scenarios including the evolution of vaccine escape mutations in large populations.