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Motivated by the biologically important and complex phenomena of A\beta\ peptide aggregation in Alzheimer's disease, we introduce a model and simulation methodology for studying protein aggregation that includes extra-cellular aggregation,…
This paper studies the estimation of characteristic-based quantile factor models where the factor loadings are unknown functions of observed individual characteristics while the idiosyncratic error terms are subject to conditional quantile…
Mechanical unfolding and refolding of ubiquitin are studied by Monte Carlo simulations of a Go model with binary variables. The exponential dependence of the time constants on the force is verified, and folding and unfolding lengths are…
We present a mathematical model describing the time development of a population of tumors subject to mutual angiogenic inhibitory signaling. Based on biophysical derivations, it describes organism-scale population dynamics under the…
This work continues the study of the earlier constructed mathematical model of the metabolic process running in a cell. We will consider auto-oscillations arising on the level of enzyme-substrate interactions in the nutrient and respiratory…
We introduce a stochastic model describing aggregation of misfolded proteins and degradation by the protein quality control system in a single cell. In analogy with existing literature, aggregates can grow, nucleate and fragment…
In this paper we study the statistical properties of a reversible cellular automaton in two out-of-equilibrium settings. In the first part we consider two instances of the initial value problem, corresponding to the inhomogeneous quench and…
Inside a cell, heterotypic proteins assemble in inhomogeneous, crowded systems where the abundance of these proteins vary with cell types. While some protein complexes form putative structures that can be visualized with imaging, there are…
Autophagy is an intracellular degradation process that is mediated by de novo formation of autophagosomes. Autophagosome formation involves dynamic morphological changes; a disk-shaped membrane cisterna grows, bends to become a cup-shaped…
Unfolded protein aggregation in cellular system is a problem causing various types of diseases depending on which type unfolded proteins aggregate. This phenomenon of aggregation may take place during production, storage, shipment or…
This paper provides a unified mathematical analysis of a family of non-local diffuse interface models for tumor growth describing evolutions driven by long-range interactions. These integro-partial differential equations model cell-to-cell…
We propose and discuss two variants of kinetic particle models - cellular automata in 1+1 dimensions, which have some appeal due to their simplicity and intriguing properties which could warrant further research and applications. The first…
An approach to modeling the oligomer composition distribution function in the irreversible step growth homopolymerization process based on a mixture of oligomers of arbitrary composition is developed. The approach is based on consideration…
We introduce a simple "patchy particle" model to study the thermodynamics and dynamics of self-assembly of homomeric protein complexes. Our calculations allow us to rationalize recent results for dihedral complexes. Namely, why evolution of…
In this paper, a novel isogeometric method for Biot's consolidation model is constructed and analyzed, using a four-field formulation where the unknown variables are the solid displacement, solid pressure, fluid flux, and fluid pressure.…
Machine learning models have emerged as a very effective strategy to sidestep time-consuming electronic-structure calculations, enabling accurate simulations of greater size, time scale and complexity. Given the interpolative nature of…
Cellular self-assembly and organization are fundamental steps for the development of biological tissues. In this paper, within the framework of a cellular automata model, we address how an ordered tissue pattern spontaneously emerges from a…
Peptides are ubiquitous and important biologically derived molecules, that have been found to self-assemble to form a wide array of structures. Extensive research has explored the impacts of both internal chemical composition and external…
We study a kinetic mean-field equation for a system of particles with different sizes, in which particles are allowed to coagulate only if their sizes sum up to a prescribed time-dependent value. We prove well-posedness of this model, study…
We develop and apply a learning framework for parameter estimation in initial value problems that are assessed only indirectly via aggregate data such as sample means and/or standard deviations. Our comprehensive framework follows Bayesian…