Dimensional Dependence of Binding Kinetics.

In the context of protein-protein binding, the dissociation constant is used to describe the affinity between two proteins. For protein-protein interactions, most experimentally-measured dissociation constants are measured in solution and reported in units of volume concentration. However, many protein interactions take place on membranes.

DEVELOPMENT OF FIBRIN BRANCH STRUCTURE BEFORE AND AFTER GELATION.

In [Fogelson and Keener, , 81 (2010), 051922], we introduced a kinetic model of fibrin polymerization during blood clotting that captured salient experimental observations about how the gel branching structure depends on the conditions under which the polymerization occurs. Our analysis there used a moment-based approach that is valid only before the finite time blow-up that indicates formation of a gel. Here, we extend our analyses of the model to include both pre-gel and post-gel dynamics using the PDE-based framework we introduced in [Fogelson and Keener, .

Modeling and Simulation of the Ion-Binding-Mediated Swelling Dynamics of Mucin-like Polyelectrolyte Gels.

Volume phase transitions in polyeletrolyte gels play important roles in many biophysical processes such as DNA packaging, nerve excitation, and cellular secretion. The swelling and deswelling of these charged polymer gels depend strongly on their ionic environment. In this paper, we present an extension to our previous two-fluid model for ion-binding-mediated gel swelling.

Bifurcation Analysis of a Heat-Sensitive Epigenetic Regulatory Network.

An epigenetic regulatory network that influences transgenerational inheritance of a heat-altered phenotype was recently discovered in Arabidopsis. Our analysis shows that transgenerational inheritance of the heat-altered phenotype operates in a switch-like manner and can be turned on or off as a function of heat. We also show that trans-acting small interfering RNAs act as an "inverse amplifier" of HTT5, the protein that controls the heat-altered phenotype by a currently unknown mechanism.

Principles of slowed hydrogen diffusion through a mucus layer.

The control of transport through mucus layers is a ubiquitous phenomenon in physiological systems. Mucus is often tasked with the mediation of passive, diffusive transport of small ionic species. However, questions remain regarding how mucin gel characteristics (charge density of the polymeric network, binding affinity of ions with mucus) govern the rate at which ions diffuse through mucus layers.

Initiation and entrainment of multicellular automaticity via diffusion limited extracellular domains.

Electrically excitable cells often spontaneously and synchronously depolarize in vitro and in vivo preparations. It remains unclear how cells entrain and autorhythmically activate above the intrinsic mean activation frequency of isolated cells with or without pacemaking mechanisms. Recent studies suggest that cyclic ion accumulation and depletion in diffusion-limited extracellular volumes modulate electrophysiology by ephaptic mechanisms (nongap junction or synaptic coupling).

Lumped parameter models for two-ventricle and healthy and failing extracardiac Fontan circulations.

Fontan circulations are surgical strategies to treat infants born with single ventricle physiology. Clinical and mathematical definitions of Fontan failure are lacking, and understanding is needed of parameters indicative of declining physiologies. Our objective is to develop lumped parameter models of two-ventricle and single-ventricle circulations.

ENHANCED ELECTRODIFFUSIVE TRANSPORT ACROSS A MUCUS LAYER.

Diffusive transport of small ionic species through mucus layers is a ubiquitous phenomenon in physiology. However, some debate remains regarding how the various characteristics of mucus (charge of the polymers themselves, binding affinity of ions with mucus) impact the rate at which small ions may diffuse through a hydrated mucus gel. Indeed it is not even clear if small ionic species diffuse through mucus gel at an appreciably different rate than they do in aqueous solution.

A systematic search for switch-like behavior in type II toxin-antitoxin systems.

Bistable switch-like behavior is a ubiquitous feature of gene regulatory networks with decision-making capabilities. Type II toxin-antitoxin (TA) systems are hypothesized to facilitate a bistable switch in toxin concentration that influences the dormancy transition in persister cells. However, a series of recent retractions has raised fundamental questions concerning the exact mechanism of toxin propagation in persister cells and the relationship between type II TA systems and cellular dormancy.

A mathematical model of flagellar gene regulation and construction in Salmonella enterica.

Millions of people worldwide develop foodborne illnesses caused by Salmonella enterica (S. enterica) every year. The pathogenesis of S.

The PafBC-mediated response sensitizes a bistable DNA damage response in Mycobacteria.

Due to the genotoxically challenging environments in which they live in, Mycobacteria have a complex DNA damage repair system that is governed by two major DNA damage responses, namely, the LexA/RecA-dependent response and the newly characterized PafBC-mediated response (Müller et al., 2018). The LexA/RecA-dependent response is a well-known bistable response found in different types of bacteria, and the Mycobacteria-specific PafBC-mediated response interacts with and modifies the LexA/RecA-dependent response (Müller et al.

A Mathematical Model for Inheritance of DNA Methylation Patterns in Somatic Cells.

DNA methylation is an essential epigenetic mechanism used by cells to regulate gene expression. Interestingly, DNA replication, a function necessary for cell division, disrupts the methylation pattern. Since perturbed methylation patterns are associated with aberrant gene expression and many diseases, including cancer, restoration of the correct pattern following DNA replication is crucial.

Kinetic model of two-monomer polymerization.

We propose a kinetic gelation model of polymer growth with two monomeric types that have distinct functionalities (reaction sites), and can polymerize using different reaction types. The heterotypic aggregation of two monomer types is modeled using a moment generating function approach by tracking the temporal evolution of a closed system of moment equations up until gelation. We investigate several scenarios of polymerization with two distinct monomers that differ in the types of reactions that can occur.

Electrodiffusion-Mediated Swelling of a Two-Phase Gel Model of Gastric Mucus.

Gastric mucus gel is known to exhibit dramatic and unique swelling behaviors in response to the ionic composition of the hydrating solution. This swelling behavior is important in the maintenance of the mucus layer lining the stomach wall, as the layer is constantly digested by enzymes in the lumen, and must be replenished by new mucus that swells as it is secreted from the gastric wall. One hypothesis suggests that the condensed state of mucus at secretion is maintained by transient bonds with calcium that form crosslinks.

The computation of biomarkers in pharmacokinetics with the aid of singular perturbation methods.

In pharmacokinetics, exact solutions to one-compartment models with nonlinear elimination kinetics cannot be found analytically, if dosages are assumed to be administered repetitively through extravascular routes (Tang and Xiao in J Pharmacokinet Pharmacodyn 34(6):807-827, 2007). Hence, for the corresponding impulsed dynamical system, alternative methods need to be developed to find approximate solutions. The primary purpose of this paper is to use the method of matched asymptotic expansions (Holmes Introduction to Perturbation Methods, vol 20.

Enhanced Nucleocytoplasmic Transport due to Competition for Elastic Binding Sites.

Nuclear pore complexes (NPCs) control all traffic into and out of the cell nucleus. NPCs are molecular machines that simultaneously achieve high selectivity and high transport rates. The biophysical details of how cargoes rapidly traverse the pore remain unclear but are known to be mediated by interactions between cargo-binding chaperone proteins and natively unstructured nucleoporin proteins containing many phenylalanine-glycine repeats (FG nups) that line the pore's central channel.

A physics-based model for maintenance of the pH gradient in the gastric mucus layer.

It is generally accepted that the gastric mucus layer provides a protective barrier between the lumen and the mucosa, shielding the mucosa from acid and digestive enzymes and preventing autodigestion of the stomach epithelium. However, the precise mechanisms that contribute to this protective function are still up for debate. In particular, it is not clear what physical processes are responsible for transporting hydrogen protons, secreted within the gastric pits, across the mucus layer to the lumen without acidifying the environment adjacent to the epithelium.

Molecular and Physical Mechanisms of Fibrinolysis and Thrombolysis from Mathematical Modeling and Experiments.

Despite the common use of thrombolytic drugs, especially in stroke treatment, there are many conflicting studies on factors affecting fibrinolysis. Because of the complexity of the fibrinolytic system, mathematical models closely tied with experiments can be used to understand relationships within the system. When tPA is introduced at the clot or thrombus edge, lysis proceeds as a front.

Bidirectionality from cargo thermal fluctuations in motor-mediated transport.

Molecular motor proteins serve as an essential component of intracellular transport by generating forces to haul cargoes along cytoskeletal filaments. Two species of motors that are directed oppositely (e.g.

Rebinding in biochemical reactions on membranes.

The behavior of many biochemical processes depends crucially on molecules rapidly rebinding after dissociating. In the case of multisite protein modification, the importance of rebinding has been demonstrated both experimentally and through several recent computational studies involving stochastic spatial simulations. As rebinding stems from spatio-temporal correlations, theorists have resorted to models that explicitly include space to properly account for the effects of rebinding.

Bacterial flagella grow through an injection-diffusion mechanism.

The bacterial flagellum is a self-assembling nanomachine. The external flagellar filament, several times longer than a bacterial cell body, is made of a few tens of thousands subunits of a single protein: flagellin. A fundamental problem concerns the molecular mechanism of how the flagellum grows outside the cell, where no discernible energy source is available.

Including Rebinding Reactions in Well-Mixed Models of Distributive Biochemical Reactions.

The behavior of biochemical reactions requiring repeated enzymatic substrate modification depends critically on whether the enzymes act processively or distributively. Whereas processive enzymes bind only once to a substrate before carrying out a sequence of modifications, distributive enzymes release the substrate after each modification and thus require repeated bindings. Recent experimental and computational studies have revealed that distributive enzymes can act processively due to rapid rebindings (so-called quasi-processivity).

Potassium channels in the Cx43 gap junction perinexus modulate ephaptic coupling: an experimental and modeling study.

It was recently demonstrated that cardiac sodium channels (Nav1.5) localized at the perinexus, an intercalated disc (ID) nanodomain associated with gap junctions (GJ), may contribute to electrical coupling between cardiac myocytes via an ephaptic mechanism. Impairment of ephaptic coupling by acute interstitial edema (AIE)-induced swelling of the perinexus was associated with arrhythmogenic, anisotropic conduction slowing.

Mathematical modeling of bacterial track-altering motors: Track cleaving through burnt-bridge ratchets.

The generation of directed movement of cellular components frequently requires the rectification of Brownian motion. Molecular motor enzymes that use ATP to walk on filamentous tracks are typically involved in cell transport, however, a track-altering motor can arise when an enzyme interacts with and alters its track. In Caulobacter crescentus and other bacteria, an active DNA partitioning (Par) apparatus is employed to segregate replicated chromosome regions to specific locations in dividing cells.

Extracellular sodium and potassium levels modulate cardiac conduction in mice heterozygous null for the Connexin43 gene.

Unlabelled: Several studies have disagreed on measurements of cardiac conduction velocity (CV) in mice with a heterozygous knockout of the connexin gene Gja1--a mutation that reduces the gap junction (GJ) protein, Connexin43 (Cx43), by 50 %. We noted that perfusate ionic composition varied between studies and hypothesized that extracellular ionic concentration modulates CV dependence on GJs. CV was measured by optically mapping wild-type (WT) and heterozygous null (HZ) hearts serially perfused with solutions previously associated with no change (Solution 1) or CV slowing (Solution 2).