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. These interactions have dissociation constants with units of areal concentration, rather than volume concentration. Here, we present a novel, stochastic approach to understanding the dimensional dependence of binding kinetics. Using stochastic exit time calculations, in discrete and continuous space, we derive general reaction rates for protein-protein binding in one, two, and three dimensions and demonstrate that dimensionality greatly affects binding kinetics. Further, we present a formula to transform three-dimensional experimentally-measured dissociation constants to two-dimensional dissociation constants. This conversion can be used to mathematically model binding events that occur on membranes.

Top-down mass spectrometry of native proteoforms and their complexes: a community study.

The combination of native electrospray ionization with top-down fragmentation in mass spectrometry (MS) allows simultaneous determination of the stoichiometry of noncovalent complexes and identification of their component proteoforms and cofactors. Although this approach is powerful, both native MS and top-down MS are not yet well standardized, and only a limited number of laboratories regularly carry out this type of research. To address this challenge, the Consortium for Top-Down Proteomics initiated a study to develop and test protocols for native MS combined with top-down fragmentation of proteins and protein complexes across 11 instruments in nine laboratories. Here we report the summary of the outcomes to provide robust benchmarks and a valuable entry point for the scientific community.

Top-Down Characterization of Bacterial Lipopolysaccharides and Lipooligosaccharides Using Activated-Electron Photodetachment Mass Spectrometry.

Lipopolysaccharides (LPS) and lipooligosaccharides (LOS) are located in the outer membrane of Gram-negative bacteria and are comprised of three distinctive parts: lipid A, core oligosaccharide (OS), and O-antigen. The structure of each region influences bacterial stability, toxicity, and pathogenesis. Here, we highlight the use of targeted activated-electron photodetachment (a-EPD) tandem mass spectrometry to characterize LPS and LOS from two crucial players in the human gut microbiota, Escherichia coli Nissle and Bacteroides fragilis. a-EPD is a hybrid activation method that uses ultraviolet photoirradiation to generate charge-reduced radical ions followed by collisional activation to produce informative fragmentation patterns. We benchmark the a-EPD method for top-down characterization of triacyl LOS from E. coli R2, then focus on characterization of LPS from E. coli Nissle and B. fragilis. Notably, a-EPD affords extensive fragmentation throughout the backbone of the core OS and O-antigen regions of LPS from E. coli Nissle. This hybrid approach facilitated the elucidation of structural details for LPS from B. fragilis, revealing a putative hexuronic acid (HexA) conjugated to lipid A.

Polyproline peptide targets Klebsiella pneumoniae polysaccharides to collapse biofilms.

Hypervirulent Klebsiella pneumoniae is known for its increased extracellular polysaccharide production. Biofilm matrices of hypervirulent K. pneumoniae have increased polysaccharide abundance and are uniquely susceptible to disruption by peptide bactenecin 7 (bac7 (1-35)). Here, using confocal microscopy, we show that polysaccharides within the biofilm matrix collapse following bac7 (1-35) treatment. This collapse led to the release of cells from the biofilm, which were then killed by the peptide. Characterization of truncated peptide analogs revealed that their interactions with polysaccharide were responsible for the biofilm matrix changes that accompany bac7 (1-35) treatment. Ultraviolet photodissociation mass spectrometry with the parental peptide or a truncated analog bac7 (10-35) reveal the important regions for bac7 (1-35) complexing with polysaccharides. Finally, we tested bac7 (1-35) using a murine skin abscess model and observed a significant decrease in the bacterial burden. These findings unveil the potential of bac7 (1-35) polysaccharide interactions to collapse K. pneumoniae biofilms.

Top-down mass spectrometry of native proteoforms and their complexes: A community study.

The combination of native electrospray ionisation with top-down fragmentation in mass spectrometry allows simultaneous determination of the stoichiometry of noncovalent complexes and identification of their component proteoforms and co-factors. While this approach is powerful, both native mass spectrometry and top-down mass spectrometry are not yet well standardised, and only a limited number of laboratories regularly carry out this type of research. To address this challenge, the Consortium for Top-Down Proteomics (CTDP) initiated a study to develop and test protocols for native mass spectrometry combined with top-down fragmentation of proteins and protein complexes across eleven instruments in nine laboratories. The outcomes are summarised in this report to provide robust benchmarks and a valuable entry point for the scientific community.

Modeling the kinetics of heteromeric potassium channels.

Mechanistic mathematical modeling has long been used as a tool for answering questions in cellular physiology. To mathematically describe cellular processes such as cell excitability, volume regulation, neurotransmitter release, and hormone secretion requires accurate descriptions of ion channel kinetics. One class of ion channels currently lacking a physiological model framework is the class of channels built with multiple different potassium protein subunits called heteromeric voltage gated potassium channels. Here we present a novel mathematical model for heteromeric potassium channels that captures both the number and type of protein subunits present in each channel. Key model assumptions are validated by showing our model is the reduction of a Markov model and through observations about voltage clamp data. We then show our model's success in replicating kinetic properties of concatemeric channels with different numbers of K v 1.1 and K v 1.2 subunits. Finally, through comparisons with multiple expression experiments across multiple voltage gated potassium families, we use the model to make predictions about the importance and effect of genetic mutations in heteromeric channel formation.

DEVELOPMENT OF FIBRIN BRANCH STRUCTURE BEFORE AND AFTER GELATION.

In [Fogelson and Keener, Phys. Rev. E, 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, SIAM J. Appl. Math., 75 (2015), pp. 1346-1368]. We also extend the model to include spatial heterogeneity and spatial transport processes. Studies of the behavior of the model reveal different spatial-temporal dynamics as the time scales of the key processes of branch formation, monomer introduction, and diffusion are varied.

Investigating the Lipid Selectivity of Membrane Proteins in Heterogeneous Nanodiscs.

The structure and function of membrane proteins can be significantly impacted by the surrounding lipid environment, but membrane protein-lipid interactions in lipid bilayers are often difficult to study due to their transient and polydisperse nature. Here, we used two native mass spectrometry (MS) approaches to investigate how the Escherichia coli ammonium transporter trimer (AmtB) and aquaporin Z (AqpZ) selectively remodel their local lipid environment in heterogeneous lipoprotein nanodiscs. First, we used gas-phase ejection to isolate the membrane protein with bound lipids from heterogeneous nanodiscs with different combinations of lipids. Second, we used solution-phase detergent extraction as an orthogonal approach to study membrane protein remodeling of lipids in the nanodisc with native MS. Our results showed that Triton X-100 and lauryldimethylamine oxide retain lipid selectivity that agrees with gas-phase ejection, but C8E4 distorts some preferential lipid interactions. Both approaches reveal that AmtB has a few selective binding sites for phosphatidylcholine (PC) lipids, is selective for binding phosphatidylglycerols (PG) overall, and is nonselective for phosphatidylethanolamines (PE). In contrast, AqpZ prefers either PC or PG over PE and prefers PC over PG. Overall, these experiments provide a picture of how membrane proteins bind different lipid head groups in the context of mixed lipid bilayers.

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. Our analysis uses the resultant to find an analytic expression for a cusp curve in parameter space and to find a parameter bound on switch-like behavior.

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. The extended model eliminates the assumptions about the size similarity between the network and solvent particles, which makes it suitable for investigating of a large family of biologically relevant problems. The model treats the polyeletrolyte gel as a mixture of two materials, the network and the solvent. The dynamics of gel swelling is governed by the balance between the mechanical and chemical forces on each of these two materials. Simulations based on the model illustrate that the chemical forces are significantly influenced by the binding/unbinding reactions between the ions and the network, as well as the resulting distribution of charges within the gel. The dependence of the swelling rate on ionic bath concentrations is analyzed and this analysis highlights the importance of the electromigration of ions and the induced electric field in regulating gel swelling.

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). This report explores how potassium accumulation and depletion in a restricted extracellular domain induces spontaneous action potentials in two different computational models of excitable cells without gap junctional coupling: Hodgkin-Huxley and Luo-Rudy. Importantly, neither model will spontaneously activate on its own without external stimuli. Simulations demonstrate that cells sharing a diffusion-limited extracellular compartment can become autorhythmic and entrained despite intercellular electrical heterogeneity. Autorhythmic frequency is modulated by the cleft volume and potassium fluxes through the cleft. Additionally, inexcitable cells can suppress or induce autorhythmic activity in an excitable cell via a shared cleft. Diffusion-limited shared clefts can also entrain repolarization. Critically, this model predicts a mechanism by which diffusion-limited shared clefts can initiate, entrain, and modulate multicellular automaticity in the absence of gap junctions.

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. Experimental studies measuring hydrogen diffusion through gastric mucus have provided conflicting results, and it is not clear if the rate of ionic diffusion through mucus layers is appreciably different than in aqueous environments (depending on experimental preparation). Here, we present a mathematical analysis of electrodiffussion of two ionic species (hydrogen and chloride) through a mucus layer. In addition to accounting for the chemical binding of hydrogen to the mucus network, we enforce a zero net current condition (as mucus layers in physiological systems are not generally electrogenic) and calculate the Donnan potential that occurs at the edge of the mucus layer. The model predicts the steady-state fluxes of ionic species and the induced potential across the layer. We characterize the dependence of these quantities on the chemical properties of the mucus gel, the composition of the bath solution, and the molecular mobility of the dissolved anion, and we show that the model predictions are consistent with a large portion of the experimental literature. Our analysis predicts that mucus layers generically slow the diffusive transport of hydrogen, but that chemical binding with the network attenuates this effect.

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. These models, their mathematical formulations and a proof of existence of periodic solutions are presented. Sensitivity analyses are performed to identify key parameters. Systemic venous and systolic left ventricular compliances and systemic capillary and pulmonary venous resistances are identified as key parameters. Our models serve as a framework to study the differences between two-ventricle and single-ventricle physiologies and healthy and failing Fontan 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. Here, we present a mathematical description of the transport of two ionic species (hydrogen and chloride) through a mucus layer based on the Nernst-Planck equations of electrodiffusion. The model explicitly accounts for the binding affinity of hydrogen to the mucus material, as well as the Donnan potential that occurs at the interface between regions with and without mucus. Steady state fluxes of ionic species are quantified, as are their dependencies on the chemical properties of the mucus gel and the composition of the bath solution. We outline a mechanism for generating enhanced diffusive flux of hydrogen across the gel region, and hypothesize how this mechanism may be relevant to the apparently contradictory experimental data in the literature.

Structural basis of omega-3 fatty acid transport across the blood-brain barrier.

Docosahexaenoic acid is an omega-3 fatty acid that is essential for neurological development and function, and it is supplied to the brain and eyes predominantly from dietary sources1-6. This nutrient is transported across the blood-brain and blood-retina barriers in the form of lysophosphatidylcholine by major facilitator superfamily domain containing 2A (MFSD2A) in a Na+-dependent manner7,8. Here we present the structure of MFSD2A determined using single-particle cryo-electron microscopy, which reveals twelve transmembrane helices that are separated into two pseudosymmetric domains. The transporter is in an inward-facing conformation and features a large amphipathic cavity that contains the Na+-binding site and a bound lysolipid substrate, which we confirmed using native mass spectrometry. Together with our functional analyses and molecular dynamics simulations, this structure reveals details of how MFSD2A interacts with substrates and how Na+-dependent conformational changes allow for the release of these substrates into the membrane through a lateral gate. Our work provides insights into the molecular mechanism by which this atypical major facility superfamily transporter mediates the uptake of lysolipids into the brain, and has the potential to aid in the delivery of neurotherapeutic agents.

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. Through a careful modeling search, we identify how sp: bistablilty can emerge in type II TA systems by systematically modifying a basic model for the RelBE system with other common biological mechanisms. Our systematic search uncovers a new combination of mechanisms influencing bistability in type II TA systems and explores how toxin bistability emerges through synergistic interactions between paired type II TA systems. Our analysis also illustrates how Descartes' rule of signs and the resultant can be used as a powerful delineator of bistability in mathematical systems regardless of application.

Red Light and the Dormancy-Germination Decision in Arabidopsis Seeds.

The Arabidopsis dormancy-germination transition is known to be environmentally cued and controlled by the competing hormones abscisic acid (ABA) and gibberellin (GA) produced by the seed. Recently, new molecular details have emerged concerning the propagation of red light through a complex gene regulatory network involving PhyB, PIF1, and RVE1. This network influences the formation of the PIF1-RVE1 complex [1,2]. The PIF1-RVE1 complex is a transcription factor that regulates the production of ABA and GA and helps shift the balance to high concentration of ABA and low concentration of GA, which corresponds to a dormant seed state. This newly discovered gene regulatory network has not been analyzed mathematically. Our analysis shows that this gene regulatory network exhibits switch-like bistability as a function of the red light input and makes a suite of biologically testable predictions concerning seed dormancy and germination in response to the amplitude and periodicity of an oscillatory red light input.

Native Mass Spectrometry Reveals the Simultaneous Binding of Lipids and Zinc to Rhodopsin.

Rhodopsin, a prototypical G-protein-coupled receptor, is responsible for scoptic vision at low-light levels. Although rhodopsin's photoactivation cascade is well understood, it remains unclear how lipid and zinc binding to the receptor are coupled. Using native mass spectrometry, we developed a novel data analysis strategy to deconvolve zinc and lipid bound to the proteoforms of rhodopsin and investigated the allosteric interaction between lipids and zinc binding. We discovered that phosphatidylcholine bound to rhodopsin with a greater affinity than phosphatidylserine or phosphatidylethanolamine, and that binding of all lipids was influenced by zinc but with different effects. In contrast, zinc binding was relatively unperturbed by lipids. Overall, these data reveal that lipid binding can be strongly and differentially influenced by metal ions.

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., 2018). The interaction between the LexA/RecA-dependent response and the PafBC-mediated response has not been characterized mathematically. Our analysis shows that the addition of the PafBC-mediated response sensitizes the overall DNA damage response, effectively lowering the DNA damage rate threshold for activation.