Bilayer tension-induced clustering of the UPR sensor IRE1.

The endoplasmic reticulum acts as a protein quality control center where a range of chaperones and foldases facilitates protein folding. IRE1 is a sensory transmembrane protein that transduces signals of proteotoxic stress by forming clusters and activating a cellular program called the unfolded protein response (UPR). Recently, membrane thickness variation due to membrane compositional changes have been shown to drive IRE1 cluster formation, activating the UPR even in the absence of proteotoxic stress. Here, we demonstrate a direct relationship between bilayer tension and UPR activation based on IRE1 dimer stability. The stability of the IRE1 dimer in a (50%DOPC-50%POPC) membrane at different applied bilayer tensions was analyzed via molecular dynamics simulations. The potential of mean force for IRE1 dimerization predicts a higher concentration of IRE1 dimers for both tensed and compressed ER membranes. This study shows that IRE1 may be a mechanosensitive membrane protein and establishes a direct biophysical relationship between bilayer tension and UPR activation.

Concentration sensing in crowded environments.

Signal transduction within crowded cellular compartments is essential for the physiological function of cells. Although the accuracy with which receptors can probe the concentration of ligands has been thoroughly investigated in dilute systems, the effect of macromolecular crowding on the inference of concentration remains unclear. In this work, we develop an algorithm to simulate reversible reactions between reacting Brownian particles. Our algorithm facilitates the calculation of reaction rates and correlation times for ligand-receptor systems in the presence of macromolecular crowding. Using this method, we show that it is possible for crowding to increase the accuracy of estimated ligand concentration based on receptor occupancy. In particular, we find that crowding can enhance the effective association rates between small ligands and receptors to a degree sufficient to overcome the increased chance of rebinding due to caging by crowding molecules. For larger ligands, crowding decreases the accuracy of the receptor's estimate primarily by decreasing the microscopic association and dissociation rates.

Information processing by endoplasmic reticulum stress sensors.

The unfolded protein response (UPR) is a collection of cellular feedback mechanisms that seek to maintain protein folding homeostasis in the endoplasmic reticulum (ER). When the ER is 'stressed', through either high protein folding demand or undersupply of chaperones and foldases, stress sensing proteins in the ER membrane initiate the UPR. Recently, experiments have indicated that these signalling molecules detect stress by being both sequestered by free chaperones and activated by free unfolded proteins. However, it remains unclear what advantage this bidirectional sensor control offers stressed cells. Here, we show that combining positive regulation of sensor activity by unfolded proteins with negative regulation by chaperones allows the sensor to make a more informative measurement of ER stress. The increase in the information capacity of the combined sensing mechanism stems from stretching of the active range of the sensor, at the cost of increased uncertainty due to the integration of multiple signals. These results provide a possible rationale for the evolution of the observed stress-sensing mechanism.

Characteristic, completion or matching timescales? An analysis of temporary boundaries in enzyme kinetics.

Scaling analysis exploiting timescale separation has been one of the most important techniques in the quantitative analysis of nonlinear dynamical systems in mathematical and theoretical biology. In the case of enzyme catalyzed reactions, it is often overlooked that the characteristic timescales used for the scaling the rate equations are not ideal for determining when concentrations and reaction rates reach their maximum values. In this work, we first illustrate this point by considering the classic example of the single-enzyme, single-substrate Michaelis-Menten reaction mechanism. We then extend this analysis to a more complicated reaction mechanism, the auxiliary enzyme reaction, in which a substrate is converted to product in two sequential enzyme-catalyzed reactions. In this case, depending on the ordering of the relevant timescales, several dynamic regimes can emerge. In addition to the characteristic timescales for these regimes, we derive matching timescales that determine (approximately) when the transitions from transient to quasi-steady-state kinetics occurs. The approach presented here is applicable to a wide range of singular perturbation problems in nonlinear dynamical systems.

A theory of reactant-stationary kinetics for a mechanism of zymogen activation.

A theoretical analysis is performed on the nonlinear ordinary differential equations that govern the dynamics of a reaction mechanism of zymogen activation. The reaction consists of a primary non-observable zymogen activation reaction that it is coupled to an indicator (observable) reaction. The product of the first reaction is the enzyme of the indicator reaction, and both reactions are governed by the Michaelis-Menten reaction mechanism. Using singular perturbation methods, we derive asymptotic solutions that are valid under the quasi-steady-state and reactant-stationary assumptions. In particular, we obtain closed form solutions that are analogous to the Schnell-Mendoza equation for Michaelis-Menten type reactions. These closed-form solutions approximate the evolution of the observable reaction and provide the mathematical link necessary to measure the enzyme activity of the non-observable reaction. Conditions for the validity of the asymptotic solutions are also derived, and we demonstrate that these asymptotic expressions are applicable under reactant-stationary kinetics.

Phase-plane geometries in coupled enzyme assays.

The determination of a substrate or enzyme activity by coupling one enzymatic reaction with another easily detectable (indicator) reaction is a common practice in the biochemical sciences. Usually, the kinetics of enzyme reactions is simplified with singular perturbation analysis to derive rate or time course expressions valid under the quasi-steady-state and reactant stationary state assumptions. In this paper, the dynamical behavior of coupled enzyme catalyzed reaction mechanisms is studied by analysis of the phase-plane. We analyze two types of time-dependent slow manifolds - Sisyphus and Laelaps manifolds - that occur in the asymptotically autonomous vector fields that arise from enzyme coupled reactions. Projection onto slow manifolds yields various reduced models, and we present a geometric interpretation of the slow/fast dynamics that occur in the phase-planes of these reactions.

How to design an optimal sensor network for the unfolded protein response.

Cellular protein homeostasis requires continuous monitoring of stress in the endoplasmic reticulum (ER). Stress-detection networks control protein homeostasis by mitigating the deleterious effects of protein accumulation, such as aggregation and misfolding, with precise modulation of chaperone production. Here, we develop a coarse model of the unfolded protein response in yeast and use multi-objective optimization to determine which sensing and activation strategies optimally balance the trade-off between unfolded protein accumulation and chaperone production. By comparing a stress-sensing mechanism that responds directly to the level of unfolded protein in the ER to a mechanism that is negatively regulated by unbound chaperones, we show that chaperone-mediated sensors are more efficient than sensors that detect unfolded proteins directly. This results from the chaperone-mediated sensor having separate thresholds for activation and deactivation. Finally, we demonstrate that a sensor responsive to both unfolded protein and unbound chaperone does not further optimize homeostatic control. Our results suggest a strategy for designing stress sensors and may explain why BiP-mitigated ER stress-sensing networks have evolved.

Do Cellular Condensates Accelerate Biochemical Reactions? Lessons from Microdroplet Chemistry.

Cellular condensates-phase-separated concentrates of proteins and nucleic acids-provide organizational structure for biochemistry that is distinct from membrane-bound compartments. It has been suggested that one major function of cellular condensates is to accelerate biochemical processes that are normally slow or thermodynamically unfavorable. Yet, the mechanisms leading to increased reaction rates within cellular condensates remain poorly understood. In this article, we highlight recent advances in microdroplet chemistry that accelerate reaction rates by many orders of magnitude as compared to bulk and suggest that similar mechanisms may also affect reaction kinetics in cellular condensates.

Gonadotropin-Releasing Hormone (GnRH) Neuron Excitability Is Regulated by Estradiol Feedback and Kisspeptin.

Gonadotropin-releasing hormone (GnRH) neurons produce the central output controlling fertility and are regulated by steroid feedback. A switch from estradiol negative to positive feedback initiates the GnRH surge, ultimately triggering ovulation. This occurs on a daily basis in ovariectomized, estradiol-treated (OVX+E) mice; GnRH neurons are suppressed in the morning and activated in the afternoon. To test the hypotheses that estradiol and time of day signals alter GnRH neuron responsiveness to stimuli, GFP-identified GnRH neurons in brain slices from OVX+E or OVX female mice were recorded during the morning or afternoon. No differences were observed in baseline membrane potential. Current-clamp revealed GnRH neurons fired more action potentials in response to current injection during positive feedback relative to all other groups, which were not different from each other despite reports of differing ionic conductances. Kisspeptin increased GnRH neuron response in cells from OVX and OVX+E mice in the morning but not afternoon. Paradoxically, excitability in kisspeptin knock-out mice was similar to the maximum observed in control mice but was unchanged by time of day or estradiol. A mathematical model applying a Markov Chain Monte Carlo method to estimate probability distributions for estradiol- and time of day-dependent parameters was used to predict intrinsic properties underlying excitability changes. A single identifiable distribution of solutions accounted for similar GnRH neuron excitability in all groups other than positive feedback despite different underlying conductance properties; this was attributable to interdependence of voltage-gated potassium channel properties. In contrast, redundant solutions may explain positive feedback, perhaps indicative of the importance of this state for species survival.SIGNIFICANCE STATEMENT Infertility affects 15%-20% of couples; failure to ovulate is a common cause. Understanding how the brain controls ovulation is critical for new developments in both infertility treatment and contraception. Gonadotropin-releasing hormone (GnRH) neurons are the final common pathway for central neural control of ovulation. We studied how estradiol feedback regulates GnRH excitability, a key determinant of neural firing rate using laboratory and computational approaches. GnRH excitability is upregulated during positive feedback, perhaps driving increased neural firing rate at this time. Kisspeptin increased GnRH excitability and was essential for estradiol regulation of excitability. Modeling predicts that multiple combinations of changes to GnRH intrinsic conductances can produce the firing response in positive feedback, suggesting the brain has many ways to induce ovulation.

On the origin of non-membrane-bound organelles, and their physiological function.

The origin of cellular compartmentalization has long been viewed as paralleling the origin of life. Historically, membrane-bound organelles have been presented as the canonical examples of compartmentalization. However, recent interest in cellular compartments that lack encompassing membranes has forced biologists to reexamine the form and function of cellular organization. The intracellular environment is now known to be full of transient macromolecular structures that are essential to cellular function, especially in relation to RNA regulation. Here we discuss key findings regarding the physicochemical principles governing the formation and function of non-membrane-bound organelles. Particularly, we focus how the physiological function of non-membrane-bound organelles depends on their molecular structure. We also present a potential mechanism for the formation of non-membrane-bound organelles. We conclude with suggestions for future inquiry into the diversity of roles played by non-membrane bound organelles.

On the validity and errors of the pseudo-first-order kinetics in ligand-receptor binding.

The simple bimolecular ligand-receptor binding interaction is often linearized by assuming pseudo-first-order kinetics when one species is present in excess. Here, a phase-plane analysis allows the derivation of a new condition for the validity of pseudo-first-order kinetics that is independent of the initial receptor concentration. The validity of the derived condition is analyzed from two viewpoints. In the first, time courses of the exact and approximate solutions to the ligand-receptor rate equations are compared when all rate constants are known. The second viewpoint assesses the validity through the error induced when the approximate equation is used to estimate kinetic constants from data. Although these two interpretations of validity are often assumed to coincide, we show that they are distinct, and that large errors are possible in estimated kinetic constants, even when the linearized and exact rate equations provide nearly identical solutions.

On the estimation errors of KM and V from time-course experiments using the Michaelis-Menten equation.

The conditions under which the Michaelis-Menten equation accurately captures the steady-state kinetics of a simple enzyme-catalyzed reaction is contrasted with the conditions under which the same equation can be used to estimate parameters, KM and V, from progress curve data. Validity of the underlying assumptions leading to the Michaelis-Menten equation are shown to be necessary, but not sufficient to guarantee accurate estimation of KM and V. Detailed error analysis and numerical "experiments" show the required experimental conditions for the independent estimation of both KM and V from progress curves. A timescale, tQ, measuring the portion of the time course over which the progress curve exhibits substantial curvature provides a novel criterion for accurate estimation of KM and V from a progress curve experiment. It is found that, if the initial substrate concentration is of the same order of magnitude as KM, the estimated values of the KM and V will correspond to their true values calculated from the microscopic rate constants of the corresponding mass-action system, only so long as the initial enzyme concentration is less than KM.

Hydrodynamics of capillary imbibition under nanoconfinement.

Understanding fluid flow in nanoconfined geometries is crucial for a broad range of scientific problems relevant to the behavior of porous materials in biology, nanotechnology, and the built environment. Because of the dominant importance of surface effects at the nanoscale, long-standing assumptions that are valid for macroscopic systems must be revisited when modeling nanoconfined fluids, because boundary conditions and the confined behavior of liquids are challenging to discern from experiments. To address this issue, here we present a novel coarse-grained model that combines parameters calibrated for water with a dissipative particle dynamics thermostat for the purpose of investigating hydrodynamics under confinement at scales exceeding current capabilities with all-atomistic simulations. Conditions pertaining to slip boundary conditions and confinement emerge naturally from particle interactions, with no need for assumptions a priori. The model is used to systematically investigate the imbibition dynamics of water into cylindrical nanopores of different diameters. Interestingly, we find that the dynamic contact angle depends on the size of the nanopore in a way that cannot be explained through a relationship between contact line velocity and dynamic contact angle, suggesting nonlocal effects of the flow field may be important. Additionally, a size-dependent characteristic time scale for imbibition is found, which could be useful for the interpretation of experiments and design of novel nanofluidic devices. We present the first systematic study that explains how contact angle dynamics and imbibition dynamics vary with nanopore radius. Our modeling approach lays the foundation for broader investigations on the dynamics of fluids in nanoporous materials in conjunction with experimental efforts.