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During mouse gametogenesis, germ cells derived from the same progenitor are connected via intercellular bridges forming germline cysts, within which asymmetrical or symmetrical cell fate occurs in female and male germ cells, respectively. Here, we have identified branched cyst structures in mice, and investigated their formation and function in oocyte determination. In fetal female cysts, 16.8% of the germ cells are connected by three or four bridges, namely branching germ cells. These germ cells are preferentially protected from cell death and cyst fragmentation and accumulate cytoplasm and organelles from sister germ cells to become primary oocytes. Changes in cyst structure and differential cell volumes among cyst germ cells suggest that cytoplasmic transport in germline cysts is conducted in a directional manner, in which cellular content is first transported locally between peripheral germ cells and further enriched in branching germ cells, a process causing selective germ cell loss in cysts. Cyst fragmentation occurs extensively in female cysts, but not in male cysts. Male cysts in fetal and adult testes have branched cyst structures, without differential cell fates between germ cells. During fetal cyst formation, E-cadherin (E-cad) junctions between germ cells position intercellular bridges to form branched cysts. Disrupted junction formation in E-cad-depleted cysts led to an altered ratio in branched cysts. Germ cell-specific E-cad knockout resulted in reductions in primary oocyte number and oocyte size. These findings shed light on how oocyte fate is determined within mouse germline cysts.

Free Article from Systems Biologists Seek Fuller Integration of Systems Biology Approaches in New Cancer Research Programs

Systems biology takes an interdisciplinary approach to the systematic study of complex interactions in biological systems. This approach seeks to decipher the emergent behaviors of complex systems rather than focusing only on their constituent properties. As an increasing number of examples illustrate the value of systems biology approaches to understand the initiation, progression, and treatment of cancer, systems biologists from across Europe and the United States hope for changes in the way their field is currently perceived among cancer researchers. In a recent EU-US workshop, supported by the European Commission, the German Federal Ministry for Education and Research, and the National Cancer Institute of the NIH, the participants discussed the strengths, weaknesses, hurdles, and opportunities in cancer systems biology. Cancer Res; 70(1); 12–3

CLEC16A is an E3 ubiquitin ligase that regulates mitochondrial quality control through mitophagy and is associated with over 20 human diseases. CLEC16A forms a complex with another E3 ligase, RNF41, and a ubiquitin-specific peptidase, USP8; however, regions that regulate CLEC16A activity or the assembly of the tripartite mitophagy regulatory complex are unknown. Here, we report that CLEC16A contains an internal intrinsically disordered protein region (IDPR) that is crucial for CLEC16A function and turnover. IDPRs lack a fixed secondary structure and possess emerging yet still equivocal roles in protein stability, interactions, and enzymatic activity. We find that the internal IDPR of CLEC16A is crucial for its degradation. CLEC16A turnover was promoted by RNF41, which binds and acts upon the internal IDPR to destabilize CLEC16A. Loss of this internal IDPR also destabilized the ubiquitin-dependent tripartite CLEC16A–RNF41–USP8 complex. Finally, the presence of an internal IDPR within CLEC16A was confirmed using NMR and CD spectroscopy. Together, our studies reveal that an IDPR is essential to control the reciprocal regulatory balance between CLEC16A and RNF41, which could be targeted to improve mitochondrial health in disease.

We consider reaction networks that admit a singular perturbation reduction in a certain parameter range. The focus of this paper is on deriving "small parameters" (briefly for small perturbation parameters), to gauge the accuracy of the reduction, in a manner that is consistent, amenable to computation and permits an interpretation in chemical or biochemical terms. Our work is based on local timescale estimates via ratios of the real parts of eigenvalues of the Jacobian near critical manifolds. This approach modifies the one introduced by Segel and Slemrod and is familiar from computational singular perturbation theory. While parameters derived by this method cannot provide universal quantitative estimates for the accuracy of a reduction, they represent a critical first step toward this end. Working directly with eigenvalues is generally unfeasible, and at best cumbersome. Therefore we focus on the coefficients of the characteristic polynomial to derive parameters, and relate them to timescales. Thus, we obtain distinguished parameters for systems of arbitrary dimension, with particular emphasis on reduction to dimension one. As a first application, we discuss the Michaelis--Menten reaction mechanism system in various settings, with new and perhaps surprising results. We proceed to investigate more complex enzyme catalyzed reaction mechanisms (uncompetitive, competitive inhibition and cooperativity) of dimension three, with reductions to dimension one and two. The distinguished parameters we derive for these three-dimensional systems are new. In fact, no rigorous derivation of small parameters seems to exist in the literature so far. Numerical simulations are included to illustrate the efficacy of the parameters obtained, but also to show that certain limitations must be observed., 58 pages, 17 figures

During mouse gametogenesis, germ cells derived from the same progenitor are connected via intercellular bridges forming germline cysts, within which asymmetrical or symmetrical cell fate occurs in female and male germ cells respectively. Here, we have identified branched cyst structures in mice, and investigated their formation and function in oocyte determination. In fetal female cysts, 16.8% of the germ cells are connected by three or four bridges, namely branching germ cells. These germ cells are preferentially protected from cell death and cyst fragmentation, and to accumulate organelles and cytoplasm from sister germ cells to become primary oocytes. Changes in cyst structure and single-cell mRNA profiles suggested that cytoplasmic transport in germline cysts is conducted in a directional manner, in which cellular content is first transported locally between peripheral germ cells and further enriched in branching germ cells, a process causing selective germ cell loss in cysts. Cyst fragmentation occurs extensively in female cysts, but not in male cysts. Male cysts in fetal and adult testes have branched cyst structures, without differential cell fates between germ cells. During cyst formation, E-cadherin junctions between germ cells position intercellular bridges to form branched cysts. Disrupted junction formation in E-cadherin-depleted cysts led to an altered ratio in branched cysts. Germ cell-specific E-cadherin knockout resulted in reductions in primary oocyte number and oocyte size. These findings shed light on the mechanism of how the size of the ovarian reserve, the number of primary oocytes available to sustain adult ovarian function, is determined during ovary formation.

Signal transduction within crowded cellular compartments is essential for the physiological function of cells and organisms. While 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 unknown. In this work we develop a novel algorithm to simulate reversible reactions between reacting Brownian particles. This 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 large enough degree 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.SIGNIFICANCEDeveloping an understanding of how cells effectively transmit signals within or between compartments under physical constraints is an important challenge for biophysics. This work investigates the effect that macromolecular crowding can have on the accuracy of a simple ligand-receptor signaling system. We show that the accuracy of an inferred ligand concentration based on the occupancy of the receptor can be enhanced by crowding under certain circumstances. Additionally, we develop a simulation algorithm that speeds the calculation of reaction rates in crowded environments and can be readily applied to other, more complex systems.

The linear noise approximation models the random fluctuations from the mean-field model of a chemical reaction that unfolds near the thermodynamic limit. Specifically, the fluctuations obey a linear Langevin equation up to order $\Omega^{-1/2}$, where $\Omega$ is the size of the chemical system (usually the volume). In the presence of disparate timescales, the linear noise approximation admits a quasi-steady-state reduction referred to as the \textit{slow scale} linear noise approximation (ssLNA). Curiously, the ssLNAs reported in the literature are slightly different. The differences in the reported ssLNAs lie at the mathematical heart of the derivation. In this work, we derive the ssLNA directly from geometric singular perturbation theory and explain the origin of the different ssLNAs in the literature. Moreover, we discuss the loss of normal hyperbolicity and we extend the ssLNA derived from geometric singular perturbation theory to a non-classical singularly perturbed problem. In so doing, we disprove a commonly-accepted qualifier for the validity of stochastic quasi-steady-state approximation of the Michaelis--Menten reaction mechanism., Comment: 25 pages, 4 figures

CLEC16A regulates mitochondrial health through mitophagy and is associated with over 20 human diseases. However, the key structural and functional regions of CLEC16A, and their relevance for human disease, remain unknown. Here, we report that a disease-associated CLEC16A variant lacks a C-terminal intrinsically disordered protein region (IDPR) that is critical for mitochondrial quality control. IDPRs comprise nearly half of the human proteome, yet their mechanistic roles in human disease are poorly understood. Using carbon detect NMR, we find that the CLEC16A C terminus lacks secondary structure, validating the presence of an IDPR. Loss of the CLEC16A C-terminal IDPR in vivo impairs mitophagy, mitochondrial function, and glucose-stimulated insulin secretion, ultimately causing glucose intolerance. Deletion of the CLEC16A C-terminal IDPR increases CLEC16A ubiquitination and degradation, thus impairing assembly of the mitophagy regulatory machinery. Importantly, CLEC16A stability is dependent on proline bias within the C-terminal IDPR, but not amino acid sequence order or charge. Together, we elucidate how an IDPR in CLEC16A regulates mitophagy and implicate pathogenic human gene variants that disrupt IDPRs as novel contributors to diabetes and other CLEC16A-associated diseases. Abbreviations : CAS: carbon-detect amino-acid specific; IDPR: intrinsically disordered protein region; MEFs: mouse embryonic fibroblasts; NMR: nuclear magnetic resonance.

CLEC16A regulates mitochondrial health through mitophagy and is associated with over 20 human diseases. However, the key structural and functional regions of CLEC16A, and their relevance for human disease, remain unknown. Here, we report that a disease-associated CLEC16A variant lacks a C-terminal intrinsically disordered protein region (IDPR) that is critical for mitochondrial quality control. IDPRs comprise nearly half of the human proteome, yet their mechanistic roles in human disease are poorly understood. Using carbon detect NMR, we find that the CLEC16A C terminus lacks secondary structure, validating the presence of an IDPR. Loss of the CLEC16A C-terminal IDPR in vivo impairs mitophagy, mitochondrial function, and glucose-stimulated insulin secretion, ultimately causing glucose intolerance. Deletion of the CLEC16A C-terminal IDPR increases CLEC16A ubiquitination and degradation, thus impairing assembly of the mitophagy regulatory machinery. Importantly, CLEC16A stability is dependent on proline bias within the C-terminal IDPR, but not amino acid sequence order or charge. Together, we elucidate how an IDPR in CLEC16A regulates mitophagy and implicate pathogenic human gene variants that disrupt IDPRs as novel contributors to diabetes and other CLEC16A-associated diseases. Abbreviations : CAS: carbon-detect amino-acid specific; IDPR: intrinsically disordered protein region; MEFs: mouse embryonic fibroblasts; NMR: nuclear magnetic resonance.

Mistakes in trunk neural crest (NC) cell migration may lead to birth defects of the sympathetic nervous system (SNS) and neuroblastoma (NB) cancer. Receptor tyrosine kinase B (TrkB) and its ligand BDNF critically regulate NC cell migration during normal SNS development and elevated expression of TrkB is correlated with high-risk NB patients. However, in the absence of a model with in vivo interrogation of human NB cell and gene expression dynamics, the mechanistic role of TrkB in NB disease progression remains unclear. Here, we study the functional relationship between TrkB, cell invasion and plasticity of human NB cells by taking advantage of our validated in vivo chick embryo transplant model. We find that LAN5 (high TrkB) and SHSY5Y (moderate TrkB) human NB cells aggressively invade host embryos and populate typical NC targets, however loss of TrkB function significantly reduces cell invasion. In contrast, NB1643 (low TrkB) cells remain near the transplant site, but over-expression of TrkB leads to significant cell invasion. Invasive NB cells show enhanced expression of genes indicative of the most invasive host NC cells. In contrast, transplanted human NB cells down-regulate known NB tumor initiating and stem cell markers. Human NB cells that remain within the dorsal neural tube transplant also show enhanced expression of cell differentiation genes, resulting in an improved disease outcome as predicted by a computational algorithm. These in vivo data support TrkB as an important biomarker and target to control NB aggressiveness and identify the chick embryonic trunk neural crest microenvironment as a source of signals to drive NB to a less aggressive state, likely acting at the dorsal neural tube.

The quasi-steady-state approximation is widely used to develop simplified deterministic or stochastic models of enzyme catalyzed reactions. In deterministic models, the quasi-steady-state approximation can be mathematically justified from singular perturbation theory. For several closed enzymatic reactions, the homologous extension of the quasi-steady-state approximation to the stochastic regime, known as the stochastic quasi-steady-state approximation, has been shown to be accurate under the analogous conditions that permit the quasi-steady-state reduction of the deterministic counterpart. However, it was recently demonstrated that the extension of the stochastic quasi-steady-state approximation to an open Michaelis--Menten reaction mechanism is only valid under a condition that is far more restrictive than the qualifier that ensures the validity of its corresponding deterministic quasi-steady-state approximation. In this paper, we suggest a possible explanation for this discrepancy from the lens of geometric singular perturbation theory. In so doing, we illustrate a misconception in the application of the quasi-steady-state approximation: timescale separation does not imply singular perturbation., Comment: 19 pages, 1 Figure

EnzymeML is an XML-based data exchange format that supports the comprehensive documentation of enzymatic data by describing reaction conditions, time courses of substrate and product concentrations, the kinetic model, and the estimated kinetic constants. EnzymeML is based on the Systems Biology Markup Language, which was extended by implementing the STRENDA Guidelines. An EnzymeML document serves as a container to transfer data between experimental platforms, modeling tools, and databases. EnzymeML supports the scientific community by introducing a standardized data exchange format to make enzymatic data findable, accessible, interoperable, and reusable according to the FAIR data principles. An application programming interface in Python supports the integration of software tools for data acquisition, data analysis, and publication. The feasibility of a seamless data flow using EnzymeML is demonstrated by creating an EnzymeML document from a structured spreadsheet or from a STRENDA DB database entry, by kinetic modeling using the modeling platform COPASI, and by uploading to the enzymatic reaction kinetics database SABIO-RK.

The ability to construct a functional system from its individual components is foundational to understanding how it works. Synthetic biology is a broad field that draws from principles of engineering and computer science to create new biological systems or parts with novel function. While this has drawn well-deserved acclaim within the biotechnology community, application of synthetic biology methodologies to study biological systems has potential to fundamentally change how biomedical research is conducted by providing researchers with improved experimental control. While the concepts behind synthetic biology are not new, we present evidence supporting why the current research environment is conducive for integration of synthetic biology approaches within biomedical research. In this perspective we explore the idea of synthetic biology as a discovery science research tool and provide examples of both top-down and bottom-up approaches that have already been used to answer important physiology questions at both the organismal and molecular level.

We identified autoantibodies (AAb) reacting with a variant IA-2 molecule (IA-2var) that has three amino acid substitutions (Cys27, Gly608, and Pro671) within the full-length molecule. We examined IA-2var AAb in first-degree relatives of type 1 diabetes (T1D) probands from the TrialNet Pathway to Prevention Study. The presence of IA-2var–specific AAb in relatives was associated with accelerated progression to T1D in those positive for AAb to GAD65 and/or insulin but negative in the standard test for IA-2 AAb. Furthermore, relatives with single islet AAb (by traditional assays) and carrying both IA-2var AAb and the high-risk HLA-DRB1*04-DQB1*03:02 haplotype progress rapidly to onset of T1D. Molecular modeling of IA-2var predicts that the genomic variation that alters the three amino acids induces changes in the three-dimensional structure of the molecule, which may lead to epitope unmasking in the IA-2 extracellular domain. Our observations suggest that the presence of AAb to IA-2var would identify high-risk subjects who would benefit from participation in prevention trials who have one islet antibody by traditional testing and otherwise would be misclassified as “low risk” relatives.

The estimation of the kinetic parameters requires the careful design of experiments under a constrained set of conditions. Many estimates reported in the literature incorporate protocols that leverage simplified mathematical models known as quasi-steady-state reductions. Such reductions often - but not always - emerge as the result of a singular perturbation scenario. However, the utilization of the singular perturbation reduction method requires knowledge of a dimensionless parameter, $\varepsilon$, that is proportional to the ratio of the reaction's fast and slow timescales. Using techniques from differential equations, Fenichel theory, and center manifold theory, we derive the appropriate $\varepsilon$ whose magnitude regulates the validity of the quasi-steady-state reduction employed in the reported experimental procedures for intermolecular autocatalytic zymogen activation reaction. Although the model equations are two-dimensional, the fast/slow dynamics are rich. The phase plane exhibits a dynamic transcritical bifurcation point in a particular singular limit. The existence of such a bifurcation is relevant, because the critical manifold losses normal hyperbolicity and classical Fenichel theory is inapplicable. Furthermore, we show that in some cases chemical reversibility can be interpreted dynamically as an imperfection, since the presence of reversibility can destroy the bifurcation structure present in the singular limit. We show that the reduction method by which QSS reductions are justified can depend on the path taken in parameter space. Specifically, we show that the standard quasi-steady-state reduction for this reaction is justifiable by center manifold theory in one limit, and via Fenichel theory in a different limit., 27 pages, 9 Figures, 1 Table

CLEC16A regulates mitochondrial health through mitophagy and is associated with over 20 human diseases. While CLEC16A has ubiquitin ligase activity, the key structural and functional regions of CLEC16A, and their relevance for human disease, remain unknown. Here, we report that a disease-associated CLEC16A variant lacks a C-terminal intrinsically disordered protein region (IDPR) that is critical for mitochondrial quality control. Using carbon detect NMR, we find that the CLEC16A C terminus lacks secondary structure, validating the presence of an IDPR. Loss of the CLEC16A C-terminal IDPR in vivo impairs pancreatic β-cell mitophagy, mitochondrial function, and glucose-stimulated insulin secretion, ultimately causing glucose intolerance. Deletion of the CLEC16A C-terminal IDPR increases its self-ubiquitination and destabilizes CLEC16A, thus impairing formation of a critical CLEC16A-dependent mitophagy complex. Importantly, CLEC16A stability is dependent on proline bias within the C-terminal IDPR, but not amino acid sequence order or charge. Together, we clarify how an IDPR in CLEC16A prevents diabetes, thus implicating the disruption of IDPRs as novel pathological contributors to diabetes and other CLEC16A-associated diseases.

The nematode Caenorhabditis elegans is a powerful model organism for studying cell development, apoptosis, neuronal circuits, and aging. The isolate N2 is recognized by the C. elegans community as the reference wild-type strain. Interestingly, the lifespan of presumably isogenic C. elegans N2 worms—even when grown under comparable conditions—varies significantly amongst distinct laboratories. This hinders the inter-laboratory comparability of C. elegans lifespan data and raises questions regarding data interpretation and reproducibility. Here, we hypothesized slight alterations in experimental design and worm handling could explain the observed discrepancies. To test this hypothesis, we collected and assessed data from over 1000 published C. elegans N2 lifespan assays as well as corresponding methodological meta-data. We find that mean N2 lifespans range from approximately 7 days to upwards of 35 days, despite laboratories disclosing seemingly comparable experimental conditions. We further demonstrate that, in addition to temperature, the use of the chemical sterilizer 5-fluoro-2′-deoxyuridine (FUDR) may change N2 lifespan. Additionally, we observed differences in average N2 lifespan from experiments originating from distinct geographic locations, indicating a potential effect of location-specific factors on experimental outcomes. Taken as a whole, our work indicates the sum of many small, rather than a few critical, differences in experimental conditions may account for the observed variance in N2 lifespan. We also find that the absence of standardized experimental methods and the insufficient disclosure of experiment details in the peer-reviewed literature limits the inter-lab comparability of published results. We thus propose the establishment of a succinct reporting standard for C. elegans lifespan experiments to increase the reliability and reproducibility, and thus scientific value, of these studies.

Covalent crosslinking and mass spectrometry techniques hold great potential in the study of multiprotein complexes, but a major challenge is the inability to differentiate intra- and inter- protein crosslinks in homomeric complexes. In the current study we use CYP102A1, a well-characterized homodimeric P450, to examine a subtractive method that utilizes limited crosslinking with disuccinimidyl dibutyric urea (DSBU) and isolation of the monomer, in addition to the crosslinked dimer, to identify inter-monomer crosslinks. The utility of this approach was examined with the use of MS-cleavable crosslinker DSBU and recently published cryo-EM based structures of the CYP102A1 homodimer. Of the 31 unique crosslinks found, 26 could be fit to the reported structures whereas 5 exceeded the spatial constraints. Not only did these crosslinks validate the cryo-EM structure, they point to new conformations of CYP102A1 that bring the flavins in closer proximity to the heme.

Quasi-steady state reductions for the irreversible Michaelis--Menten reaction mechanism are of interest both from a theoretical and an experimental design perspective. A number of publications have been devoted to extending the parameter range where reduction is possible, via improved sufficient conditions. In the present note, we complement these results by exhibiting local conditions that preclude quasi-steady-state reductions (anti-quasi-steady-state), in the classical as well as in a broader sense. To this end, one needs to obtain necessary (as opposed to sufficient) conditions and determine parameter regions where these do not hold. In particular, we explicitly describe parameter regions where no quasi-steady-state reduction (in any sense) is applicable (anti-quasi-steady-state conditions), and we also show that -- in a well defined sense -- these parameter regions are small. From another perspective, we obtain local conditions for the accuracy of standard or total quasi-steady-state. Perhaps surprisingly, our conditions do not involve initial substrate., 19 pages, 7 figures

As technological and analytical innovations rapidly advance our ability to reveal increasingly complex biological processes, the importance of understanding the assumptions behind biological measurements and sources of uncertainty are essential for data interpretation. This is particularly important in fields such as cell signaling, as due to its importance for both homeostatic and pathogenic biological processes, a quantitative understanding of the basic mechanisms of these transient events is fundamental to drug development. While developed decades ago, western blotting remains an indispensible research tool to probe cell signaling, protein expression, and protein-protein interactions. While improvements in statistical and methodology reporting have improved data quality, understanding the basic experimental assumptions and visual inspection of western blots provides additional information that is useful when evaluating experimental conclusions. Using agonist-induced receptor post-translational modification as an example we highlight the assumptions of western blotting and showcase how clues from raw western blots can hint at experimental variability that is not captured by statistics and methods that influences quantification. The purpose of this article is not to serve as a detailed review of the technical nuances and caveats of western blotting. Instead using an example we illustrate how experimental assumptions, design, and data normalization can be identified in raw data and influence data interpretation.

The conditions for the validity of the standard quasi-steady-state approximation in the Michaelis--Menten mechanism in a closed reaction vessel have been well studied, but much less so the conditions for the validity of this approximation for the system with substrate inflow. We analyze quasi-steady-state scenarios for the open system attributable to singular perturbations, as well as less restrictive conditions. For both settings we obtain distinguished invariant slow manifolds and time scale estimates, and we highlight the special role of singular perturbation parameters in higher order approximations of slow manifolds. We close the paper with a discussion of distinguished invariant manifolds in the global phase portrait., 32 pages, 6 figures

The SARS-CoV-2 virus has spread across the world, testing each nation’s ability to understand the state of the pandemic in their country and control it. As we looked into the epidemiological data to uncover the impact of the COVID-19 pandemic, we discovered that critical metadata is missing which is meant to give context to epidemiological parameters. In this review, we identify key metadata for the COVID-19 fatality rate after a thorough analysis of mathematical models, serology-informed studies and determinants of causes of death for the COVID-19 pandemic. In doing so, we find reasons to establish a set of standard-based guidelines to record and report the data from epidemiological studies. Additionally, we discuss why standardizing nomenclature is be a necessary component of these guidelines to improve communication and reproducibility. The goal of establishing these guidelines is to facilitate the interpretation of COVID-19 epidemiological findings and data by the general public, health officials, policymakers and fellow researchers. Our suggestions may not address all aspects of this issue; rather, they are meant to be the foundation for which experts can establish and encourage future guidelines throughout the appropriate communities., Highlights • Reported SARS-CoV-2 quantitative data is missing critical details to provide context. • It is important to establish standard-based guidelines to report epidemiological data. • Standards will make it easier to interpret SARS-CoV-2 epidemiological data. • Standard-based guidelines improve communication, rigor and reproducibility.

A zymogen is an inactive precursor of an enzyme that needs to go through a chemical change to become an active enzyme. The general intermolecular mechanism for the autocatalytic activation of zymogens is governed by the single-enzyme, single-substrate catalyzed reaction following the Michaelis-Menten mechanism of enzyme action, where the substrate is the zymogen and the product is the same enzyme that is catalyzing the reaction. In this article we investigate the nonlinear chemical dynamics of the intermolecular autocatalytic zymogen activation reaction mechanism. In so doing, we develop a general strategy for obtaining dimensionless parameters that, when sufficiently small, legitimize the application of the quasi-steady-state approximation. Our methodology combines energy methods and exploits the phase-plane geometry of the mathematical model, and we obtain sufficient conditions that support the validity of the standard, reverse and total quasi-steady-state approximations for the intermolecular autocatalytic zymogen activation reaction mechanism. The utility of the procedure we develop is that it circumnavigates the direct need for a priori timescale estimation, scaling, and non-dimensionalization. At the same time, a novel result emerges from our analysis: the discovery of a dynamic transcritical bifurcation that exists in the singular limit of the model equations. Moreover, associated with the dynamic transcritical bifurcation is an imperfect term. We prove that when the imperfect term vanishes and the singular vector field is perturbed, there exists a canard that follows a repulsive slow invariant manifold over timescales of O(1). This is the first report of such a solution for the intermolecular and autocatalytic zymogen activation reaction. By extension, our results illustrate that canards also exist in the classic single enzyme, single-substrate reversible Michaelis-Menten reaction mechanism.

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. Lastly, 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.

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 STATEMENTInfertility 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.