Dynamic Recruitment of Single RNAs to Processing Bodies Depends on RNA Functionality.

Cellular RNAs often colocalize with cytoplasmic, membrane-less ribonucleoprotein (RNP) granules enriched for RNA-processing enzymes, termed processing bodies (PBs). Here we track the dynamic localization of individual miRNAs, mRNAs, and long non-coding RNAs (lncRNAs) to PBs using intracellular single-molecule fluorescence microscopy. We find that unused miRNAs stably bind to PBs, whereas functional miRNAs, repressed mRNAs, and lncRNAs both transiently and stably localize within either the core or periphery of PBs, albeit to different extents. Consequently, translation potential and 3' versus 5' placement of miRNA target sites significantly affect the PB localization dynamics of mRNAs. Using computational modeling and supporting experimental approaches, we show that partitioning in the PB phase attenuates mRNA silencing, suggesting that physiological mRNA turnover occurs predominantly outside of PBs. Instead, our data support a PB role in sequestering unused miRNAs for surveillance and provide a framework for investigating the dynamic assembly of RNP granules by phase separation at single-molecule resolution.

EnzymeML: seamless data flow and modeling of enzymatic data.

The design of biocatalytic reaction systems is highly complex owing to the dependency of the estimated kinetic parameters on the enzyme, the reaction conditions, and the modeling method. Consequently, reproducibility of enzymatic experiments and reusability of enzymatic data are challenging. We developed the XML-based markup language EnzymeML to enable storage and exchange of enzymatic data such as reaction conditions, the time course of the substrate and the product, kinetic parameters and the kinetic model, thus making enzymatic data findable, accessible, interoperable and reusable (FAIR). The feasibility and usefulness of the EnzymeML toolbox is demonstrated in six scenarios, for which data and metadata of different enzymatic reactions are collected and analyzed. EnzymeML serves as a seamless communication channel between experimental platforms, electronic lab notebooks, tools for modeling of enzyme kinetics, publication platforms and enzymatic reaction databases. EnzymeML is open and transparent, and invites the community to contribute. All documents and codes are freely available at https://enzymeml.org .

Branched germline cysts and female-specific cyst fragmentation facilitate oocyte determination in mice.

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.

Reciprocal regulatory balance within the CLEC16A-RNF41 mitophagy complex depends on an intrinsically disordered protein region.

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.

The unreasonable effectiveness of the total quasi-steady state approximation, and its limitations.

In this note, we discuss the range of parameters for which the total quasi-steady-state approximation of the Michaelis-Menten reaction mechanism holds validity. We challenge the prevalent notion that total quasi-steady-state approximation is "roughly valid" across all parameters, showing that its validity cannot be assumed, even roughly, across the entire parameter space - when the initial substrate concentration is high. On the positive side, we show that the linearized one-dimensional equation for total substrate is a valid approximation when the initial reduced substrate concentration s0/KM is small. Moreover, we obtain a precise picture of the long-term time course of both substrate and complex.

The Michaelis-Menten Reaction at Low Substrate Concentrations: Pseudo-First-Order Kinetics and Conditions for Timescale Separation.

We demonstrate that the Michaelis-Menten reaction mechanism can be accurately approximated by a linear system when the initial substrate concentration is low. This leads to pseudo-first-order kinetics, simplifying mathematical calculations and experimental analysis. Our proof utilizes a monotonicity property of the system and Kamke's comparison theorem. This linear approximation yields a closed-form solution, enabling accurate modeling and estimation of reaction rate constants even without timescale separation. Building on prior work, we establish that the sufficient condition for the validity of this approximation is s 0 ≪ K , where K = k 2 / k 1 is the Van Slyke-Cullen constant. This condition is independent of the initial enzyme concentration. Further, we investigate timescale separation within the linear system, identifying necessary and sufficient conditions and deriving the corresponding reduced one-dimensional equations.

Natural Parameter Conditions for Singular Perturbations of Chemical and Biochemical Reaction Networks.

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.

The embryonic trunk neural crest microenvironment regulates the plasticity and invasion of human neuroblastoma via TrkB signaling.

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.

Stochastic enzyme kinetics and the quasi-steady-state reductions: Application of the slow scale linear noise approximation à la Fenichel.

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 [Formula: see text], where [Formula: see text] 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 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.

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.

On the Validity of the Stochastic Quasi-Steady-State Approximation in Open Enzyme Catalyzed Reactions: Timescale Separation or Singular Perturbation?

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 in 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.

Changes in Both Neuron Intrinsic Properties and Neurotransmission Are Needed to Drive the Increase in GnRH Neuron Firing Rate during Estradiol-Positive Feedback.

Central output of gonadotropin-releasing hormone (GnRH) neurons controls fertility and is sculpted by sex-steroid feedback. A switch of estradiol action from negative to positive feedback initiates a surge of GnRH release, culminating in ovulation. In ovariectomized mice bearing constant-release estradiol implants (OVX+E), GnRH neuron firing is suppressed in the morning (AM) by negative feedback and activated in the afternoon (PM) by positive feedback; no time-of-day-dependent changes occur in OVX mice. In this daily surge model, GnRH neuron intrinsic properties are shifted to favor increased firing during positive feedback. It is unclear whether this shift and the observed concomitant increase in GABAergic transmission, which typically excites GnRH neurons, are independently sufficient for increasing GnRH neuron firing rate during positive feedback or whether both are needed. To test this, we used dynamic clamp to inject selected previously recorded trains of GABAergic postsynaptic conductances (PSgs) collected during the different feedback states of the daily surge model into GnRH neurons from OVX, OVX+E AM, and OVX+E PM mice. PSg trains mimicking positive feedback initiated more action potentials in cells from OVX+E PM mice than negative feedback or OVX (open feedback loop) trains in all three animal models, but the positive-feedback train was most effective when applied to cells during positive feedback. In silico studies of model GnRH neurons in which >1000 PSg trains were tested exhibited the same results. These observations support the hypothesis that GnRH neurons integrate fast-synaptic and intrinsic changes to increase firing rates during positive feedback.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. Ovarian estradiol alters both the intrinsic properties of gonadotropin-releasing hormone (GnRH) neurons and synaptic inputs to these cells coincident with production of sustained GnRH release that ultimately triggers ovulation. We demonstrate here using dynamic clamp and mathematical modeling that estradiol-induced shifts in synaptic transmission alone can increase firing output, but that the intrinsic properties of GnRH neurons during positive feedback further poise these cells for increased response to higher frequency synaptic transmission. These data suggest that GnRH neurons integrate fast-synaptic and intrinsic changes to increase firing rates during the preovulatory GnRH surge.

On the Need to Develop Guidelines for Characterizing and Reporting Intrinsic Disorder in Proteins.

Since the early 2000s, numerous computational tools have been created and used to predict intrinsic disorder in proteins. At present, the output from these algorithms is difficult to interpret in the absence of standards or references for comparison. There are many reasons to establish a set of standard-based guidelines to evaluate computational protein disorder predictions. This viewpoint explores a handful of these reasons, including standardizing nomenclature to improve communication, rigor and reproducibility, and making it easier for newcomers to enter the field. An approach for reporting predicted disorder in single proteins with respect to whole proteomes is discussed. The suggestions are not intended to be formulaic; they should be viewed as a starting point to establish guidelines for interpreting and reporting computational protein disorder predictions.

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.

Villification in the mouse: Bmp signals control intestinal villus patterning.

In the intestine, finger-like villi provide abundant surface area for nutrient absorption. During murine villus development, epithelial Hedgehog (Hh) signals promote aggregation of subepithelial mesenchymal clusters that drive villus emergence. Clusters arise first dorsally and proximally and spread over the entire intestine within 24 h, but the mechanism driving this pattern in the murine intestine is unknown. In chick, the driver of cluster pattern is tensile force from developing smooth muscle, which generates deep longitudinal epithelial folds that locally concentrate the Hh signal, promoting localized expression of cluster genes. By contrast, we show that in mouse, muscle-induced epithelial folding does not occur and artificial deformation of the epithelium does not determine the pattern of clusters or villi. In intestinal explants, modulation of Bmp signaling alters the spatial distribution of clusters and changes the pattern of emerging villi. Increasing Bmp signaling abolishes cluster formation, whereas inhibiting Bmp signaling leads to merged clusters. These dynamic changes in cluster pattern are faithfully simulated by a mathematical model of a Turing field in which an inhibitor of Bmp signaling acts as the Turing activator. In vivo, genetic interruption of Bmp signal reception in either epithelium or mesenchyme reveals that Bmp signaling in Hh-responsive mesenchymal cells controls cluster pattern. Thus, unlike in chick, the murine villus patterning system is independent of muscle-induced epithelial deformation. Rather, a complex cocktail of Bmps and Bmp signal modulators secreted from mesenchymal clusters determines the pattern of villi in a manner that mimics the spread of a self-organizing Turing field.

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.

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.

"Reproducible" Research in Mathematical Sciences Requires Changes in our Peer Review Culture and Modernization of our Current Publication Approach.

The nature of scientific research in mathematical and computational biology allows editors and reviewers to evaluate the findings of a scientific paper. Replication of a research study should be the minimum standard for judging its scientific claims and considering it for publication. This requires changes in the current peer review practice and a strict adoption of a replication policy similar to those adopted in experimental fields such as organic synthesis. In the future, the culture of replication can be easily adopted by publishing papers through dynamic computational notebooks combining formatted text, equations, computer algebra and computer code.

A Kinetic Analysis of Coupled (or Auxiliary) Enzyme Reactions.

As a case study, we consider a coupled (or auxiliary) enzyme assay of two reactions obeying the Michaelis-Menten mechanism. The coupled reaction consists of a single-substrate, single-enzyme non-observable reaction followed by another single-substrate, single-enzyme observable reaction (indicator reaction). In this assay, the product of the non-observable reaction is the substrate of the indicator reaction. A mathematical analysis of the reaction kinetics is performed, and it is found that after an initial fast transient, the coupled reaction is described by a pair of interacting Michaelis-Menten equations. Moreover, we show that when the indicator reaction is fast, the quasi-steady-state dynamics are governed by three fast variables and one slow variable. Timescales that approximate the respective lengths of the indicator and non-observable reactions, as well as conditions for the validity of the Michaelis-Menten equations, are derived. The theory can be extended to deal with more complex sequences of enzyme-catalyzed reactions.

Inferring Intracellular Signal Transduction Circuitry from Molecular Perturbation Experiments.

The development of network inference methodologies that accurately predict connectivity in dysregulated pathways may enable the rational selection of patient therapies. Accurately inferring an intracellular network from data remains a very challenging problem in molecular systems biology. Living cells integrate extremely robust circuits that exhibit significant heterogeneity, but still respond to external stimuli in predictable ways. This phenomenon allows us to introduce a network inference methodology that integrates measurements of protein activation from perturbation experiments. The methodology relies on logic-based networks to provide a predictive approximation of the transfer of signals in a network. The approach presented was validated in silico with a set of test networks and applied to investigate the epidermal growth factor receptor signaling of a breast epithelial cell line, MFC10A. In our analysis, we predict the potential signaling circuitry most likely responsible for the experimental readouts of several proteins in the mitogen-activated protein kinase and phosphatidylinositol-3 kinase pathways. The approach can also be used to identify additional necessary perturbation experiments to distinguish between a set of possible candidate networks.