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 iss 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.

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.

Seeing beyond the blot: A critical look at assumptions and raw data interpretation in Western blotting

Rapid advancements in technology refine our understanding of intricate biological processes, but a crucial emphasis remains on understanding the assumptions and sources of uncertainty underlying biological measurements. This is particularly critical in cell signaling research, where a quantitative understanding of the fundamental mechanisms governing these transient events is essential for drug development, given their importance in both homeostatic and pathogenic processes. Western blotting, a technique developed decades ago, remains an indispensable tool for investigating cell signaling, protein expression, and protein-protein interactions. While improvements in statistical analysis and methodology reporting have undoubtedly enhanced data quality, understanding the underlying assumptions and limitations of visual inspection in Western blotting can provide valuable additional information for evaluating experimental conclusions. Using the example of agonist-induced receptor post-translational modification, we highlight the theoretical and experimental assumptions associated with Western blotting and demonstrate how raw blot data can offer clues to experimental variability that may not be fully captured by statistical analyses and reported methodologies. This article is not intended as a comprehensive technical review of Western blotting. Instead, we leverage an illustrative example to demonstrate how assumptions about experimental design and data normalization can be revealed within raw data and subsequently influence data interpretation.

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.

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.

Cerebrovascular super-resolution 4D Flow MRI - Sequential combination of resolution enhancement by deep learning and physics-informed image processing to non-invasively quantify intracranial velocity, flow, and relative pressure

The development of cerebrovascular disease is tightly coupled to regional changes in intracranial flow and relative pressure. Image-based assessment using phase contrast magnetic resonance imaging has particular promise for non-invasive full-field mapping of cerebrovascular hemodynamics. However, estimations are complicated by the narrow and tortuous intracranial vasculature, with accurate image-based quantification directly dependent on sufficient spatial resolution. Further, extended scan times are required for high-resolution acquisitions, and most clinical acquisitions are performed at comparably low resolution (>1 mm) where biases have been observed with regard to the quantification of both flow and relative pressure. The aim of our study was to develop an approach for quantitative intracranial super-resolution 4D Flow MRI, with effective resolution enhancement achieved by a dedicated deep residual network, and with accurate quantification of functional relative pressures achieved by subsequent physics-informed image processing. To achieve this, our two-step approach was trained and validated in a patient-specific in-silico cohort, showing good accuracy in estimating velocity (relative error: 15.0 ± 0.1%, mean absolute error (MAE): 0.07 ± 0.06 m/s, and cosine similarity: 0.99 ± 0.06 at peak velocity) and flow (relative error: 6.6 ± 4.7%, root mean square error (RMSE): 0.56 mL/s at peak flow), and with the coupled physics-informed image analysis allowing for maintained recovery of functional relative pressure throughout the circle of Willis (relative error: 11.0 ± 7.3%, RMSE: 0.3 ± 0.2 mmHg). Furthermore, the quantitative super-resolution approach is applied to an in-vivo volunteer cohort, effectively generating intracranial flow images at <0.5 mm resolution and showing reduced low-resolution bias in relative pressure estimation. Our work thus presents a promising two-step approach to non-invasively quantify cerebrovascular hemodynamics, being applicable to dedicated clinical cohorts in the future.

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 .

Agave fructans enhance the effects of fermented milk products on obesity biomarkers: a randomised trial

Dysbiosis has been implicated in childhood obesity. Oral intake of fermented milk containing Lacticaseibacillus casei strain Shirota preserves gut microbiota (GM) diversity in children and adults. This study was a double-blind trial involving 37 overweight or obese children aged 6-10 years. Children were followed over a 6-week intervention period in which they received different fermented milk products containing L. casei Shirota: 10 in the first group received just L. casei Shirota; 13 received L. casei Shirota with 3 g/day of inulin (L. casei+inulin); and 14 received L. casei Shirota with 3 g/day of fructans from Agave salmiana (L. casei+fructans). Principal component analysis showed the relationship between microbial abundance, GM metabolites, and other obesity-related markers. Supplementation with probiotics and synbiotics improved the HDL-cholesterol levels of overweight and obese children, although no changes in body composition were detected. We observed an increase in butyrate or propionate concentrations in the L. casei+fructans group compared to the end of the intervention (P<0.03). A diminished level of ANGPTL4 within the L. casei+fructans group (P=0.04) was also found, but no differences when lipopolysaccharide-binding protein was evaluated. The FFAR2+ cell frequency decreased between baseline and at the end of 6-week intervention in L. casei+inulin (P=0.02) and L. casei+fructans groups (P=0.04). In contrast, the percentage of CD14+FFAR3+ frequency increased in the same groups (P=0.04). The L. casei Shirota with inulin or fructans modulates GM, which improves the lipid profile and changes at a molecular level, such as expression of FFAR3 and FFAR2, ANGPTL4, propionate, and butyrate. It, therefore, could be considered an interesting therapeutic possibility for treating childhood overweight and obesity. The study was registered at ClinicalTrials.gov (ID: NCT05423015).

An intrinsically disordered protein region encoded by the human disease gene CLEC16A regulates mitophagy

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.

On the anti-quasi-steady-state conditions of enzyme kinetics

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.

EnzymeML-a data exchange format for biocatalysis and enzymology

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.

Explaining inter-lab variance in C. elegans N2 lifespan: Making a case for standardized reporting to enhance reproducibility

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.

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.

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.

On the quasi-steady-state approximation in an open Michaelis-Menten reaction mechanism

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 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.

Mapping protein-protein interactions in homodimeric CYP102A1 by crosslinking and mass spectrometry

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.

Interpreting SARS-CoV-2 seroprevalence, deaths, and fatality rate - Making a case for standardized reporting to improve communication

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.

β-arrestin mediates communication between plasma membrane and intracellular GPCRs to regulate signaling

It has become increasingly apparent that G protein-coupled receptor (GPCR) localization is a master regulator of cell signaling. However, the molecular mechanisms involved in this process are not well understood. To date, observations of intracellular GPCR activation can be organized into two categories: a dependence on OCT3 cationic channel-permeable ligands or the necessity of endocytic trafficking. Using CXC chemokine receptor 4 (CXCR4) as a model, we identified a third mechanism of intracellular GPCR signaling. We show that independent of membrane permeable ligands and endocytosis, upon stimulation, plasma membrane and internal pools of CXCR4 are post-translationally modified and collectively regulate EGR1 transcription. We found that β-arrestin-1 (arrestin 2) is necessary to mediate communication between plasma membrane and internal pools of CXCR4. Notably, these observations may explain that while CXCR4 overexpression is highly correlated with cancer metastasis and mortality, plasma membrane localization is not. Together these data support a model where a small initial pool of plasma membrane-localized GPCRs are capable of activating internal receptor-dependent signaling events.

DeNies et al. identify a new mechanism of intracellular GPCR signalling. Using CXC chemokine receptor 4 (CXCR4) as a model, they show that upon stimulation with receptor agonists that not only plasma membrane-localized receptors, but also intracellular CXCR4 molecules are post-translationally modified and regulate transcription. This study suggests that a small pool of plasma membrane-localized GPCRs can activate internal receptor-dependent signaling, and that β-arrestin-1 mediates this activation.

Firing patterns of gonadotropin-releasing hormone neurons are sculpted by their biologic state

Gonadotropin-releasing hormone (GnRH) neurons form the final pathway for the central neuronal control of fertility. GnRH is released in pulses that vary in frequency in females, helping drive hormonal changes of the reproductive cycle. In the common fertility disorder polycystic ovary syndrome (PCOS), persistent high-frequency hormone release is associated with disrupted cycles. We investigated long- and short-term action potential patterns of GnRH neurons in brain slices before and after puberty in female control and prenatally androgenized (PNA) mice, which mimic aspects of PCOS. A Monte Carlo (MC) approach was used to randomize action potential interval order. Dataset distributions were analysed to assess (i) if organization persists in GnRH neuron activity in vitro, and (ii) to determine if any organization changes with development and/or PNA treatment. GnRH neurons in adult control, but not PNA, mice produce long-term patterns different from MC distributions. Short-term patterns differ from MC distributions before puberty but become absorbed into the distributions with maturation, and the distributions narrow. These maturational changes are blunted by PNA treatment. Firing patterns of GnRH neurons in brain slices thus maintain organization dictated at least in part by the biologic status of the source and are disrupted in models of disease.

The quasi-steady-state approximations revisited: Timescales, small parameters, singularities, and normal forms in enzyme kinetics

In this work, we revisit the scaling analysis and commonly accepted conditions for the validity of the standard, reverse and total quasi-steady-state approximations through the lens of dimensional Tikhonov-Fenichel parameters and their respective critical manifolds. By combining Tikhonov-Fenichel parameters with scaling analysis and energy methods, we derive improved upper bounds on the approximation error for the standard, reverse and total quasi-steady-state approximations. Furthermore, previous analyses suggest that the reverse quasi-steady-state approximation is only valid when initial enzyme concentrations greatly exceed initial substrate concentrations. However, our results indicate that this approximation can be valid when initial enzyme and substrate concentrations are of equal magnitude. Using energy methods, we find that the condition for the validity of the reverse quasi-steady-state approximation is far less restrictive than was previously assumed, and we derive a new "small" parameter that determines the validity of this approximation. In doing so, we extend the established domain of validity for the reverse quasi-steady-state approximation. Consequently, this opens up the possibility of utilizing the reverse quasi-steady-state approximation to model enzyme catalyzed reactions and estimate kinetic parameters in enzymatic assays at much lower enzyme to substrate ratios than was previously thought. Moreover, we show for the first time that the critical manifold of the reverse quasi-steady-state approximation contains a singular point where normal hyperbolicity is lost. Associated with this singularity is a transcritical bifurcation, and the corresponding normal form of this bifurcation is recovered through scaling analysis.

Are the biomedical sciences ready for synthetic biology?

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.

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.

Autoantibodies Directed Toward a Novel IA-2 Variant Protein Enhance Prediction of Type 1 Diabetes

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.

Disorder Atlas: Web-based software for the proteome-based interpretation of intrinsic disorder predictions

Intrinsically disordered proteins lack a stable three-dimensional structure under physiological conditions. While this property has gained considerable interest within the past two decades, disorder poses substantial challenges to experimental characterization efforts. In effect, numerous computational tools have been developed to predict disorder from primary sequences, however, interpreting the output of these algorithms remains a challenge. To begin to bridge this gap, we present Disorder Atlas, web-based software that facilitates the interpretation of intrinsic disorder predictions using proteome-based descriptive statistics. This service is also equipped to facilitate large-scale systematic exploratory searches for proteins encompassing disorder features of interest, and further allows users to browse the prevalence of multiple disorder features at the proteome level. As a result, Disorder Atlas provides a user-friendly tool that places algorithm-generated disorder predictions in the context of the proteome, thereby providing an instrument to compare the results of a query protein against predictions made for an entire population. Disorder Atlas currently supports ten eukaryotic proteomes and is freely available for non-commercial users at http://www.disorderatlas.org.

Clathrin Heavy Chain Knockdown Impacts CXCR4 Signaling and Post-translational Modification

Recent research has implicated endocytic pathways as important regulators of receptor signaling. However, the role of endocytosis in regulating chemokine CXC receptor 4 (CXCR4) signaling remains largely unknown. In the present work we systematically investigate the impact of clathrin knockdown on CXCR4 internalization, signaling, and receptor post-translational modification. Inhibition of clathrin-mediated endocytosis (CME) significantly reduced CXCR4 internalization. In contrast to other receptors, clathrin knockdown increased CXCL12-dependent ERK1/2 signaling. Simultaneous inhibition of CME and lipid raft disruption abrogated this increase in ERK1/2 phosphorylation suggesting that endocytic pathway compensation can influence signaling outcomes. Interestingly, using an antibody sensitive to CXCR4 post-translational modification, we also found that our ability to detect CXCR4 was drastically reduced upon clathrin knockdown. We hypothesize that this effect was due to differences in receptor post-translational modification as total CXCR4 protein and mRNA levels were unchanged. Lastly, we show that clathrin knockdown reduced CXCL12-dependent cell migration irrespective of an observed increase in ERK1/2 phosphorylation. Altogether, this work supports a complex model by which modulation of endocytosis affects not only receptor signaling and internalization but also receptor post-translational modification.

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.

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.

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.

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.

"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.

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.

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.

Radial WNT5A-Guided Post-mitotic Filopodial Pathfinding Is Critical for Midgut Tube Elongation

The early midgut undergoes intensive elongation, but the underlying cellular and molecular mechanisms are unknown. The early midgut epithelium is pseudostratified, and its nuclei travel between apical and basal surfaces in concert with cell cycle. Using 3D confocal imaging and 2D live imaging, we profiled behaviors of individual dividing cells. As nuclei migrate apically for mitosis, cells maintain a basal process (BP), which splits but is inherited by only one daughter. After mitosis, some daughters directly use the inherited BP as a "conduit" to transport the nucleus basally, while >50% of daughters generate a new basal filopodium and use it as a path to return the nucleus. Post-mitotic filopodial "pathfinding" is guided by mesenchymal WNT5A. Without WNT5A, some cells fail to tether basally and undergo apoptosis, leading to a shortened midgut. Thus, these studies reveal previously unrecognized strategies for efficient post-mitotic nuclear trafficking, which is critical for early midgut elongation.

Predicting neuroblastoma using developmental signals and a logic-based model

Genomic information from human patient samples of pediatric neuroblastoma cancers and known outcomes have led to specific gene lists put forward as high risk for disease progression. However, the reliance on gene expression correlations rather than mechanistic insight has shown limited potential and suggests a critical need for molecular network models that better predict neuroblastoma progression. In this study, we construct and simulate a molecular network of developmental genes and downstream signals in a 6-gene input logic model that predicts a favorable/unfavorable outcome based on the outcome of the four cell states including cell differentiation, proliferation, apoptosis, and angiogenesis. We simulate the mis-expression of the tyrosine receptor kinases, trkA and trkB, two prognostic indicators of neuroblastoma, and find differences in the number and probability distribution of steady state outcomes. We validate the mechanistic model assumptions using RNAseq of the SHSY5Y human neuroblastoma cell line to define the input states and confirm the predicted outcome with antibody staining. Lastly, we apply input gene signatures from 77 published human patient samples and show that our model makes more accurate disease outcome predictions for early stage disease than any current neuroblastoma gene list. These findings highlight the predictive strength of a logic-based model based on developmental genes and offer a better understanding of the molecular network interactions during neuroblastoma disease progression.

STRENDA DB: enabling the validation and sharing of enzyme kinetics data

Standards for reporting enzymology data (STRENDA) DB is a validation and storage system for enzyme function data that incorporates the STRENDA Guidelines. It provides authors who are preparing a manuscript with a user-friendly, web-based service that checks automatically enzymology data sets entered in the submission form that they are complete and valid before they are submitted as part of a publication to a journal.

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.

Globalization and changing trends of biomedical research output

The US continues to lead the world in research and development (R&D) expenditures, but there is concern that stagnation in federal support for biomedical research in the US could undermine the leading role the US has played in biomedical and clinical research discoveries. As a readout of research output in the US compared with other countries, assessment of original research articles published by US-based authors in ten clinical and basic science journals during 2000 to 2015 showed a steady decline of articles in high-ranking journals or no significant change in mid-ranking journals. In contrast, publication output originating from China-based investigators, in both high- and mid-ranking journals, has steadily increased commensurate with significant growth in R&D expenditures. These observations support the current concerns of stagnant and year-to-year uncertainty in US federal funding of biomedical research.

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.

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.

The importance of accurately correcting for the natural abundance of stable isotopes

The use of isotopically labeled tracer substrates is an experimental approach for measuring in vivo and in vitro intracellular metabolic dynamics. Stable isotopes that alter the mass but not the chemical behavior of a molecule are commonly used in isotope tracer studies. Because stable isotopes of some atoms naturally occur at non-negligible abundances, it is important to account for the natural abundance of these isotopes when analyzing data from isotope labeling experiments. Specifically, a distinction must be made between isotopes introduced experimentally via an isotopically labeled tracer and the isotopes naturally present at the start of an experiment. In this tutorial review, we explain the underlying theory of natural abundance correction of stable isotopes, a concept not always understood by metabolic researchers. We also provide a comparison of distinct methods for performing this correction and discuss natural abundance correction in the context of steady state 13C metabolic flux, a method increasingly used to infer intracellular metabolic flux from isotope experiments.

Novel Hybrid Phenotype Revealed in Small Cell Lung Cancer by a Transcription Factor Network Model That Can Explain Tumor Heterogeneity

Small cell lung cancer (SCLC) is a devastating disease due to its propensity for early invasion and refractory relapse after initial treatment response. Although these aggressive traits have been associated with phenotypic heterogeneity, our understanding of this association remains incomplete. To fill this knowledge gap, we inferred a set of 33 transcription factors (TF) associated with gene signatures of the known neuroendocrine/epithelial (NE) and non-neuroendocrine/mesenchymal-like (ML) SCLC phenotypes. The topology of this SCLC TF network was derived from prior knowledge and was simulated using Boolean modeling. These simulations predicted that the network settles into attractors, or TF expression patterns, that correlate with NE or ML phenotypes, suggesting that TF network dynamics underlie the emergence of heterogeneous SCLC phenotypes. However, several cell lines and patient tumor specimens failed to correlate with either the NE or ML attractors. By flow cytometry, single cells within these cell lines simultaneously expressed surface markers of both NE and ML differentiation, confirming the existence of a "hybrid" phenotype. Upon exposure to standard-of-care cytotoxic drugs or epigenetic modifiers, NE and ML cell populations converged toward the hybrid state, suggesting possible escape from treatment. Our findings indicate that SCLC phenotypic heterogeneity can be specified dynamically by attractor states of a master regulatory TF network. Thus, SCLC heterogeneity may be best understood as states within an epigenetic landscape. Understanding phenotypic transitions within this landscape may provide insights to clinical applications. Cancer Res; 77(5); 1063-74. ©2016 AACR.

A computational approach to studying ageing at the individual level

The ageing process is actively regulated throughout an organism's life, but studying the rate of ageing in individuals is difficult with conventional methods. Consequently, ageing studies typically make biological inference based on population mortality rates, which often do not accurately reflect the probabilities of death at the individual level. To study the relationship between individual and population mortality rates, we integrated in vivo switch experiments with in silico stochastic simulations to elucidate how carefully designed experiments allow key aspects of individual ageing to be deduced from group mortality measurements. As our case study, we used the recent report demonstrating that pheromones of the opposite sex decrease lifespan in Drosophila melanogaster by reversibly increasing population mortality rates. We showed that the population mortality reversal following pheromone removal was almost surely occurring in individuals, albeit more slowly than suggested by population measures. Furthermore, heterogeneity among individuals due to the inherent stochasticity of behavioural interactions skewed population mortality rates in middle-age away from the individual-level trajectories of which they are comprised. This article exemplifies how computational models function as important predictive tools for designing wet-laboratory experiments to use population mortality rates to understand how genetic and environmental manipulations affect ageing in the individual.