TRPV4 is expressed by enteric glia and muscularis macrophages of the colon but does not play a prominent role in colonic motility.

Background: Mechanosensation is an important trigger of physiological processes in the gastrointestinal tract. Aberrant responses to mechanical input are associated with digestive disorders, including visceral hypersensitivity. Transient Receptor Potential Vanilloid 4 (TRPV4) is a mechanosensory ion channel with proposed roles in visceral afferent signaling, intestinal inflammation, and gut motility. While TRPV4 is a potential therapeutic target for digestive disease, current mechanistic understanding of how TRPV4 may influence gut function is limited by inconsistent reports of TRPV4 expression and distribution. Methods: In this study we profiled functional expression of TRPV4 using Ca2+ imaging of wholemount preparations of the mouse, monkey, and human intestine in combination with immunofluorescent labeling for established cellular markers. The involvement of TRPV4 in colonic motility was assessed in vitro using videomapping and contraction assays. Results: The TRPV4 agonist GSK1016790A evoked Ca2+ signaling in muscularis macrophages, enteric glia, and endothelial cells. TRPV4 specificity was confirmed using TRPV4 KO mouse tissue or antagonist pre-treatment. Calcium responses were not detected in other cell types required for neuromuscular signaling including enteric neurons, interstitial cells of Cajal, PDGFRα+ cells, and intestinal smooth muscle. TRPV4 activation led to rapid Ca2+ responses by a subpopulation of glial cells, followed by sustained Ca2+ signaling throughout the enteric glial network. Propagation of these waves was suppressed by inhibition of gap junctions or Ca2+ release from intracellular stores. Coordinated glial signaling in response to GSK1016790A was also disrupted in acute TNBS colitis. The involvement of TRPV4 in the initiation and propagation of colonic motility patterns was examined in vitro. Conclusions: We reveal a previously unappreciated role for TRPV4 in the initiation of distension-evoked colonic motility. These observations provide new insights into the functional role of TRPV4 activation in the gut, with important implications for how TRPV4 may influence critical processes including inflammatory signaling and motility.

IP3R activity increases propensity of RyR-mediated sparks by elevating dyadic [Ca2＋].

Calcium (Ca2＋) plays a critical role in the excitation contraction coupling (ECC) process that mediates the contraction of cardiomyocytes during each heartbeat. While ryanodine receptors (RyRs) are the primary Ca2＋ channels responsible for generating the cell-wide Ca2＋ transients during ECC, Ca2＋ release, via inositol 1,4,5-trisphosphate (IP3) receptors (IP3Rs) are also reported in cardiomyocytes to elicit ECC-modulating effects. Recent studies suggest that the localization of IP3Rs at dyads grant their ability to modify the occurrence of Ca2＋ sparks (elementary Ca2＋ release events that constitute cell wide Ca2＋ releases associated with ECC) which may underlie their modulatory influence on ECC. Here, we aim to uncover the mechanism by which dyad-localized IP3Rs influence Ca2＋ spark dynamics. To this end, we developed a mathematical model of the dyad that incorporates the behaviour of IP3Rs, in addition to RyRs, to reveal the impact of their activity on local Ca2＋ handling and consequent Ca2＋ spark occurrence and its properties. Consistent with published experimental data, our model predicts that the propensity for Ca2＋ spark formation increases in the presence of IP3R activity. Our simulations support the hypothesis that IP3Rs elevate Ca2＋ in the dyad, sensitizing proximal RyRs towards activation and hence Ca2＋ spark formation. The stochasticity of IP3R gating is an important aspect of this mechanism. However, dyadic IP3R activity lowers the Ca2＋ available in the junctional sarcoplasmic reticulum (JSR) for release, thus resulting in Ca2＋ sparks with similar durations but lower amplitudes.

SBML to bond graphs: From conversion to composition.

The Systems Biology Markup Language (SBML) is a popular software-independent XML-based format for describing models of biological phenomena. The BioModels Database is the largest online repository of SBML models. Several tools and platforms are available to support the reuse and composition of SBML models. However, these tools do not explicitly assess whether models are physically plausible or thermodynamically consistent. This often leads to ill-posed models that are physically impossible, impeding the development of realistic complex models in biology. Here, we present a framework that can automatically convert SBML models into bond graphs, which imposes energy conservation laws on these models. The new bond graph models are easily mergeable, resulting in physically plausible coupled models. We illustrate this by automatically converting and coupling a model of pyruvate distribution to a model of the pentose phosphate pathway.

Modelling realistic 3D deformations of simple epithelia in dynamic homeostasis.

The maintenance of tissue and organ structures during dynamic homeostasis is often not well understood. In order for a system to be stable, cell renewal, cell migration and cell death must be finely balanced. Moreover, a tissue's shape must remain relatively unchanged. Simple epithelial tissues occur in various structures throughout the body, such as the endothelium, mesothelium, linings of the lungs, saliva and thyroid glands, and gastrointestinal tract. Despite the prevalence of simple epithelial tissues, there are few models which accurately describe how these tissues maintain a stable structure. Here, we present a novel, 3D, deformable, multilayer, cell-centre model of a simple epithelium. Cell movement is governed by the minimisation of a bending potential across the epithelium, cell-cell adhesion, and viscous effects. We show that the model is capable of maintaining a consistent tissue structure while undergoing self renewal. We also demonstrate the model's robustness under tissue renewal, cell migration and cell removal. The model presented here is a valuable advancement towards the modelling of tissues and organs with complex and generalised structures.

A semantics, energy-based approach to automate biomodel composition.

Hierarchical modelling is essential to achieving complex, large-scale models. However, not all modelling schemes support hierarchical composition, and correctly mapping points of connection between models requires comprehensive knowledge of each model's components and assumptions. To address these challenges in integrating biosimulation models, we propose an approach to automatically and confidently compose biosimulation models. The approach uses bond graphs to combine aspects of physical and thermodynamics-based modelling with biological semantics. We improved on existing approaches by using semantic annotations to automate the recognition of common components. The approach is illustrated by coupling a model of the Ras-MAPK cascade to a model of the upstream activation of EGFR. Through this methodology, we aim to assist researchers and modellers in readily having access to more comprehensive biological systems models.

Spatio-temporal analysis of nanoparticles in live tumor spheroids impacted by cell origin and density.

Nanoparticles hold great preclinical promise in cancer therapy but continue to suffer attrition through clinical trials. Advanced, three dimensional (3D) cellular models such as tumor spheroids can recapitulate elements of the tumor environment and are considered the superior model to evaluate nanoparticle designs. However, there is an important need to better understand nanoparticle penetration kinetics and determine how different cell characteristics may influence this nanoparticle uptake. A key challenge with current approaches for measuring nanoparticle accumulation in spheroids is that they are often static, losing spatial and temporal information which may be necessary for effective nanoparticle evaluation in 3D cell models. To overcome this challenge, we developed an analysis platform, termed the Determination of Nanoparticle Uptake in Tumor Spheroids (DONUTS), which retains spatial and temporal information during quantification, enabling evaluation of nanoparticle uptake in 3D tumor spheroids. Outperforming linear profiling methods, DONUTS was able to measure silica nanoparticle uptake to 10 µm accuracy in both isotropic and irregularly shaped cancer cell spheroids. This was then extended to determine penetration kinetics, first by a forward-in-time, center-in-space model, and then by mathematical modelling, which enabled the direct evaluation of nanoparticle penetration kinetics in different spheroid models. Nanoparticle uptake was shown to inversely relate to particle size and varied depending on the cell type, cell stiffness and density of the spheroid model. The automated analysis method we have developed can be applied to live spheroids in situ, for the advanced evaluation of nanoparticles as delivery agents in cancer therapy.

Analysing and simulating energy-based models in biology using BondGraphTools.

Like all physical systems, biological systems are constrained by the laws of physics. However, mathematical models of biochemistry frequently neglect the conservation of energy, leading to unrealistic behaviour. Energy-based models that are consistent with conservation of mass, charge and energy have the potential to aid the understanding of complex interactions between biological components, and are becoming easier to develop with recent advances in experimental measurements and databases. In this paper, we motivate the use of bond graphs (a modelling tool from engineering) for energy-based modelling and introduce, BondGraphTools, a Python library for constructing and analysing bond graph models. We use examples from biochemistry to illustrate how BondGraphTools can be used to automate model construction in systems biology while maintaining consistency with the laws of physics.

Modular assembly of dynamic models in systems biology.

It is widely acknowledged that the construction of large-scale dynamic models in systems biology requires complex modelling problems to be broken up into more manageable pieces. To this end, both modelling and software frameworks are required to enable modular modelling. While there has been consistent progress in the development of software tools to enhance model reusability, there has been a relative lack of consideration for how underlying biophysical principles can be applied to this space. Bond graphs combine the aspects of both modularity and physics-based modelling. In this paper, we argue that bond graphs are compatible with recent developments in modularity and abstraction in systems biology, and are thus a desirable framework for constructing large-scale models. We use two examples to illustrate the utility of bond graphs in this context: a model of a mitogen-activated protein kinase (MAPK) cascade to illustrate the reusability of modules and a model of glycolysis to illustrate the ability to modify the model granularity.

Modular dynamic biomolecular modelling with bond graphs: the unification of stoichiometry, thermodynamics, kinetics and data.

Renewed interest in dynamic simulation models of biomolecular systems has arisen from advances in genome-wide measurement and applications of such models in biotechnology and synthetic biology. In particular, genome-scale models of cellular metabolism beyond the steady state are required in order to represent transient and dynamic regulatory properties of the system. Development of such whole-cell models requires new modelling approaches. Here, we propose the energy-based bond graph methodology, which integrates stoichiometric models with thermodynamic principles and kinetic modelling. We demonstrate how the bond graph approach intrinsically enforces thermodynamic constraints, provides a modular approach to modelling, and gives a basis for estimation of model parameters leading to dynamic models of biomolecular systems. The approach is illustrated using a well-established stoichiometric model of Escherichia coli and published experimental data.

Hierarchical semantic composition of biosimulation models using bond graphs.

Simulating complex biological and physiological systems and predicting their behaviours under different conditions remains challenging. Breaking systems into smaller and more manageable modules can address this challenge, assisting both model development and simulation. Nevertheless, existing computational models in biology and physiology are often not modular and therefore difficult to assemble into larger models. Even when this is possible, the resulting model may not be useful due to inconsistencies either with the laws of physics or the physiological behaviour of the system. Here, we propose a general methodology for composing models, combining the energy-based bond graph approach with semantics-based annotations. This approach improves model composition and ensures that a composite model is physically plausible. As an example, we demonstrate this approach to automated model composition using a model of human arterial circulation. The major benefit is that modellers can spend more time on understanding the behaviour of complex biological and physiological systems and less time wrangling with model composition.

Understanding nano-engineered particle-cell interactions: biological insights from mathematical models.

Understanding the interactions between nano-engineered particles and cells is necessary for the rational design of particles for therapeutic, diagnostic and imaging purposes. In particular, the informed design of particles relies on the quantification of the relationship between the physicochemical properties of the particles and the rate at which cells interact with, and subsequently internalise, particles. Quantitative models, both mathematical and computational, provide a powerful tool for elucidating this relationship, as well as for understanding the mechanisms governing the intertwined processes of interaction and internalisation. Here we review the different types of mathematical and computational models that have been used to examine particle-cell interactions and particle internalisation. We detail the mathematical methodology for each type of model, the benefits and limitations associated with the different types of models, and highlight the advances in understanding gleaned from the application of these models to experimental observations of particle internalisation. We discuss the recent proposal and ongoing community adoption of standardised experimental reporting, and how this adoption is an important step toward unlocking the full potential of modelling approaches. Finally, we consider future directions in quantitative models of particle-cell interactions and highlight the need for hybrid experimental and theoretical investigations to address hitherto unanswered questions.

Ca2+ Release via IP3 Receptors Shapes the Cardiac Ca2+ Transient for Hypertrophic Signaling.

Calcium (Ca2+) plays a central role in mediating both contractile function and hypertrophic signaling in ventricular cardiomyocytes. L-type Ca2+ channels trigger release of Ca2+ from ryanodine receptors for cellular contraction, whereas signaling downstream of G-protein-coupled receptors stimulates Ca2+ release via inositol 1,4,5-trisphosphate receptors (IP3Rs), engaging hypertrophic signaling pathways. Modulation of the amplitude, duration, and duty cycle of the cytosolic Ca2+ contraction signal and spatial localization have all been proposed to encode this hypertrophic signal. Given current knowledge of IP3Rs, we develop a model describing the effect of functional interaction (cross talk) between ryanodine receptor and IP3R channels on the Ca2+ transient and examine the sensitivity of the Ca2+ transient shape to properties of IP3R activation. A key result of our study is that IP3R activation increases Ca2+ transient duration for a broad range of IP3R properties, but the effect of IP3R activation on Ca2+ transient amplitude is dependent on IP3 concentration. Furthermore we demonstrate that IP3-mediated Ca2+ release in the cytosol increases the duty cycle of the Ca2+ transient, the fraction of the cycle for which [Ca2+] is elevated, across a broad range of parameter values and IP3 concentrations. When coupled to a model of downstream transcription factor (NFAT) activation, we demonstrate that there is a high correspondence between the Ca2+ transient duty cycle and the proportion of activated NFAT in the nucleus. These findings suggest increased cytosolic Ca2+ duty cycle as a plausible mechanism for IP3-dependent hypertrophic signaling via Ca2+-sensitive transcription factors such as NFAT in ventricular cardiomyocytes.

Predicting population extinction in lattice-based birth-death-movement models.

The question of whether a population will persist or go extinct is of key interest throughout ecology and biology. Various mathematical techniques allow us to generate knowledge regarding individual behaviour, which can be analysed to obtain predictions about the ultimate survival or extinction of the population. A common model employed to describe population dynamics is the lattice-based random walk model with crowding (exclusion). This model can incorporate behaviour such as birth, death and movement, while including natural phenomena such as finite size effects. Performing sufficiently many realizations of the random walk model to extract representative population behaviour is computationally intensive. Therefore, continuum approximations of random walk models are routinely employed. However, standard continuum approximations are notoriously incapable of making accurate predictions about population extinction. Here, we develop a new continuum approximation, the state-space diffusion approximation, which explicitly accounts for population extinction. Predictions from our approximation faithfully capture the behaviour in the random walk model, and provides additional information compared to standard approximations. We examine the influence of the number of lattice sites and initial number of individuals on the long-term population behaviour, and demonstrate the reduction in computation time between the random walk model and our approximation.

Insights From Computational Modeling Into the Contribution of Mechano-Calcium Feedback on the Cardiac End-Systolic Force-Length Relationship.

In experimental studies on cardiac tissue, the end-systolic force-length relation (ESFLR) has been shown to depend on the mode of contraction: isometric or isotonic. The isometric ESFLR is derived from isometric contractions spanning a range of muscle lengths while the isotonic ESFLR is derived from shortening contractions across a range of afterloads. The ESFLR of isotonic contractions consistently lies below its isometric counterpart. Despite the passing of over a hundred years since the first insight by Otto Frank, the mechanism(s) underlying this protocol-dependent difference in the ESFLR remain incompletely explained. Here, we investigate the role of mechano-calcium feedback in accounting for the difference between these two ESFLRs. Previous studies have compared the dynamics of isotonic contractions to those of a single isometric contraction at a length that produces maximum force, without considering isometric contractions at shorter muscle lengths. We used a mathematical model of cardiac excitation-contraction to simulate isometric and force-length work-loop contractions (the latter being the 1D equivalent of the whole-heart pressure-volume loop), and compared Ca2+ transients produced under equivalent force conditions. We found that the duration of the simulated Ca2+ transient increases with decreasing sarcomere length for isometric contractions, and increases with decreasing afterload for work-loop contractions. At any given force, the Ca2+ transient for an isometric contraction is wider than that during a work-loop contraction. By driving simulated work-loops with wider Ca2+ transients generated from isometric contractions, we show that the duration of muscle shortening was prolonged, thereby shifting the work-loop ESFLR toward the isometric ESFLR. These observations are explained by an increase in the rate of binding of Ca2+ to troponin-C with increasing force. However, the leftward shift of the work-loop ESFLR does not superimpose on the isometric ESFLR, leading us to conclude that while mechano-calcium feedback does indeed contribute to the difference between the two ESFLRs, it does not completely account for it.

Isolating the sources of heterogeneity in nano-engineered particle-cell interactions.

Nano-engineered particles have the potential to enhance therapeutic success and reduce toxicity-based treatment side effects via the targeted delivery of drugs to cells. This delivery relies on complex interactions between numerous biological, chemical and physical processes. The intertwined nature of these processes has thus far hindered attempts to understand their individual impact. Variation in experimental data, such as the number of particles inside each cell, further inhibits understanding. Here, we present a mathematical framework that is capable of examining the impact of individual processes during particle delivery. We demonstrate that variation in experimental particle uptake data can be explained by three factors: random particle motion; variation in particle-cell interactions; and variation in the maximum particle uptake per cell. Without all three factors, the experimental data cannot be explained. This work provides insight into biological mechanisms that cause heterogeneous responses to treatment, and enables precise identification of treatment-resistant cell subpopulations.

Physically-plausible modelling of biomolecular systems: A simplified, energy-based model of the mitochondrial electron transport chain.

Advances in systems biology and whole-cell modelling demand increasingly comprehensive mathematical models of cellular biochemistry. Such models require the development of simplified representations of specific processes which capture essential biophysical features but without unnecessarily complexity. Recently there has been renewed interest in thermodynamically-based modelling of cellular processes. Here we present an approach to developing of simplified yet thermodynamically consistent (hence physically plausible) models which can readily be incorporated into large scale biochemical descriptions but which do not require full mechanistic detail of the underlying processes. We illustrate the approach through development of a simplified, physically plausible model of the mitochondrial electron transport chain and show that the simplified model behaves like the full system.

Assessing Cardiomyocyte Excitation-Contraction Coupling Site Detection From Live Cell Imaging Using a Structurally-Realistic Computational Model of Calcium Release.

Calcium signaling plays a pivotal role in cardiomyocytes, coupling electrical excitation to mechanical contraction of the heart. Determining locations of active calcium release sites, and how their recruitment changes in response to stimuli and in disease states is therefore of central interest in cardiac physiology. Current algorithms for detecting release sites from live cell imaging data are however not easily validated against a known "ground truth," which makes interpretation of the output of such algorithms, in particular the degree of confidence in site detection, a challenging task. Computational models are capable of integrating findings from multiple sources into a consistent, predictive framework. In cellular physiology, such models have the potential to reveal structure and function beyond the temporal and spatial resolution limitations of individual experimental measurements. Here, we create a spatially detailed computational model of calcium release in an eight sarcomere section of a ventricular cardiomyocyte, using electron tomography reconstruction of cardiac ultrastructure and confocal imaging of protein localization. This provides a high-resolution model of calcium diffusion from intracellular stores, which can be used as a platform to simulate confocal fluorescence imaging in the context of known ground truth structures from the higher resolution model. We use this capability to evaluate the performance of a recently proposed method for detecting the functional response of calcium release sites in live cells. Model permutations reveal how calcium release site density and mitochondria acting as diffusion barriers impact the detection performance of the algorithm. We demonstrate that site density has the greatest impact on detection precision and recall, in particular affecting the effective detectable depth of sites in confocal data. Our findings provide guidance on how such detection algorithms may best be applied to experimental data and give insights into limitations when using two-dimensional microscopy images to analyse three-dimensional cellular structures.

Revisiting cell-particle association in vitro: A quantitative method to compare particle performance.

Nanoengineering has the potential to revolutionize medicine by designing drug delivery systems that are both efficacious and highly selective. Determination of the affinity between cell lines and nanoparticles is thus of central importance, both to enable comparison of particles and to facilitate prediction of in vivo response. Attempts to compare particle performance can be dominated by experimental artifacts (including settling effects) or variability in experimental protocol. Instead, qualitative methods are generally used, limiting the reusability of many studies. Herein, we introduce a mathematical model-based approach to quantify the affinity between a cell-particle pairing, independent of the aforementioned confounding artifacts. The analysis presented can serve as a quantitative metric of the stealth, fouling, and targeting performance of nanoengineered particles in vitro. We validate this approach using a newly created in vitro dataset, consisting of seven different disulfide-stabilized poly(methacrylic acid) particles ranging from ~100 to 1000 nm in diameter that were incubated with three different cell lines (HeLa, THP-1, and RAW 264.7). We further expanded this dataset through the inclusion of previously published data and use it to determine which of five mathematical models best describe cell-particle association. We subsequently use this model to perform a quantitative comparison of cell-particle association for cell-particle pairings in our dataset. This analysis reveals a more complex cell-particle association relationship than a simplistic interpretation of the data, which erroneously assigns high affinity for all cell lines examined to large particles. Finally, we provide an online tool (http://bionano.xyz/estimator), which allows other researchers to easily apply this modeling approach to their experimental results.

Link between Low-Fouling and Stealth: A Whole Blood Biomolecular Corona and Cellular Association Analysis on Nanoengineered Particles.

Upon exposure to human blood, nanoengineered particles interact with a multitude of plasma components, resulting in the formation of a biomolecular corona. This corona modulates downstream biological responses, including recognition by and association with human immune cells. Considerable research effort has been directed toward the design of materials that can demonstrate a low affinity for various proteins (low-fouling materials) and materials that can exhibit low association with human immune cells (stealth materials). An implicit assumption common to bio-nano research is that nanoengineered particles that are low-fouling will also exhibit stealth. Herein, we investigated the link between the low-fouling properties of a particle and its propensity for stealth in whole human blood. High-fouling mesoporous silica (MS) particles and low-fouling zwitterionic poly(2-methacryloyloxyethyl phosphorylcholine) (PMPC) particles were synthesized, and their interaction with blood components was assessed before and after precoating with serum albumin, immunoglobulin G, or complement protein C1q. We performed an in-depth proteomics characterization of the biomolecular corona that both identifies specific proteins and measures their relative abundance. This was compared with observations from a whole blood association assay that identified with which cell type each particle system associates. PMPC-based particles displayed reduced association both with cells and with serum proteins compared with MS-based particles. Furthermore, the enrichment of specific proteins within the biomolecular corona was found to correlate with association with specific cell types. This study demonstrates how the low-fouling properties of a material are indicative of its stealth with respect to immune cell association.