Modeling and analysis of the molecular basis of pain in sensory neurons

Finding new analgesics: Computational pharmacology faces drug discovery challenges

Despite the worldwide prevalence and huge burden of pain, pain is an undertreated phenomenon. Currently used analgesics have several limitations regarding their efficacy and safety. The discovery of analgesics possessing a novel mechanism of action has faced multiple challenges, including a limited understanding of biological processes underpinning pain and analgesia and poor animal-to-human translation. Computational pharmacology is currently employed to face these challenges. In this review, we discuss the theory, methods, and applications of computational pharmacology in pain research. Computational pharmacology encompasses a wide variety of theoretical concepts and practical methodological approaches, with the overall aim of gaining biological insight through data acquisition and analysis. Data are acquired from patients or animal models with pain or analgesic treatment, at different levels of biological organization (molecular, cellular, physiological, and behavioral). Distinct methodological algorithms can then be used to analyze and integrate data. This helps to facilitate the identification of biological molecules and processes associated with pain phenotype, build quantitative models of pain signaling, and extract translatable features between humans and animals. However, computational pharmacology has several limitations, and its predictions can provide false positive and negative findings. Therefore, computational predictions are required to be validated experimentally before drawing solid conclusions. In this review, we discuss several case study examples of combining and integrating computational tools with experimental pain research tools to meet drug discovery challenges.

Mathematical Modeling of PI3K/Akt Pathway in Microglia

The motility of microglia involves intracellular signaling pathways that are predominantly controlled by changes in cytosolic Ca2+ and activation of PI3K/Akt (phosphoinositide-3-kinase/protein kinase B). In this letter, we develop a novel biophysical model for cytosolic Ca2+ activation of the PI3K/Akt pathway in microglia where Ca2+ influx is mediated by both P2Y purinergic receptors (P2YR) and P2X purinergic receptors (P2XR). The model parameters are estimated by employing optimization techniques to fit the model to phosphorylated Akt (pAkt) experimental modeling/in vitro data. The integrated model supports the hypothesis that Ca2+ influx via P2YR and P2XR can explain the experimentally reported biphasic transient responses in measuring pAkt levels. Our predictions reveal new quantitative insights into P2Rs on how they regulate Ca2+ and Akt in terms of physiological interactions and transient responses. It is shown that the upregulation of P2X receptors through a repetitive application of agonist results in a continual increase in the baseline [Ca2+], which causes the biphasic response to become a monophasic response which prolongs elevated levels of pAkt.

Pareto optimality, economy-effectiveness trade-offs and ion channel degeneracy: improving population modelling for single neurons

Neurons encounter unavoidable evolutionary trade-offs between multiple tasks. They must consume as little energy as possible while effectively fulfilling their functions. Cells displaying the best performance for such multi-task trade-offs are said to be Pareto optimal, with their ion channel configurations underpinning their functionality. Ion channel degeneracy, however, implies that multiple ion channel configurations can lead to functionally similar behaviour. Therefore, instead of a single model, neuroscientists often use populations of models with distinct combinations of ionic conductances. This approach is called population (database or ensemble) modelling. It remains unclear, which ion channel parameters in the vast population of functional models are more likely to be found in the brain. Here we argue that Pareto optimality can serve as a guiding principle for addressing this issue by helping to identify the subpopulations of conductance-based models that perform best for the trade-off between economy and functionality. In this way, the high-dimensional parameter space of neuronal models might be reduced to geometrically simple low-dimensional manifolds, potentially explaining experimentally observed ion channel correlations. Conversely, Pareto inference might also help deduce neuronal functions from high-dimensional Patch-seq data. In summary, Pareto optimality is a promising framework for improving population modelling of neurons and their circuits.

JuPOETs: a constrained multiobjective optimization approach to estimate biochemical model ensembles in the Julia programming language

Background

Ensemble modeling is a promising approach for obtaining robust predictions and coarse grained population behavior in deterministic mathematical models. Ensemble approaches address model uncertainty by using parameter or model families instead of single best-fit parameters or fixed model structures. Parameter ensembles can be selected based upon simulation error, along with other criteria such as diversity or steady-state performance. Simulations using parameter ensembles can estimate confidence intervals on model variables, and robustly constrain model predictions, despite having many poorly constrained parameters.

Results

In this software note, we present a multiobjective based technique to estimate parameter or models ensembles, the Pareto Optimal Ensemble Technique in the Julia programming language (JuPOETs). JuPOETs integrates simulated annealing with Pareto optimality to estimate ensembles on or near the optimal tradeoff surface between competing training objectives. We demonstrate JuPOETs on a suite of multiobjective problems, including test functions with parameter bounds and system constraints as well as for the identification of a proof-of-concept biochemical model with four conflicting training objectives. JuPOETs identified optimal or near optimal solutions approximately six-fold faster than a corresponding implementation in Octave for the suite of test functions. For the proof-of-concept biochemical model, JuPOETs produced an ensemble of parameters that gave both the mean of the training data for conflicting data sets, while simultaneously estimating parameter sets that performed well on each of the individual objective functions.

Conclusions

JuPOETs is a promising approach for the estimation of parameter and model ensembles using multiobjective optimization. JuPOETs can be adapted to solve many problem types, including mixed binary and continuous variable types, bilevel optimization problems and constrained problems without altering the base algorithm. JuPOETs is open source, available under an MIT license, and can be installed using the Julia package manager from the JuPOETs GitHub repository

Modelling and analysis of an ensemble of eukaryotic translation initiation models

Programmed protein synthesis plays an important role in the cell cycle. Deregulated translation has been observed in several cancers. In this study, the authors constructed an ensemble of mathematical models describing the integration of growth factor signals with translation initiation. Using these models, the authors estimated critical structural features of the translation architecture. Sensitivity and robustness analysis with and without growth factors suggested that a balance between competing regulatory programmes governed translation initiation. Proteins such as Akt and mTor promoted initiation by integrating growth factor signals with the assembly of the 80S initiation complex. However, negative regulators such as PTEN and 4EBP1 restrained initiation in the absence of stimulation. Other proteins such as eIF4E were also found to be structurally critical as deletion of amplification of these components resulted in a network incapable of nominal operation. These findings could help understand the molecular basis of translation deregulation observed in cancer and perhaps lead to new anti-cancer therapeutic strategies. [Includes supplementary material].

Neuronal calcium signaling in chronic pain

Acute physiological pain, the unpleasant sensory response to a noxious stimulus, is essential for animals and humans to avoid potential injury. Pathological pain that persists after the original insult or injury has subsided, however, not only results in individual suffering but also imposes a significant cost on society. Improving treatments for long-lasting pathological pain requires a comprehensive understanding of the biological mechanisms underlying pain perception and the development of pain chronicity. In this review, we aim to highlight some of the major findings related to the involvement of neuronal calcium signaling in the processes that mediate chronic pain.

Ionic mechanisms in peripheral pain

Chronic pain constitutes an important and growing problem in society with large unmet needs with respect to treatment and clear implications for quality of life. Computational modeling is used to complement experimental studies to elucidate mechanisms involved in pain states. Models representing the peripheral nerve ending often address questions related to sensitization or reduction in pain detection threshold. In models of the axon or the cell body of the unmyelinated C-fiber, a large body of work concerns the role of particular sodium channels and mutations of these. Furthermore, in central structures: spinal cord or higher structures, sensitization often refers not only to enhanced synaptic efficacy but also to elevated intrinsic neuronal excitability. One of the recent developments in computational neuroscience is the emergence of computational neuropharmacology. In this area, computational modeling is used to study mechanisms of pathology with the objective of finding the means of restoring healthy function. This research has received increased attention from the pharmaceutical industry as ion channels have gained increased interest as drug targets. Computational modeling has several advantages, notably the ability to provide mechanistic links between molecular and cellular levels on the one hand and functions at the systems level on the other hand. These characteristics make computational modeling an additional tool to be used in the process of selecting pharmaceutical targets. Furthermore, large-scale simulations can provide a framework to systematically study the effects of several interacting disease parameters or effects from combinations of drugs.

Inhibition of P2X4 function by P2Y6 UDP receptors in microglia

ATP-gated P2X4 receptor channels expressed in spinal microglia actively participate in central sensitization, making their functional regulation a key process in chronic pain pathologies. P2Y6 metabotropic Gq -coupled receptors, also expressed in microglia, are involved in the initial response to nerve injury, triggering phagocytosis upon activation by UDP. It has been reported recently that expression of both P2X4 and P2Y6 is upregulated in activated microglia following nerve injury. We show here, in resting as well as LPS-activated primary microglia, that P2Y6 decreases P2X4-mediated calcium entry and inhibits the dilation of P2X4 channels into a large-conductance pore measured with a YO-PRO-1 uptake assay. Furthermore, P2Y6 activation modulates the ATP-dependent migration of microglia, a process likely involved in their shift from migratory to phagocytic phenotype. Reconstituting the P2X4-P2Y6 interaction in recombinant systems shows that P2Y6 activation decreases P2X4 current amplitude, activation and desensitization rates, and reduces P2X4 channel permeability to the large cation NMDG(+) . Phospholipase C-mediated hydrolysis of the phosphoinositide PI(4,5)P2 , a necessary cofactor for P2X4 channel function, underlies this inhibitory crosstalk. As extracellular levels of both ATP and UDP are increased in the spinal cord following nerve injury, the control of P2X4 activity by P2Y6 might play a critical role in regulating neuropathic pain-inducing microglial responses.

Multiscale models of breast cancer progression

Breast cancer initiation, invasion and metastasis span multiple length and time scales. Molecular events at short length scales lead to an initial tumorigenic population, which left unchecked by immune action, acts at increasingly longer length scales until eventually the cancer cells escape from the primary tumor site. This series of events is highly complex, involving multiple cell types interacting with (and shaping) the microenvironment. Multiscale mathematical models have emerged as a powerful tool to quantitatively integrate the convective-diffusion-reaction processes occurring on the systemic scale, with the molecular signaling processes occurring on the cellular and subcellular scales. In this study, we reviewed the current state of the art in cancer modeling across multiple length scales, with an emphasis on the integration of intracellular signal transduction models with pro-tumorigenic chemical and mechanical microenvironmental cues. First, we reviewed the underlying biomolecular origin of breast cancer, with a special emphasis on angiogenesis. Then, we summarized the development of tissue engineering platforms which could provide high-fidelity ex vivo experimental models to identify and validate multiscale simulations. Lastly, we reviewed top-down and bottom-up multiscale strategies that integrate subcellular networks with the microenvironment. We present models of a variety of cancers, in addition to breast cancer specific models. Taken together, we expect as the sophistication of the simulations increase, that multiscale modeling and bottom-up agent-based models in particular will become an increasingly important platform technology for basic scientific discovery, as well as the identification and validation of potentially novel therapeutic targets.

Ensemble models of neutrophil trafficking in severe sepsis

A hallmark of severe sepsis is systemic inflammation which activates leukocytes and can result in their misdirection. This leads to both impaired migration to the locus of infection and increased infiltration into healthy tissues. In order to better understand the pathophysiologic mechanisms involved, we developed a coarse-grained phenomenological model of the acute inflammatory response in CLP (cecal ligation and puncture)-induced sepsis in rats. This model incorporates distinct neutrophil kinetic responses to the inflammatory stimulus and the dynamic interactions between components of a compartmentalized inflammatory response. Ensembles of model parameter sets consistent with experimental observations were statistically generated using a Markov-Chain Monte Carlo sampling. Prediction uncertainty in the model states was quantified over the resulting ensemble parameter sets. Forward simulation of the parameter ensembles successfully captured experimental features and predicted that systemically activated circulating neutrophils display impaired migration to the tissue and neutrophil sequestration in the lung, consequently contributing to tissue damage and mortality. Principal component and multiple regression analyses of the parameter ensembles estimated from survivor and non-survivor cohorts provide insight into pathologic mechanisms dictating outcome in sepsis. Furthermore, the model was extended to incorporate hypothetical mechanisms by which immune modulation using extracorporeal blood purification results in improved outcome in septic rats. Simulations identified a sub-population (about 18% of the treated population) that benefited from blood purification. Survivors displayed enhanced neutrophil migration to tissue and reduced sequestration of lung neutrophils, contributing to improved outcome. The model ensemble presented herein provides a platform for generating and testing hypotheses in silico, as well as motivating further experimental studies to advance understanding of the complex biological response to severe infection, a problem of growing magnitude in humans.

Millimeter wave-induced modulation of calcium dynamics in an engineered skin co-culture model: role of secreted ATP on calcium spiking

We have previously designed and characterized a 94 GHz exposure system that allows real-time monitoring of subcellular interactions induced by millimeter wave (MMW) stimulation. For example, studies of the calcium dynamics in neuronal cells in response to 94 GHz irradiation suggested that MMW stimulation increased calcium spiking. In this study, we engineered a 3D co-culture model that represents the major constituents of skin. We used this experimental model along with the custom-designed MMW exposure system to investigate the effects of 94 GHz irradiation in the skin-like tissue construct. Unlike typical non-excitable cells, keratinocytes exhibited calcium spikes in their resting state. Exposure to a 94 GHz irradiation induced a statistically significant increase in the calcium spiking. When co-cultured with neuronal cells in the 3D co-culture skin model, changes in the calcium spiking in neuronal cells depended on the MMW input power. Further, the 94 GHz irradiation caused ATP secretion by keratincytes. ATP is a major factor that modulates the calcium spiking in neuronal cells. Surprisingly, while a 5-fold increase in the ATP secretion enhanced the calcium spiking in neuronal cells, a 10-fold increase significantly hindered the calcium dynamics. Computational simulation of ATP-induced calcium dynamics was in general agreement with the experimental findings, suggesting the involvement of the ATP-sensitive purinergic receptors. The engineered co-culture skin model offers a physiologically relevant environment in which the calcium dynamics is regulated both by the cell-MMW and cell-cell interactions.

Modeling and analysis of retinoic acid induced differentiation of uncommitted precursor cells

Manipulation of differentiation programs has therapeutic potential in a spectrum of human cancers and neurodegenerative disorders. In this study, we integrated computational and experimental methods to unravel the response of a lineage uncommitted precursor cell-line, HL-60, to Retinoic Acid (RA). HL-60 is a human myeloblastic leukemia cell-line used extensively to study human differentiation programs. Initially, we focused on the role of the BLR1 receptor in RA-induced differentiation and G1/0-arrest in HL-60. BLR1, a putative G protein-coupled receptor expressed following RA exposure, is required for RA-induced cell-cycle arrest and differentiation and causes persistent MAPK signaling. A mathematical model of RA-induced cell-cycle arrest and differentiation was formulated and tested against BLR1 wild-type (wt) knock-out and knock-in HL-60 cell-lines with and without RA. The current model described the dynamics of 729 proteins and protein complexes interconnected by 1356 interactions. An ensemble strategy was used to compensate for uncertain model parameters. The ensemble of HL-60 models recapitulated the positive feedback between BLR1 and MAPK signaling. The ensemble of models also correctly predicted Rb and p47phox regulation and the correlation between p21-CDK4-cyclin D formation and G1/0-arrest following exposure to RA. Finally, we investigated the robustness of the HL-60 network architecture to structural perturbations and generated experimentally testable hypotheses for future study. Taken together, the model presented here was a first step toward a systematic framework for analysis of programmed differentiation. These studies also demonstrated that mechanistic network modeling can help prioritize experimental directions by generating falsifiable hypotheses despite uncertainty.

Ensembles of signal transduction models using Pareto Optimal Ensemble Techniques (POETs)

Mathematical modeling of complex gene expression programs is an emerging tool for understanding disease mechanisms. However, identification of large models sometimes requires training using qualitative, conflicting or even contradictory data sets. One strategy to address this challenge is to estimate experimentally constrained model ensembles using multiobjective optimization. In this study, we used Pareto Optimal Ensemble Techniques (POETs) to identify a family of proof-of-concept signal transduction models. POETs integrate Simulated Annealing (SA) with Pareto optimality to identify models near the optimal tradeoff surface between competing training objectives. We modeled a prototypical-signaling network using mass-action kinetics within an ordinary differential equation (ODE) framework (64 ODEs in total). The true model was used to generate synthetic immunoblots from which the POET algorithm identified the 117 unknown model parameters. POET generated an ensemble of signaling models, which collectively exhibited population-like behavior. For example, scaled gene expression levels were approximately normally distributed over the ensemble following the addition of extracellular ligand. Also, the ensemble recovered robust and fragile features of the true model, despite significant parameter uncertainty. Taken together, these results suggest that experimentally constrained model ensembles could capture qualitatively important network features without exact parameter information.

Analysis of the molecular networks in androgen dependent and independent prostate cancer revealed fragile and robust subsystems

Androgen ablation therapy is currently the primary treatment for metastatic prostate cancer. Unfortunately, in nearly all cases, androgen ablation fails to permanently arrest cancer progression. As androgens like testosterone are withdrawn, prostate cancer cells lose their androgen sensitivity and begin to proliferate without hormone growth factors. In this study, we constructed and analyzed a mathematical model of the integration between hormone growth factor signaling, androgen receptor activation, and the expression of cyclin D and Prostate-Specific Antigen in human LNCaP prostate adenocarcinoma cells. The objective of the study was to investigate which signaling systems were important in the loss of androgen dependence. The model was formulated as a set of ordinary differential equations which described 212 species and 384 interactions, including both the mRNA and protein levels for key species. An ensemble approach was chosen to constrain model parameters and to estimate the impact of parametric uncertainty on model predictions. Model parameters were identified using 14 steady-state and dynamic LNCaP data sets taken from literature sources. Alterations in the rate of Prostatic Acid Phosphatase expression was sufficient to capture varying levels of androgen dependence. Analysis of the model provided insight into the importance of network components as a function of androgen dependence. The importance of androgen receptor availability and the MAPK/Akt signaling axes was independent of androgen status. Interestingly, androgen receptor availability was important even in androgen-independent LNCaP cells. Translation became progressively more important in androgen-independent LNCaP cells. Further analysis suggested a positive synergy between the MAPK and Akt signaling axes and the translation of key proliferative markers like cyclin D in androgen-independent cells. Taken together, the results support the targeting of both the Akt and MAPK pathways. Moreover, the analysis suggested that direct targeting of the translational machinery, specifically eIF4E, could be efficacious in androgen-independent prostate cancers.