Simple, Fast and Accurate Implementation of the Diffusion Approximation Algorithm for Stochastic Ion Channels with Multiple States

The phenomena that emerge from the interaction of the stochastic opening and closing of ion channels (channel noise) with the non-linear neural dynamics are essential to our understanding of the operation of the nervous system. The effects that channel noise can have on neural dynamics are generally studied using numerical simulations of stochastic models. Algorithms based on discrete Markov Chains (MC) seem to be the most reliable and trustworthy, but even optimized algorithms come with a non-negligible computational cost. Diffusion Approximation (DA) methods use Stochastic Differential Equations (SDE) to approximate the behavior of a number of MCs, considerably speeding up simulation times. However, model comparisons have suggested that DA methods did not lead to the same results as in MC modeling in terms of channel noise statistics and effects on excitability. Recently, it was shown that the difference arose because MCs were modeled with coupled activation subunits, while the DA was modeled using uncoupled activation subunits. Implementations of DA with coupled subunits, in the context of a specific kinetic scheme, yielded similar results to MC. However, it remained unclear how to generalize these implementations to different kinetic schemes, or whether they were faster than MC algorithms. Additionally, a steady state approximation was used for the stochastic terms, which, as we show here, can introduce significant inaccuracies. We derived the SDE explicitly for any given ion channel kinetic scheme. The resulting generic equations were surprisingly simple and interpretable - allowing an easy and efficient DA implementation. The algorithm was tested in a voltage clamp simulation and in two different current clamp simulations, yielding the same results as MC modeling. Also, the simulation efficiency of this DA method demonstrated considerable superiority over MC methods.Comment: 32 text pages, 10 figures, 1 supplementary text + figur

Clinical Utility of Random Anti–Tumor Necrosis Factor Drug–Level Testing and Measurement of Antidrug Antibodies on the Long-Term Treatment Response in Rheumatoid Arthritis

Objective: To investigate whether antidrug antibodies and/or drug non-trough levels predict the long-term treatment response in a large cohort of patients with rheumatoid arthritis (RA) treated with adalimumab or etanercept and to identify factors influencing antidrug antibody and drug levels to optimize future treatment decisions.  Methods: A total of 331 patients from an observational prospective cohort were selected (160 patients treated with adalimumab and 171 treated with etanercept). Antidrug antibody levels were measured by radioimmunoassay, and drug levels were measured by enzyme-linked immunosorbent assay in 835 serial serum samples obtained 3, 6, and 12 months after initiation of therapy. The association between antidrug antibodies and drug non-trough levels and the treatment response (change in the Disease Activity Score in 28 joints) was evaluated.  Results: Among patients who completed 12 months of followup, antidrug antibodies were detected in 24.8% of those receiving adalimumab (31 of 125) and in none of those receiving etanercept. At 3 months, antidrug antibody formation and low adalimumab levels were significant predictors of no response according to the European League Against Rheumatism (EULAR) criteria at 12 months (area under the receiver operating characteristic curve 0.71 [95% confidence interval (95% CI) 0.57, 0.85]). Antidrug antibody–positive patients received lower median dosages of methotrexate compared with antidrug antibody–negative patients (15 mg/week versus 20 mg/week; P = 0.01) and had a longer disease duration (14.0 versus 7.7 years; P = 0.03). The adalimumab level was the best predictor of change in the DAS28 at 12 months, after adjustment for confounders (regression coefficient 0.060 [95% CI 0.015, 0.10], P = 0.009). Etanercept levels were associated with the EULAR response at 12 months (regression coefficient 0.088 [95% CI 0.019, 0.16], P = 0.012); however, this difference was not significant after adjustment. A body mass index of ≥30 kg/m2 and poor adherence were associated with lower drug levels.  Conclusion: Pharmacologic testing in anti–tumor necrosis factor–treated patients is clinically useful even in the absence of trough levels. At 3 months, antidrug antibodies and low adalimumab levels are significant predictors of no response according to the EULAR criteria at 12 months

Expecting to lift a box together makes the load look lighter

The action abilities of an individual observer modulate his or her perception of spatial properties of the environment and of objects. The present study investigated how joint action abilities shape perception. Four experiments examined how the intention to lift an object with another individual affects perceived weight. In Experiments 1, 2a, and 2b, participants judged the perceived weight of boxes while expecting to lift them either alone or with a co-actor. In Experiment 3, the co-actor was healthy or injured. Participants intending to lift a box with a co-actor perceived the box as lighter than participants intending to lift the same box alone, provided that the co-actor appeared healthy and therefore capable of helping. These findings suggest that anticipated effort modulates the perception of object properties in the context of joint action. We discuss implications for the role of action prediction and action simulation processes in social interaction

Structural and Mutational Analysis of Functional Differentiation between Synaptotagmins-1 and -7

Synaptotagmins are known to mediate diverse forms of Ca2+-triggered exocytosis through their C2 domains, but the principles underlying functional differentiation among them are unclear. Synaptotagmin-1 functions as a Ca2+ sensor in neurotransmitter release at central nervous system synapses, but synaptotagmin-7 does not, and yet both isoforms act as Ca2+ sensors in chromaffin cells. To shed light into this apparent paradox, we have performed rescue experiments in neurons from synaptotagmin-1 knockout mice using a chimera that contains the synaptotagmin-1 sequence with its C2B domain replaced by the synaptotagmin-7 C2B domain (Syt1/7). Rescue was not achieved either with the WT Syt1/7 chimera or with nine mutants where residues that are distinct in synaptotagmin-7 were restored to those present in synaptotagmin-1. To investigate whether these results arise because of unique conformational features of the synaptotagmin-7 C2B domain, we determined its crystal structure at 1.44 Å resolution. The synaptotagmin-7 C2B domain structure is very similar to that of the synaptotagmin-1 C2B domain and contains three Ca2+-binding sites. Two of the Ca2+-binding sites of the synaptotagmin-7 C2B domain are also present in the synaptotagmin-1 C2B domain and have analogous ligands to those determined for the latter by NMR spectroscopy, suggesting that a discrepancy observed in a crystal structure of the synaptotagmin-1 C2B domain arose from crystal contacts. Overall, our results suggest that functional differentiation in synaptotagmins arises in part from subtle sequence changes that yield dramatic functional differences

Phosphoproteomics-Based Modeling Defines the Regulatory Mechanism Underlying Aberrant EGFR Signaling

BACKGROUND: Mutation of the epidermal growth factor receptor (EGFR) results in a discordant cell signaling, leading to the development of various diseases. However, the mechanism underlying the alteration of downstream signaling due to such mutation has not yet been completely understood at the system level. Here, we report a phosphoproteomics-based methodology for characterizing the regulatory mechanism underlying aberrant EGFR signaling using computational network modeling. METHODOLOGY/PRINCIPAL FINDINGS: Our phosphoproteomic analysis of the mutation at tyrosine 992 (Y992), one of the multifunctional docking sites of EGFR, revealed network-wide effects of the mutation on EGF signaling in a time-resolved manner. Computational modeling based on the temporal activation profiles enabled us to not only rediscover already-known protein interactions with Y992 and internalization property of mutated EGFR but also further gain model-driven insights into the effect of cellular content and the regulation of EGFR degradation. Our kinetic model also suggested critical reactions facilitating the reconstruction of the diverse effects of the mutation on phosphoproteome dynamics. CONCLUSIONS/SIGNIFICANCE: Our integrative approach provided a mechanistic description of the disorders of mutated EGFR signaling networks, which could facilitate the development of a systematic strategy toward controlling disease-related cell signaling

Parameter estimate of signal transduction pathways

BACKGROUND: The "inverse" problem is related to the determination of unknown causes on the bases of the observation of their effects. This is the opposite of the corresponding "direct" problem, which relates to the prediction of the effects generated by a complete description of some agencies. The solution of an inverse problem entails the construction of a mathematical model and takes the moves from a number of experimental data. In this respect, inverse problems are often ill-conditioned as the amount of experimental conditions available are often insufficient to unambiguously solve the mathematical model. Several approaches to solving inverse problems are possible, both computational and experimental, some of which are mentioned in this article. In this work, we will describe in details the attempt to solve an inverse problem which arose in the study of an intracellular signaling pathway. RESULTS: Using the Genetic Algorithm to find the sub-optimal solution to the optimization problem, we have estimated a set of unknown parameters describing a kinetic model of a signaling pathway in the neuronal cell. The model is composed of mass action ordinary differential equations, where the kinetic parameters describe protein-protein interactions, protein synthesis and degradation. The algorithm has been implemented on a parallel platform. Several potential solutions of the problem have been computed, each solution being a set of model parameters. A sub-set of parameters has been selected on the basis on their small coefficient of variation across the ensemble of solutions. CONCLUSION: Despite the lack of sufficiently reliable and homogeneous experimental data, the genetic algorithm approach has allowed to estimate the approximate value of a number of model parameters in a kinetic model of a signaling pathway: these parameters have been assessed to be relevant for the reproduction of the available experimental data

Deterministic Chaos and Fractal Complexity in the Dynamics of Cardiovascular Behavior: Perspectives on a New Frontier

Physiological systems such as the cardiovascular system are capable of five kinds of behavior: equilibrium, periodicity, quasi-periodicity, deterministic chaos and random behavior. Systems adopt one or more these behaviors depending on the function they have evolved to perform. The emerging mathematical concepts of fractal mathematics and chaos theory are extending our ability to study physiological behavior. Fractal geometry is observed in the physical structure of pathways, networks and macroscopic structures such the vasculature and the His-Purkinje network of the heart. Fractal structure is also observed in processes in time, such as heart rate variability. Chaos theory describes the underlying dynamics of the system, and chaotic behavior is also observed at many levels, from effector molecules in the cell to heart function and blood pressure. This review discusses the role of fractal structure and chaos in the cardiovascular system at the level of the heart and blood vessels, and at the cellular level. Key functional consequences of these phenomena are highlighted, and a perspective provided on the possible evolutionary origins of chaotic behavior and fractal structure. The discussion is non-mathematical with an emphasis on the key underlying concepts

A multiscale systems perspective on cancer, immunotherapy, and Interleukin-12

Monoclonal antibodies represent some of the most promising molecular targeted immunotherapies. However, understanding mechanisms by which tumors evade elimination by the immune system of the host presents a significant challenge for developing effective cancer immunotherapies. The interaction of cancer cells with the host is a complex process that is distributed across a variety of time and length scales. The time scales range from the dynamics of protein refolding (i.e., microseconds) to the dynamics of disease progression (i.e., years). The length scales span the farthest reaches of the human body (i.e., meters) down to the range of molecular interactions (i.e., nanometers). Limited ranges of time and length scales are used experimentally to observe and quantify changes in physiology due to cancer. Translating knowledge obtained from the limited scales observed experimentally to predict patient response is an essential prerequisite for the rational design of cancer immunotherapies that improve clinical outcomes. In studying multiscale systems, engineers use systems analysis and design to identify important components in a complex system and to test conceptual understanding of the integrated system behavior using simulation. The objective of this review is to summarize interactions between the tumor and cell-mediated immunity from a multiscale perspective. Interleukin-12 and its role in coordinating antibody-dependent cell-mediated cytotoxicity is used illustrate the different time and length scale that underpin cancer immunoediting. An underlying theme in this review is the potential role that simulation can play in translating knowledge across scales