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We present the first machine learning-based autonomous hyperspectral neutron computed tomography experiment performed at the Spallation Neutron Source. Hyperspectral neutron computed tomography allows the characterization of samples by enabling the reconstruction of crystallographic information and elemental/isotopic composition of objects relevant to materials science. High quality reconstructions using traditional algorithms such as the filtered back projection require a high signal-to-noise ratio across a wide wavelength range combined with a large number of projections. This results in scan times of several days to acquire hundreds of hyperspectral projections, during which end users have minimal feedback. To address these challenges, a golden ratio scanning protocol combined with model-based image reconstruction algorithms have been proposed. This novel approach enables high quality real-time reconstructions from streaming experimental data, thus providing feedback to users, while requiring fewer yet a fixed number of projections compared to the filtered back projection method. In this paper, we propose a novel machine learning criterion that can terminate a streaming neutron tomography scan once sufficient information is obtained based on the current set of measurements. Our decision criterion uses a quality score which combines a reference-free image quality metric computed using a pre-trained deep neural network with a metric that measures differences between consecutive reconstructions. The results show that our method can reduce the measurement time by approximately a factor of five compared to a baseline method based on filtered back projection for the samples we studied while automatically terminating the scans., (© 2024. UT-Battelle, LLC, 2024.)

We develop a method for obtaining safe initial policies for reinforcement learning via approximate dynamic programming (ADP) techniques for uncertain systems evolving with discrete-time dynamics. We employ the kernelized Lipschitz estimation to learn multiplier matrices that are used in semidefinite programming frameworks for computing admissible initial control policies with provably high probability. Such admissible controllers enable safe initialization and constraint enforcement while providing exponential stability of the equilibrium of the closed-loop system.

Multiagent consensus equilibrium (MACE) is demonstrated for the integration of experimental observables as constraints in molecular structure determination and for the systematic merging of multiple computational architectures. MACE is founded on simultaneously determining the equilibrium point between multiple experimental and/or computational agents; the returned state description (e.g., atomic coordinates for molecular structure) represents the intersection of each manifold and is not equivalent to the average optimum state for each agent. The moment of inertia, determined directly from microwave spectroscopy measurements, serves to illustrate the mechanism through which MACE evaluations merge experimental and quantum chemical modeling. MACE results reported combine gradient descent optimization of each ab initio agent with an agent that predicts the chemical structure based on root-mean-square deviation of the predicted inertia tensor with experimentally measured moments of inertia. Successful model fusion for several small molecules was achieved as well as the larger molecule solketal. Fusing a model of moment of inertia, an underdetermined predictor of structure, with low cost computational methods yielded structure determination performance comparable to standard computational methods such as MP2/cc-pVTZ and greater agreement with experimental observables.

Magnetic Resonance Imaging (MRI) is a non-invasive diagnostic tool that provides excellent soft-tissue contrast without the use of ionizing radiation. Compared to other clinical imaging modalities (e.g., CT or ultrasound), however, the data acquisition process for MRI is inherently slow, which motivates undersampling and thus drives the need for accurate, efficient reconstruction methods from undersampled datasets. In this article, we describe the use of "plug-and-play" (PnP) algorithms for MRI image recovery. We first describe the linearly approximated inverse problem encountered in MRI. Then we review several PnP methods, where the unifying commonality is to iteratively call a denoising subroutine as one step of a larger optimization-inspired algorithm. Next, we describe how the result of the PnP method can be interpreted as a solution to an equilibrium equation, allowing convergence analysis from the equilibrium perspective. Finally, we present illustrative examples of PnP methods applied to MRI image recovery.

Mathematical modeling is a powerful tool in systems biology; we focus here on improving the reliability of model predictions by reducing the uncertainty in model dynamics through experimental design. Model-based experimental design is a process by which experiments can be systematically chosen to reduce dynamic uncertainty in a given model. We discuss the Maximally Informative Next Experiment (MINE) method for group-wise selection of points in an experimental design and present a convergence result for MINE with nonlinear models. As an application, we illustrate the method on polynomial regression and an ODE model for immune system dynamics. The MINE criterion sequentially determines experiments that can be conducted to best refine model dynamics., (Copyright © 2018. Published by Elsevier Inc.)

The national opioid epidemic is severely impacting Indian Country. In this article, we draw upon data from the Centers for Disease Control and Prevention to describe the contours of this crisis among Native Americans. While these data are subject to significant limitations, we show that Native American opioid overdose mortality rates have grown substantially over the last seventeen years. We further find that this increase appears to at least parallel increases seen among non-Hispanic whites, who are often thought to be uniquely affected by this crisis. We then profile tribal medical and legal responses to the opioid epidemic, ranging from tribally-operated medication-assisted therapy to drug diversion courts rooted in traditional tribal cultures.

The total number of data points required for image generation in Raman microscopy was greatly reduced using sparse sampling strategies, in which the preceding set of measurements informed the next most information-rich sampling location. Using this approach, chemical images of pharmaceutical materials were obtained with >99% accuracy from 15.8% sampling, representing an ∼6-fold reduction in measurement time relative to full field of view rastering with comparable image quality. This supervised learning approach to dynamic sampling (SLADS) has the distinct advantage of being directly compatible with standard confocal Raman instrumentation. Furthermore, SLADS is not limited to Raman imaging, potentially providing time-savings in image reconstruction whenever the single-pixel measurement time is the limiting factor in image generation.

The previously described optimized binary compressive detection (OB-CD) strategy enables fast hyperspectral Raman (and fluorescence) spectroscopic analysis of systems containing two or more chemical components. However, each OB-CD filter collects only a fraction of the scattered photons and the remainder of the photons are lost. Here, we present a refinement of OB-CD, the OB-CD2 strategy, in which all of the collected Raman photons are detected using a pair of complementary binary optical filters that direct photons of different colors to two photon counting detectors. The OB-CD2 filters are generated using a new optimization algorithm described in this work and implemented using a holographic volume diffraction grating and a digital micromirror device (DMD) whose mirrors are programed to selectively direct photons of different colors either to one or the other photon-counting detector. When applied to pairs of pure liquids or two-component solid powder mixtures, the resulting OB-CD2 strategy is shown to more accurately estimate Raman scattering rates of each chemical component, when compared to the original OB-CD, thus facilitating chemical classification at speeds as fast as 3 μs per measurement and the collection of Raman images in under a second.

A sparse supervised learning approach for dynamic sampling (SLADS) is described for dose reduction in diffraction-based protein crystal positioning. Crystal centering is typically a prerequisite for macromolecular diffraction at synchrotron facilities, with X-ray diffraction mapping growing in popularity as a mechanism for localization. In X-ray raster scanning, diffraction is used to identify the crystal positions based on the detection of Bragg-like peaks in the scattering patterns; however, this additional X-ray exposure may result in detectable damage to the crystal prior to data collection. Dynamic sampling, in which preceding measurements inform the next most information-rich location to probe for image reconstruction, significantly reduced the X-ray dose experienced by protein crystals during positioning by diffraction raster scanning. The SLADS algorithm implemented herein is designed for single-pixel measurements and can select a new location to measure. In each step of SLADS, the algorithm selects the pixel, which, when measured, maximizes the expected reduction in distortion given previous measurements. Ground-truth diffraction data were obtained for a 5 µm-diameter beam and SLADS reconstructed the image sampling 31% of the total volume and only 9% of the interior of the crystal greatly reducing the X-ray dosage on the crystal. Using in situ two-photon-excited fluorescence microscopy measurements as a surrogate for diffraction imaging with a 1 µm-diameter beam, the SLADS algorithm enabled image reconstruction from a 7% sampling of the total volume and 12% sampling of the interior of the crystal. When implemented into the beamline at Argonne National Laboratory, without ground-truth images, an acceptable reconstruction was obtained with 3% of the image sampled and approximately 5% of the crystal. The incorporation of SLADS into X-ray diffraction acquisitions has the potential to significantly minimize the impact of X-ray exposure on the crystal by limiting the dose and area exposed for image reconstruction and crystal positioning using data collection hardware present in most macromolecular crystallography end-stations.

A supervised learning approach for dynamic sampling (SLADS) was developed to reduce X-ray exposure prior to data collection in protein structure determination. Implementation of this algorithm allowed reduction of the X-ray dose to the central core of the crystal by up to 20-fold compared to current raster scanning approaches. This dose reduction corresponds directly to a reduction on X-ray damage to the protein crystals prior to data collection for structure determination. Implementation at a beamline at Argonne National Laboratory suggests promise for the use of the SLADS approach to aid in the analysis of X-ray labile crystals. The potential benefits match a growing need for improvements in automated approaches for microcrystal positioning.

This model-based design of experiments (MBDOE) method determines the input magnitudes of an experimental stimuli to apply and the associated measurements that should be taken to optimally constrain the uncertain dynamics of a biological system under study. The ideal global solution for this experiment design problem is generally computationally intractable because of parametric uncertainties in the mathematical model of the biological system. Others have addressed this issue by limiting the solution to a local estimate of the model parameters. Here we present an approach that is independent of the local parameter constraint. This approach is made computationally efficient and tractable by the use of: (1) sparse grid interpolation that approximates the biological system dynamics, (2) representative parameters that uniformly represent the data-consistent dynamical space, and (3) probability weights of the represented experimentally distinguishable dynamics. Our approach identifies data-consistent representative parameters using sparse grid interpolants, constructs the optimal input sequence from a greedy search, and defines the associated optimal measurements using a scenario tree. We explore the optimality of this MBDOE algorithm using a 3-dimensional Hes1 model and a 19-dimensional T-cell receptor model. The 19-dimensional T-cell model also demonstrates the MBDOE algorithm's scalability to higher dimensions. In both cases, the dynamical uncertainty region that bounds the trajectories of the target system states were reduced by as much as 86% and 99% respectively after completing the designed experiments in silico. Our results suggest that for resolving dynamical uncertainty, the ability to design an input sequence paired with its associated measurements is particularly important when limited by the number of measurements.

The recently-developed optimized binary compressive detection (OB-CD) strategy has been shown to be capable of using Raman spectral signatures to rapidly classify and quantify liquid samples and to image solid samples. Here we demonstrate that OB-CD can also be used to quantitatively separate Raman and fluorescence features, and thus facilitate Raman-based chemical analyses in the presence of fluorescence background. More specifically, we describe a general strategy for fitting and suppressing fluorescence background using OB-CD filters trained on third-degree Bernstein polynomials. We present results that demonstrate the utility of this strategy by comparing classification and quantitation results obtained from liquids and powdered mixtures, both with and without fluorescence. Our results demonstrate high-speed Raman-based quantitation in the presence of moderate fluorescence. Moreover, we show that this OB-CD based method is effective in suppressing fluorescence of variable shape, as well as fluorescence that changes during the measurement process, as a result of photobleaching.

The kinase Syk is intricately involved in early signaling events in B cells and is required for proper response when antigens bind to B cell receptors (BCRs). Experiments using an analog-sensitive version of Syk (Syk-AQL) have better elucidated its role, but have not completely characterized its behavior. We present a computational model for BCR signaling, using dynamical systems, which incorporates both wild-type Syk and Syk-AQL. Following the use of sensitivity analysis to identify significant reaction parameters, we screen for parameter vectors that produced graded responses to BCR stimulation as is observed experimentally. We demonstrate qualitative agreement between the model and dose response data for both mutant and wild-type kinases. Analysis of our model suggests that the level of NF- κ B activation, which is reduced in Syk-AQL cells relative to wild-type, is more sensitive to small reductions in kinase activity than Erkp activation, which is essentially unchanged. Since this profile of high Erkp and reduced NF- κ B is consistent with anergy, this implies that anergy is particularly sensitive to small changes in catalytic activity. Also, under a range of forward and reverse ligand binding rates, our model of Erkp and NF- κ B activation displays a dependence on a power law affinity: the ratio of the forward rate to a non-unit power of the reverse rate. This dependence implies that B cells may respond to certain details of binding and unbinding rates for ligands rather than simple affinity alone.

Computational approaches to tune the activation of intracellular signal transduction pathways both predictably and selectively will enable researchers to explore and interrogate cell biology with unprecedented precision. Techniques to control complex nonlinear systems typically involve the application of control theory to a descriptive mathematical model. For cellular processes, however, measurement assays tend to be too time consuming for real-time feedback control and models offer rough approximations of the biological reality, thus limiting their utility when considered in isolation. We overcome these problems by combining nonlinear model predictive control with a novel adaptive weighting algorithm that blends predictions from multiple models to derive a compromise open-loop control sequence. The proposed strategy uses weight maps to inform the controller of the tendency for models to differ in their ability to accurately reproduce the system dynamics under different experimental perturbations (i.e. control inputs). These maps, which characterize the changing model likelihoods over the admissible control input space, are constructed using preexisting experimental data and used to produce a model-based open-loop control framework. In effect, the proposed method designs a sequence of control inputs that force the signaling dynamics along a predefined temporal response without measurement feedback while mitigating the effects of model uncertainty. We demonstrate this technique on the well-known Erk/MAPK signaling pathway in T cells. In silico assessment demonstrates that this approach successfully reduces target tracking error by 52% or better when compared with single model-based controllers and non-adaptive multiple model-based controllers. In vitro implementation of the proposed approach in Jurkat cells confirms a 63% reduction in tracking error when compared with the best of the single-model controllers. This study provides an experimentally-corroborated control methodology that utilizes the knowledge encoded within multiple mathematical models of intracellular signaling to design control inputs that effectively direct cell behavior in open-loop.

Discovery in developmental biology is often driven by intuition that relies on the integration of multiple types of data such as fluorescent images, phenotypes, and the outcomes of biochemical assays. Mathematical modeling helps elucidate the biological mechanisms at play as the networks become increasingly large and complex. However, the available data is frequently under-utilized due to incompatibility with quantitative model tuning techniques. This is the case for stem cell regulation mechanisms explored in the Drosophila germarium through fluorescent immunohistochemistry. To enable better integration of biological data with modeling in this and similar situations, we have developed a general parameter estimation process to quantitatively optimize models with qualitative data. The process employs a modified version of the Optimal Scaling method from social and behavioral sciences, and multi-objective optimization to evaluate the trade-off between fitting different datasets (e.g. wild type vs. mutant). Using only published imaging data in the germarium, we first evaluated support for a published intracellular regulatory network by considering alternative connections of the same regulatory players. Simply screening networks against wild type data identified hundreds of feasible alternatives. Of these, five parsimonious variants were found and compared by multi-objective analysis including mutant data and dynamic constraints. With these data, the current model is supported over the alternatives, but support for a biochemically observed feedback element is weak (i.e. these data do not measure the feedback effect well). When also comparing new hypothetical models, the available data do not discriminate. To begin addressing the limitations in data, we performed a model-based experiment design and provide recommendations for experiments to refine model parameters and discriminate increasingly complex hypotheses.

We address the problem of using nonlinear models to design experiments to characterize the dynamics of cellular processes by using the approach of the Maximally Informative Next Experiment (MINE), which was introduced in W. Dong et al. (PLoS ONE 3(8):e3105, 2008) and independently in M.M. Donahue et al. (IET Syst. Biol. 4:249-262, 2010). In this approach, existing data is used to define a probability distribution on the parameters; the next measurement point is the one that yields the largest model output variance with this distribution. Building upon this approach, we introduce the Expected Dynamics Estimator (EDE), which is the expected value using this distribution of the output as a function of time. We prove the consistency of this estimator (uniform convergence to true dynamics) even when the chosen experiments cluster in a finite set of points. We extend this proof of consistency to various practical assumptions on noisy data and moderate levels of model mismatch. Through the derivation and proof, we develop a relaxed version of MINE that is more computationally tractable and robust than the original formulation. The results are illustrated with numerical examples on two nonlinear ordinary differential equation models of biomolecular and cellular processes.

A computationally efficient model-based design of experiments (MBDOE) strategy is developed to plan an optimal experiment by specifying the experimental stimulation magnitudes and measurement points. The strategy is extended from previous work which optimized the experimental design over a space of measurable species and time points. We include system inputs (stimulation conditions) in the experiment design search to investigate if the addition of perturbations enhances the ability of the MBDOE method to resolve uncertainties in system dynamics. The MBDOE problem is made computationally tractable by using a sparse-grid approximation of the model output dynamics, pre-specifying the time points at which the input or experimental perturbations can be applied, and creating scenario trees to explore the endogenous uncertainty. Consecutive scenario trees are used to determine the best input magnitudes and select the optimal associated measurement species and time points. We demonstrate the effectiveness of this strategy on a T-Cell Receptor (TCR) signaling pathway model.

The hypothalamic-pituitary-adrenal (HPA) axis is critical in maintaining homeostasis under physical and psychological stress by modulating cortisol levels in the body. Dysregulation of cortisol levels is linked to numerous stress-related disorders. In this paper, an automated treatment methodology is proposed, employing a variant of nonlinear model predictive control (NMPC), called explicit MPC (EMPC). The controller is informed by an unknown input observer (UIO), which estimates various hormonal levels in the HPA axis system in conjunction with the magnitude of the stress applied on the body, based on measured concentrations of adreno-corticotropic hormones (ACTH). The proposed closed-loop control strategy is tested on multiple in silico patients and the effectiveness of the controller performance is demonstrated.

Digital compressive detection, implemented using optimized binary (OB) filters, is shown to greatly increase the speed at which Raman spectroscopy can be used to quantify the composition of liquid mixtures and to chemically image mixed solid powders. We further demonstrate that OB filters can be produced using multivariate curve resolution (MCR) to pre-process mixture training spectra, thus facilitating the quantitation of mixtures even when no pure chemical component samples are available for training.

Model-based design of experiments (MBDOE) assists in the planning of highly effective and efficient experiments. Although the foundations of this field are well-established, the application of these techniques to understand cellular processes is a fertile and rapidly advancing area as the community seeks to understand ever more complex cellular processes and systems. This review discusses the MBDOE paradigm along with applications and challenges within the context of cellular processes and systems. It also provides a brief tutorial on Fisher information matrix (FIM)-based and Bayesian experiment design methods along with an overview of existing software packages and computational advances that support MBDOE application and adoption within the Systems Biology community. As cell-based products and biologics progress into the commercial sector, it is anticipated that MBDOE will become an essential practice for design, quality control, and production., (Copyright © 2013 Wiley Periodicals, Inc.)

A key bottleneck to high-speed chemical analysis, including hyperspectral imaging and monitoring of dynamic chemical processes, is the time required to collect and analyze hyperspectral data. Here we describe, both theoretically and experimentally, a means of greatly speeding up the collection of such data using a new digital compressive detection strategy. Our results demonstrate that detecting as few as ~10 Raman scattered photons (in as little time as ~30 μs) can be sufficient to positively distinguish chemical species. This is achieved by measuring the Raman scattered light intensity transmitted through programmable binary optical filters designed to minimize the error in the chemical classification (or concentration) variables of interest. The theoretical results are implemented and validated using a digital compressive detection instrument that incorporates a 785 nm diode excitation laser, digital micromirror spatial light modulator, and photon counting photodiode detector. Samples consisting of pairs of liquids with different degrees of spectral overlap (including benzene/acetone and n-heptane/n-octane) are used to illustrate how the accuracy of the present digital compressive detection method depends on the correlation coefficients of the corresponding spectra. Comparisons of measured and predicted chemical classification score plots, as well as linear and non-linear discriminant analyses, demonstrate that this digital compressive detection strategy is Poisson photon noise limited and outperforms total least squares-based compressive detection with analog filters., (Copyright © 2012 Elsevier B.V. All rights reserved.)

Morphogens are secreted molecules that specify cell-fate organization in developing tissues. Patterns of gene expression or signalling immediately downstream of many morphogens such as the bone morphogenetic protein (BMP) decapentaplegic (Dpp) are highly reproducible and robust to perturbations. This contrasts starkly with our expectation of a noisy interpretation that would arise out of the experimentally determined low concentration (approximately picomolar) range of Dpp activity, tight receptor binding and very slow kinetic rates. To investigate mechanisms by which the intrinsic noise can be attenuated in Dpp signalling, we focus on a class of secreted proteins that bind to Dpp in the extracellular environment and play an active role in regulating Dpp/receptor interactions. We developed a stochastic model of Dpp signalling in Drosophila melanogaster and used the model to quantify the extent that stochastic fluctuations would lead to errors in spatial patterning and extended the model to investigate how a surface-associated BMP-binding protein (SBP) such as Crossveinless-2 (Cv-2) may buffer out signalling noise. In the presence of SBPs, fluctuations in the level of ligand-bound receptor can be reduced by more than twofold depending on parameter values for the intermediate transition states. Regulation of receptor-ligand interactions by SBPs may also increase the frequency of stochastic fluctuations providing a separation of timescales between high-frequency receptor equilibration and slower morphogen patterning. High-frequency noise generated by SBP regulation is easily attenuated by the intracellular network creating a system that imitates the performance of a simple low-pass filter common in audio and communication applications. Together, these data indicate that one of the benefits of receptor-ligand regulation by secreted non-receptors may be greater reliability of morphogen patterning mechanisms.

Model-based experiment design specifies the data to be collected that will most effectively characterize the biological system under study. Existing model-based design of experiment algorithms have primarily relied on Fisher Information Matrix-based methods to choose the best experiment in a sequential manner. However, these are largely local methods that require an initial estimate of the parameter values, which are often highly uncertain, particularly when data is limited. In this paper, we provide an approach to specify an informative sequence of multiple design points (parallel design) that will constrain the dynamical uncertainty of the biological system responses to within experimentally detectable limits as specified by the estimated experimental noise. The method is based upon computationally efficient sparse grids and requires only a bounded uncertain parameter space; it does not rely upon initial parameter estimates. The design sequence emerges through the use of scenario trees with experimental design points chosen to minimize the uncertainty in the predicted dynamics of the measurable responses of the system. The algorithm was illustrated herein using a T cell activation model for three problems that ranged in dimension from 2D to 19D. The results demonstrate that it is possible to extract useful information from a mathematical model where traditional model-based design of experiments approaches most certainly fail. The experiments designed via this method fully constrain the model output dynamics to within experimentally resolvable limits. The method is effective for highly uncertain biological systems characterized by deterministic mathematical models with limited data sets. Also, it is highly modular and can be modified to include a variety of methodologies such as input design and model discrimination.

Quantitative methods such as model-based predictive control are known to facilitate the design of strategies to manipulate biological systems. This study develops a sparse-grid-based adaptive model predictive control (MPC) strategy to direct HL60 cellular differentiation. Sparse-grid sampling and interpolation support a computationally efficient adaptive MPC scheme in which multiple data-consistent regions of the model parameter space are identified and used to calculate a control compromise. The algorithm is evaluated in silico with structural model mismatch. Simulations demonstrate how the multiscenario control strategy more effectively manages the mismatch compared to a single scenario approach. Furthermore, the controller is evaluated in vitro to differentiate HL60 cells in both normal and perturbed environments. The controller-derived input sequence successfully achieves and sustains the specified target level of granulocytes when implemented in the laboratory. The results and analysis given here imply that adoption of this experiment planning technique to direct cell differentiation within more complex tissue engineered constructs will require the use of a reasonably accurate mathematical model and an extension of this algorithm to multiobjective controller design., (© 2011 IEEE)

The Steady State (SS) probability distribution is an important quantity needed to characterize the steady state behavior of many stochastic biochemical networks. In this paper, we propose an efficient and accurate approach to calculating an approximate SS probability distribution from solution of the Chemical Master Equation (CME) under the assumption of the existence of a unique deterministic SS of the system. To find the approximate solution to the CME, a truncated state-space representation is used to reduce the state-space of the system and translate it to a finite dimension. The subsequent ill-posed eigenvalue problem of a linear system for the finite state-space can be converted to a well-posed system of linear equations and solved. The proposed strategy yields efficient and accurate estimation of noise in stochastic biochemical systems. To demonstrate the approach, we applied the method to characterize the noise behavior of a set of biochemical networks of ligand-receptor interactions for Bone Morphogenetic Protein (BMP) signaling. We found that recruitment of type II receptors during the receptor oligomerization by itself doesn't not tend to lower noise in receptor signaling, but regulation by a secreted co-factor may provide a substantial improvement in signaling relative to noise. The steady state probability approximation method shortened the time necessary to calculate the probability distributions compared to earlier approaches, such as Gillespie's Stochastic Simulation Algorithm (SSA) while maintaining high accuracy.

Mitochondrial permeability transition (MPT) is a highly regulated complex phenomenon that is a type of ischemia/reperfusion injury that can lead to cell death and ultimately organ dysfunction. A novel population transition and detailed permeability transition pore regulation model were integrated with an existing bioenergetics model to describe MPT induction under a variety of conditions. The framework of the MPT induction model includes the potential states of the mitochondria (aggregated, orthodox and post-transition), their transitions from one state to another as well as their interaction with the extra-mitochondrial environment. The model encodes the three basic necessary conditions for MPT: a high calcium load, alkaline matrix pH and circumstances which favor de-energization. The MPT induction model was able to reproduce the expected bioenergetic trends observed in a population of mitochondria subjected to conditions that favor MPT. The model was corroborated and used to predict that MPT in an acidic environment is mitigated by an increase in activity of the mitochondrial potassium/hydrogen exchanger. The model was also used to present the beneficial impact of reducing the duration mitochondria spend in the orthodox state on preserving the extra-mitochondrial ATP levels. The model serves as a tool for investigators to use to understand the MPT induction phenomenon, explore alternative hypotheses for PTP regulation, as well as identify endogenous pharmacological targets and evaluate potential therapeutics for MPT mitigation., (Copyright (c) 2010 Elsevier Ltd. All rights reserved.)

The sparse grid-based experiment design algorithm sequentially selects an experimental design point to discriminate between hypotheses for given experimental conditions. Sparse grids efficiently screen the global uncertain parameter space to identify acceptable parameter subspaces. Clustering the located acceptable parameter vectors by the similarity of the simulated model trajectories characterises the data-compatible model dynamics. The experiment design algorithm capitalizes on the diversity of the experimentally distinguishable system output dynamics to select the design point that best discerns between competing model-structure and parameter-encoded hypotheses. As opposed to designing the experiments to explicitly reduce uncertainty in the model parameters, this approach selects design points to differentiate between dynamical behaviours. This approach further differs from other experimental design methods in that it simultaneously addresses both parameter- and structural-based uncertainty that is applicable to some ill-posed problems where the number of uncertain parameters exceeds the amount of data, places very few requirements on the model type, available data and a priori parameter estimates, and is performed over the global uncertain parameter space. The experiment design algorithm is demonstrated on a mitogen-activated protein kinase cascade model. The results show that system dynamics are highly uncertain with limited experimental data. Nevertheless, the algorithm requires only three additional experimental data points to simultaneously discriminate between possible model structures and acceptable parameter values. This sparse grid-based experiment design process provides a systematic and computationally efficient exploration over the entire uncertain parameter space of potential model structures to resolve the uncertainty in the non-linear systems biology model dynamics.

Mathematical models of mitochondrial bioenergetics provide powerful analytical tools to help interpret experimental data and facilitate experimental design for elucidating the supporting biochemical and physical processes. As a next step towards constructing a complete physiologically faithful mitochondrial bioenergetics model, a mathematical model was developed targeting the cardiac mitochondrial bioenergetic based upon previous efforts, and corroborated using both transient and steady state data. The model consists of several modified rate functions of mitochondrial bioenergetics, integrated calcium dynamics and a detailed description of the K(+)-cycle and its effect on mitochondrial bioenergetics and matrix volume regulation. Model simulations were used to fit 42 adjustable parameters to four independent experimental data sets consisting of 32 data curves. During the model development, a certain network topology had to be in place and some assumptions about uncertain or unobserved experimental factors and conditions were explicitly constrained in order to faithfully reproduce all the data sets. These realizations are discussed, and their necessity helps contribute to the collective understanding of the mitochondrial bioenergetics.

Determining the effect of a compound on I (Kr) is a standard screen for drug safety. Often the effect is described using a single IC(50) value, which is unable to capture complex effects of a drug. Using verapamil as an example, we present a method for using recordings from native myocytes at several drug doses along with qualitative features of I (Kr) from published studies of HERG current to estimate parameters in a mathematical model of the drug effect on I (Kr). I (Kr) was recorded from canine left ventricular myocytes using ruptured patch techniques. A voltage command protocol was used to record tail currents at voltages from -70 to -20 mV, following activating pulses over a wide range of voltages and pulse durations. Model equations were taken from a published I (Kr) Markov model and the drug was modeled as binding to the open state. Parameters were estimated using a combined global and local optimization algorithm based on collected data with two additional constraints on I (Kr) I-V relation and I (Kr) inactivation. The method produced models that quantitatively reproduce both the control I (Kr) kinetics and dose dependent changes in the current. In addition, the model exhibited use and rate dependence. The results suggest that: (1) the technique proposed here has the practical potential to develop data-driven models that quantitatively reproduce channel behavior in native myocytes; (2) the method can capture important drug effects that cannot be reproduced by the IC(50) method. Although the method was developed for I (Kr), the same strategy can be applied to other ion channels, once appropriate channel-specific voltage protocols and qualitative features are identified.

Electrophysiological studies often seek to relate changes in ion current properties caused by a chemical modifier to changes in cellular properties. Therefore, quantifying concentration-dependent effects of modifiers on ion currents is a topic of importance. In this paper, we sought a mathematical method for using ion current data to predict the effect of several theoretical ion current modifiers on cellular and tissue properties that is computationally efficient without compromising predictive power. We focused on the K+ current I(K,r) as an example case due to its link to long QT syndrome and arrhythmias, but these methods should be generally applicable to other electrophysiological studies. We compared predictions using a Markov model with mass action binding of the modifiers to specific conformational states of the channel to predictions generated by two simplified models. We investigated scaling I(K,r) conductance, and found that although this method produced predictions that agreed qualitatively with the more complicated model, it did not generate quantitatively consistent predictions for all modifiers tested. Our simulations showed that a more computationally efficient Hodgkin-Huxley model that incorporates the effect of modifiers through functional changes in the current produced quantitatively consistent predictions of concentration-dependent changes in cell and tissue properties for all modifiers tested.