Sequential identification of boundary support parameters in a fluid-structure vascular model using patient image data

Viscoelastic support has been previously established as a valuable modeling ingredient to represent the effect of surrounding tissues and organs in a fluid-structure vascular model. In this paper, we propose a complete methodological chain for the identification of the corresponding boundary support parameters, using patient image data. We consider distance maps of model to image contours as the discrepancy driving the data assimilation approach, which then relies on a combination of (1) state estimation based on the so-called SDF filtering method, designed within the realm of Luenberger observers and well adapted to handling measurements provided by image sequences, and (2) parameter estimation based on a reduced-order UKF filtering method which has no need for tangent operator computations and features natural parallelism to a high degree. Implementation issues are discussed, and we show that the resulting computational effectiveness of the complete estimation chain is comparable to that of a direct simulation. Furthermore, we demonstrate the use of this framework in a realistic application case involving hemodynamics in the thoracic aorta. The estimation of the boundary support parameters proves successful, in particular in that direct modeling simulations based on the estimated parameters are more accurate than with a previous manual expert calibration. This paves the way for complete patient-specific fluid-structure vascular modeling in which all types of available measurements could be used to estimate additional uncertain parameters of biophysical and clinical relevance.     

Dynamical estimation of neuron and network properties I: variational methods

We present a method for using measurements of membrane voltage in individual neurons to estimate the parameters and states of the voltage-gated ion channels underlying the dynamics of the neuron's behavior. Short injections of a complex time-varying current provide sufficient data to determine the reversal potentials, maximal conductances, and kinetic parameters of a diverse range of channels, representing tens of unknown parameters and many gating variables in a model of the neuron's behavior. These estimates are used to predict the response of the model at times beyond the observation window. This method of [Formula: see text] extends to the general problem of determining model parameters and unobserved state variables from a sparse set of observations, and may be applicable to networks of neurons. We describe an exact formulation of the tasks in nonlinear data assimilation when one has noisy data, errors in the models, and incomplete information about the state of the system when observations commence. This is a high dimensional integral along the path of the model state through the observation window. In this article, a stationary path approximation to this integral, using a variational method, is described and tested employing data generated using neuronal models comprising several common channels with Hodgkin-Huxley dynamics. These numerical experiments reveal a number of practical considerations in designing stimulus currents and in determining model consistency. The tools explored here are computationally efficient and have paths to parallelization that should allow large individual neuron and network problems to be addressed.     

Symbolic-numeric estimation of parameters in biochemical models by quantifier elimination

The sequencing of complete genomes allows analyses of the interactions between various biological molecules on a genomic scale, which prompted us to simulate the global behaviors of biological phenomena on the molecular level. One of the basic mathematical problems in the simulation is the parameter optimization in the kinetic model for complex dynamics, and many estimation methods have been designed. We introduce a new approach to estimate the parameters in biological kinetic models by quantifier elimination (QE), in combination with numerical simulation methods. The estimation method was applied to a model for the inhibition kinetics of HIV proteinase with ten parameters and nine variables, and attained the goodness of fit to 300 points of observed data with the same magnitude as that obtained by the previous estimation methods, remarkably by using only one or two points of data. Furthermore, the utilization of QE demonstrated the feasibility of the present method for elucidating the behavior of the parameters and the variables in the analyzed model. Therefore, the present symbolic-numeric method is a powerful approach to reveal the fundamental mechanisms of kinetic models, in addition to being a computational engine.     

Semiparametric frailty models for clustered failure time data

We consider frailty models with additive semiparametric covariate effects for clustered failure time data. We propose a doubly penalized partial likelihood (DPPL) procedure to estimate the nonparametric functions using smoothing splines. We show that the DPPL estimators could be obtained from fitting an augmented working frailty model with parametric covariate effects, whereas the nonparametric functions being estimated as linear combinations of fixed and random effects, and the smoothing parameters being estimated as extra variance components. This approach allows us to conveniently estimate all model components within a unified frailty model framework. We evaluate the finite sample performance of the proposed method via a simulation study, and apply the method to analyze data from a study of sexually transmitted infections (STI).     

A hybrid model framework for the optimization of preparative chromatographic processes

An optimization framework based on the use of hybrid models is presented for preparative chromatographic processes. The first step in the hybrid model strategy involves the experimental determination of the parameters of the physical model, which consists of the full general rate model coupled with the kinetic form of the steric mass action isotherm. These parameters are then used to carry out a set of simulations with the physical model to obtain data on the functional relationship between various objective functions and decision variables. The resulting data is then used to estimate the parameters for neural-network-based empirical models. These empirical models are developed in order to enable the exploration of a wide variety of different design scenarios without any additional computational requirements. The resulting empirical models are then used with a sequential quadratic programming optimization algorithm to maximize the objective function, production rate times yield (in the presence of solubility and purity constraints), for binary and tertiary model protein systems. The use of hybrid empirical models to represent complex preparative chromatographic systems significantly reduces the computational time required for simulation and optimization. In addition, it allows both multivariable optimization and rapid exploration of different scenarios for optimal design.     

Computational inference and experimental validation of the nitrogen assimilation regulatory network in cyanobacterium Synechococcus sp. WH 8102

Deciphering the regulatory networks encoded in the genome of an organism represents one of the most interesting and challenging tasks in the post-genome sequencing era. As an example of this problem, we have predicted a detailed model for the nitrogen assimilation network in cyanobacterium Synechococcus sp. WH 8102 (WH8102) using a computational protocol based on comparative genomics analysis and mining experimental data from related organisms that are relatively well studied. This computational model is in excellent agreement with the microarray gene expression data collected under ammonium-rich versus nitrate-rich growth conditions, suggesting that our computational protocol is capable of predicting biological pathways/networks with high accuracy. We then refined the computational model using the microarray data, and proposed a new model for the nitrogen assimilation network in WH8102. An intriguing discovery from this study is that nitrogen assimilation affects the expression of many genes involved in photosynthesis, suggesting a tight coordination between nitrogen assimilation and photosynthesis processes. Moreover, for some of these genes, this coordination is probably mediated by NtcA through the canonical NtcA promoters in their regulatory regions.     

A probabilistic methodology for integrating knowledge and experiments on biological networks.

Biological systems are traditionally studied by focusing on a specific subsystem, building an intuitive model for it, and refining the model using results from carefully designed experiments. Modern experimental techniques provide massive data on the global behavior of biological systems, and systematically using these large datasets for refining existing knowledge is a major challenge. Here we introduce an extended computational framework that combines formalization of existing qualitative models, probabilistic modeling, and integration of high-throughput experimental data. Using our methods, it is possible to interpret genomewide measurements in the context of prior knowledge on the system, to assign statistical meaning to the accuracy of such knowledge, and to learn refined models with improved fit to the experiments. Our model is represented as a probabilistic factor graph, and the framework accommodates partial measurements of diverse biological elements. We study the performance of several probabilistic inference algorithms and show that hidden model variables can be reliably inferred even in the presence of feedback loops and complex logic. We show how to refine prior knowledge on combinatorial regulatory relations using hypothesis testing and derive p-values for learned model features. We test our methodology and algorithms on a simulated model and on two real yeast models. In particular, we use our method to explore uncharacterized relations among regulators in the yeast response to hyper-osmotic shock and in the yeast lysine biosynthesis system. Our integrative approach to the analysis of biological regulation is demonstrated to synergistically combine qualitative and quantitative evidence into concrete biological predictions.     

Practical limits for reverse engineering of dynamical systems: a statistical analysis of sensitivity and parameter inferability in systems biology models

The size and complexity of cellular systems make building predictive models an extremely difficult task. In principle dynamical time-course data can be used to elucidate the structure of the underlying molecular mechanisms, but a central and recurring problem is that many and very different models can be fitted to experimental data, especially when the latter are limited and subject to noise. Even given a model, estimating its parameters remains challenging in real-world systems. Here we present a comprehensive analysis of 180 systems biology models, which allows us to classify the parameters with respect to their contribution to the overall dynamical behaviour of the different systems. Our results reveal candidate elements of control in biochemical pathways that differentially contribute to dynamics. We introduce sensitivity profiles that concisely characterize parameter sensitivity and demonstrate how this can be connected to variability in data. Systematically linking data and model sloppiness allows us to extract features of dynamical systems that determine how well parameters can be estimated from time-course measurements, and associates the extent of data required for parameter inference with the model structure, and also with the global dynamical state of the system. The comprehensive analysis of so many systems biology models reaffirms the inability to estimate precisely most model or kinetic parameters as a generic feature of dynamical systems, and provides safe guidelines for performing better inferences and model predictions in the context of reverse engineering of mathematical models for biological systems.     

Global gene expression profiling in Escherichia coli K12. The effects of leucine-responsive regulatory protein

Leucine-responsive regulatory protein (Lrp) is a global regulatory protein that affects the expression of multiple genes and operons in bacteria. Although the physiological purpose of Lrp-mediated gene regulation remains unclear, it has been suggested that it functions to coordinate cellular metabolism with the nutritional state of the environment. The results of gene expression profiles between otherwise isogenic lrp(+) and lrp(-) strains of Escherichia coli support this suggestion. The newly discovered Lrp-regulated genes reported here are involved either in small molecule or macromolecule synthesis or degradation, or in small molecule transport and environmental stress responses. Although many of these regulatory effects are direct, others are indirect consequences of Lrp-mediated changes in the expression levels of other global regulatory proteins. Because computational methods to analyze and interpret high dimensional DNA microarray data are still an early stage, much of the emphasis of this work is directed toward the development of methods to identify differentially expressed genes with a high level of confidence. In particular, we describe a Bayesian statistical framework for a posterior estimate of the standard deviation of gene measurements based on a limited number of replications. We also describe an algorithm to compute a posterior estimate of differential expression for each gene based on the experiment-wide global false positive and false negative level for a DNA microarray data set. This allows the experimenter to compute posterior probabilities of differential expression for each individual differential gene expression measurement.     

A method for solution of the multi-objective inverse problems under uncertainty

We describe a method to solve multi-objective inverse problems under uncertainty. The method was tested on non-linear models of dynamic series and population dynamics, as well as on the spatiotemporal model of gene expression in terms of non-linear differential equations. We consider how to identify model parameters when experimental data contain additive noise and measurements are performed in discrete time points. We formulate the multi-objective problem of optimization under uncertainty. In addition to a criterion of least squares difference we applied a criterion which is based on the integral of trajectories of the system spatiotemporal dynamics, as well as a heuristic criterion CHAOS based on the decision tree method. The optimization problem is formulated using a fuzzy statement and is constrained by penalty functions based on the normalized membership functions of a fuzzy set of model solutions. This allows us to reconstruct the expression pattern of hairy gene in Drosophila even-skipped mutants that is in good agreement with experimental data. The reproducibility of obtained results is confirmed by solution of inverse problems using different global optimization methods with heuristic strategies.     

SPINE: a framework for signaling-regulatory pathway inference from cause-effect experiments

MOTIVATION: The complex program of gene expression allows the cell to cope with changing genetic, developmental and environmental conditions. The accumulating large-scale measurements of gene knockout effects and molecular interactions allow us to begin to uncover regulatory and signaling pathways within the cell that connect causal to affected genes on a network of physical interactions. RESULTS: We present a novel framework, SPINE, for Signaling-regulatory Pathway INferencE. The framework aims at explaining gene expression experiments in which a gene is knocked out and as a result multiple genes change their expression levels. To this end, an integrated network of protein-protein and protein-DNA interactions is constructed, and signaling pathways connecting the causal gene to the affected genes are searched for in this network. The reconstruction problem is translated into that of assigning an activation/repression attribute with each protein so as to explain (in expectation) a maximum number of the knockout effects observed. We provide an integer programming formulation for the latter problem and solve it using a commercial solver. We validate the method by applying it to a yeast subnetwork that is involved in mating. In cross-validation tests, SPINE obtains very high accuracy in predicting knockout effects (99%). Next, we apply SPINE to the entire yeast network to predict protein effects and reconstruct signaling and regulatory pathways. Overall, we are able to infer 861 paths with confidence and assign effects to 183 genes. The predicted effects are found to be in high agreement with current biological knowledge. AVAILABILITY: The algorithm and data are available at http://cs.tau.ac.il/~roded/SPINE.html.     

Capillary Filling at the Microscale: Control of Fluid Front Using Geometry

We propose an experimental and theoretical framework for the study of capillary filling at the micro-scale. Our methodology enables us to control the fluid flow regime so that we can characterise properties of Newtonian fluids such as their viscosity. In particular, we study a viscous, non-inertial, non-Washburn regime in which the position of the fluid front increases linearly with time for the whole duration of the experiment. The operating shear-rate range of our apparatus extends over nearly two orders of magnitude. Further, we analyse the advancement of a fluid front within a microcapillary in a system of two immiscible Newtonian liquids. We observe a non-Washburn regime in which the front can accelerate or decelerate depending on the viscosity contrast between the two liquids. We then propose a theoretical model which enables us to study and explain both non-Washburn regimes. Furthermore, our theoretical model allows us to put forward ways to control the emergence of these regimes by means of geometrical parameters of the experimental set-up. Our methodology allows us to design and calibrate a micro-viscosimetre which works at constant pressure.     

Point-estimating observer models for latent cause detection

The spatial distribution of visual items allows us to infer the presence of latent causes in the world. For instance, a spatial cluster of ants allows us to infer the presence of a common food source. However, optimal inference requires the integration of a computationally intractable number of world states in real world situations. For example, optimal inference about whether a common cause exists based on N spatially distributed visual items requires marginalizing over both the location of the latent cause and 2^N possible affiliation patterns (where each item may be affiliated or non-affiliated with the latent cause). How might the brain approximate this inference? We show that subject behaviour deviates qualitatively from Bayes-optimal, in particular showing an unexpected positive effect of N (the number of visual items) on the false-alarm rate. We propose several “point-estimating” observer models that fit subject behaviour better than the Bayesian model. They each avoid a costly computational marginalization over at least one of the variables of the generative model by “committing” to a point estimate of at least one of the two generative model variables. These findings suggest that the brain may implement partially committal variants of Bayesian models when detecting latent causes based on complex real world data.     

Inferring the diameter of a biopolymer from its stretching response

We investigate the stretching response of a thick polymer model by means of extensive stochastic simulations. The computational results are synthesized in an analytic expression that characterizes how the force versus elongation curve depends on the polymer structural parameters: its thickness and granularity (spacing of the monomers). The expression is used to analyze experimental data for the stretching of various different types of biopolymers: polypeptides, polysaccharides, and nucleic acids. Besides recovering elastic parameters (such as the persistence length) that are consistent with those obtained from standard entropic models, the approach allows us to extract viable estimates for the polymers diameter and granularity. This shows that the basic structural polymer features have such a profound impact on the elastic behavior that they can be recovered with the sole input of stretching measurements.