Experimentally validated microstructural 3D constitutive model of coronary arterial media

Accurate modeling of arterial response to physiological or pathological loads may shed light on the processes leading to initiation and progression of a number of vascular diseases and may serve as a tool for prediction and diagnosis. In this study, a microstructure based hyperelastic constitutive model is developed for passive media of porcine coronary arteries. The most general model contains 12 independent parameters representing the three-dimensional inner fibrous structure of the media and includes the effects of residual stresses and osmotic swelling. Parameter estimation and model validation were based on mechanical data of porcine left anterior descending (LAD) media under radial inflation, axial extension, and twist tests. The results show that a reduced four parameter model is sufficient to reliably predict the passive mechanical properties. These parameters represent the stiffness and the helical orientation of each lamellae fiber and the stiffness of the interlamellar struts interconnecting these lamellae. Other structural features, such as orientational distribution of helical fibers and anisotropy of the interlamellar network, as well as possible transmural distribution of structural features, were found to have little effect on the global media mechanical response. It is shown that the model provides good predictions of the LAD media twist response based on parameters estimated from only biaxial tests of inflation and extension. In addition, good predictive capabilities are demonstrated for the model behavior at high axial stretch ratio based on data of law stretches.     

PconsFam: An Interactive Database of Structure Predictions of Pfam Families

At present, about half of the protein domain families lack a structural representative. However, in the last decade, predicting contact maps and using these to model the tertiary structure for these protein families have become an alternative approach to gain structural insight. At present, reliable models for several hundreds of protein families have been created using this approach. To increase the use of this approach, we present PconsFam, which is an intuitive and interactive database for predicted contact maps and tertiary structure models of the entire Pfam database. By modeling all possible families, both with and without a representative structure, using the PconsFold2 pipeline, and running quality assessment estimator on the models, we predict an estimation for how confident the contact maps and structures are for each family.     

Comparison of four modeling tools for the prediction of potential distribution for non-indigenous weeds in the United States

This study compares four models for predicting the potential distribution of non-indigenous weed species in the conterminous U.S. The comparison focused on evaluating modeling tools and protocols as currently used for weed risk assessment or for predicting the potential distribution of invasive weeds. We used six weed species (three highly invasive and three less invasive non-indigenous species) that have been established in the U.S. for more than 75 years. The experiment involved providing non-U. S. location data to users familiar with one of the four evaluated techniques, who then developed predictive models that were applied to the United States without knowing the identity of the species or its U.S. distribution. We compared a simple GIS climate matching technique known as Proto3, a simple climate matching tool CLIMEX Match Climates, the correlative model MaxEnt, and a process model known as the Thornley Transport Resistance (TTR) model. Two experienced users ran each modeling tool except TTR, which had one user. Models were trained with global species distribution data excluding any U.S. data, and then were evaluated using the current known U.S. distribution. The influence of weed species identity and modeling tool on prevalence and sensitivity effects was compared using a generalized linear mixed model. Each modeling tool itself had a low statistical significance, while weed species alone accounted for 69.1 and 48.5% of the variance for prevalence and sensitivity, respectively. These results suggest that simple modeling tools might perform as well as complex ones in the case of predicting potential distribution for a weed not yet present in the United States. Considerations of model accuracy should also be balanced with those of reproducibility and ease of use. More important than the choice of modeling tool is the construction of robust protocols and testing both new and experienced users under blind test conditions that approximate operational conditions.     

Experimental evaluation of the Liu–Beveridge dinucleotide step model of DNA structure

Methods for predicting DNA curvature have many possible applications. Dinucleotide step models describe DNA shape by characterization of helical twist, deflection angles and the direction of deflection for nearest neighbor base pairs. Liu and Beveridge have extended previous applications of dinucleotide step models with the development and qualitative validation of a predictive method for sequence-dependent DNA curvature (the LB model). We tested whether the LB model accurately predicts experimentally deduced curvature angles and helical repeat parameters for DNA sequences not in its training set, particularly when challenged with quantitative data and subtle sequence phasings. We examined a series of 17 well-characterized DNA sequences to compare electrophoretic and computational results. The LB model is superior to two other models in the prediction of helical repeat parameters. We observed a strong linear correlation between curvature magnitudes predicted using the LB model and those determined by electrophoretic ligation ladder experiments, although the LB model somewhat underestimated apparent curvature. With longer electrophoretic phasing probes the LB model slightly overestimated gel mobility anomalies, with modest deviations in predicted helical repeat parameters. Overall, our analyses suggest that the LB model provides reasonably accurate predictions for the electrophoretic behavior of DNA.     

Mathematical modeling and optimization of cellulase protein production using Trichoderma reesei RL-P37

The enzyme cellulase, a multienzyme complex made up of several proteins, catalyzes the conversion of cellulose to glucose in an enzymatic hydrolysis-based biomass-to-ethanol process. Production of cellulase enzyme proteins in large quantities using the fungus Trichoderma reesei requires understanding the dynamics of growth and enzyme production. The method of neural network parameter function modeling, which combines the approximation capabilities of neural networks with fundamental process knowledge, is utilized to develop a mathematical model of this dynamic system. In addition, kinetic models are also developed. Laboratory data from bench-scale fermentations involving growth and protein production by T. reesei on lactose and xylose are used to estimate the parameters in these models. The relative performances of the various models and the results of optimizing these models on two different performance measures are presented. An approximately 33% lower root-mean-squared error (RMSE) in protein predictions and about 40% lower total RMSE is obtained with the neural network-based model as opposed to kinetic models. Using the neural network-based model, the RMSE in predicting optimal conditions for two performance indices, is about 67% and 40% lower, respectively, when compared with the kinetic models. Thus, both model predictions and optimization results from the neural network-based model are found to be closer to the experimental data than the kinetic models developed in this work. It is shown that the neural network parameter function modeling method can be useful as a "macromodeling" technique to rapidly develop dynamic models of a process.     

Parameter Estimation of Some Epidemic Models. The Case of Recurrent Epidemics Caused by Respiratory Syncytial Virus

The research presented in this paper addresses the problem of fitting a mathematical model to epidemic data. We propose an implementation of the Landweber iteration to solve locally the arising parameter estimation problem. The epidemic models considered consist of suitable systems of ordinary differential equations. The results presented suggest that the inverse problem approach is a reliable method to solve the fitting problem. The predictive capabilities of this approach are demonstrated by comparing simulations based on estimation of parameters against real data sets for the case of recurrent epidemics caused by the respiratory syncytial virus in children.     

A Bayesian nonparametric model for zero‐inflated outcomes: Prediction,clustering, and causal estimation

Researchers are often interested in predicting outcomes, detecting distinct subgroups of their data, or estimating causal treatment effects. Pathological data distributions that exhibit skewness and zero‐inflation complicate these tasks—requiring highly flexible, data‐adaptive modeling. In this paper, we present a multipurpose Bayesian nonparametric model for continuous, zero‐inflated outcomes that simultaneously predicts structural zeros, captures skewness, and clusters patients with similar joint data distributions. The flexibility of our approach yields predictions that capture the joint data distribution better than commonly used zero‐inflated methods. Moreover, we demonstrate that our model can be coherently incorporated into a standardization procedure for computing causal effect estimates that are robust to such data pathologies. Uncertainty at all levels of this model flow through to the causal effect estimates of interest—allowing easy point estimation, interval estimation, and posterior predictive checks verifying positivity, a required causal identification assumption. Our simulation results show point estimates to have low bias and interval estimates to have close to nominal coverage under complicated data settings. Under simpler settings, these results hold while incurring lower efficiency loss than comparator methods. We use our proposed method to analyze zero‐inflated inpatient medical costs among endometrial cancer patients receiving either chemotherapy or radiation therapy in the SEER‐Medicare database.     

Structural sensitivity of biological models revisited

Enhancing the predictive power of models in biology is a challenging issue. Among the major difficulties impeding model development and implementation are the sensitivity of outcomes to variations in model parameters, the problem of choosing of particular expressions for the parametrization of functional relations, and difficulties in validating models using laboratory data and/or field observations. In this paper, we revisit the phenomenon which is referred to as structural sensitivity of a model. Structural sensitivity arises as a result of the interplay between sensitivity of model outcomes to variations in parameters and sensitivity to the choice of model functions, and this can be somewhat of a bottleneck in improving the models predictive power. We provide a rigorous definition of structural sensitivity and we show how we can quantify the degree of sensitivity of a model based on the Hausdorff distance concept. We propose a simple semi-analytical test of structural sensitivity in an ODE modeling framework. Furthermore, we emphasize the importance of directly linking the variability of field/experimental data and model predictions, and we demonstrate a way of assessing the robustness of modeling predictions with respect to data sampling variability. As an insightful illustrative example, we test our sensitivity analysis methods on a chemostat predator-prey model, where we use laboratory data on the feeding of protozoa to parameterize the predator functional response.     

Mathematical and kinetic modeling of biofilm reactor based on ant colony optimization

Inverse estimation of model parameters via mathematical modeling route, known as inverse modeling (IM), is an attractive alternative approach to the experimental methods. This approach makes use of efficient optimization techniques in the course of solution of an inverse problem with the aid of measured data. In this study, a novel optimization method based on ant colony optimization (ACO), denoted by ACO-IM, is presented for inverse estimation of kinetic and film thickness parameters of biofilm models that describe an experimental fixed bed anaerobic reactor. The proposed optimization method for parameter estimation emulates the fact that ants are capable of finding the shortest path from a food source to their nest by depositing a trial of pheromone during their walk. The efficacy of the ACO-IM for numerical estimation of bio-kinetic parameters is demonstrated through its application for the anaerobic treatment of industry wastewater in a fixed bed biofilm process. The results explain the rigorousness of mathematical models, the form of kinetic and film thickness models and the type of packing to be used with the biofilm process for accurate determination of kinetic and film thickness parameters so as to ensure reliable predictive performance of the biofilm reactor models.     

An application of Lacker's mathematical model for the prediction of ovarian response to superstimulation

Introduction. A mathematical model of ovarian follicular growth is applied to the problem of predicting ovarian response in a superstimulation protocol. Methods. Fifty-four women enrolled in an ovarian superstimulation program of therapy for the amelioration of idiopathic infertility had their ovarian cycles synchronized by taking Demulen 30 for two weeks prior to the study. Daily ultrasonographic imaging, measurements of serum estradiol and doses of hMG began on day 5 after the patients stopped taking Demulen. The diameters of individual follicles were measured and followed daily. When the largest follicle attained a diameter of 19 mm, hCG was given to induce ovulation. Individual follicle growth data were fit to a mathematical model of ovarian follicle maturation and the resulting parameters were used to classify patients into low and high ovarian response groups. Results. The parameters computed from the mathematical model fit were found to be predictive of ovarian response with a sensitivity of 71% and a specificity of 70%. The parameters were also meaningful within the context of the original mathematical model and have value for determining how doses of hMG may be adjusted during the course therapy to increase the ovarian response in individuals. Conclusion. Mathematical modeling of ultrasonographically derived follicular growth data has significant potential for clinical application in ovarian superstimulation protocols. The method of fitting follicular growth data to a mathematical follicle maturation surface furthermore provides a straightforward approach for the characterization of ovarian follicular dynamics in general.     

Predicting 3D structures of transient protein-protein complexes by homology

The paper reports a homology based approach for predicting the 3D structures of full length hetero protein complexes. We have created a database of templates that includes structures of hetero protein-protein complexes as well as domain-domain structures (), which allowed us to expand the template pool up to 418 two-chain entries (at 40% sequence identity). Two protocols were tested-a protocol based on position specific Blast search (Protocol-I) and a protocol based on structural similarity of monomers (Protocol-II). All possible combinations of two monomers (350,284 pairs) in the ProtCom database were subjected to both protocols to predict if they form complexes. The predictions were benchmarked against the ProtCom database resulting to false-true positives ratios of approximately 5:1 and approximately 7:1 and recovery of 19% and 86%, respectively for protocols I and II. From 350,284 trials Protocol-I made only approximately 500 wrong predictions resulting to 0.5% error. In addition, though it was shown that artificially created domain-domain structures can in principle be good templates for modeling full length protein complexes, more sensitive methods are needed to detect homology relations. The quality of the models was assessed using two different criteria such as interfacial residues and overall RMSD. It was found that there is no correlation between these two measures. In many cases the interface residues were predicted correctly, but the overall RMSD was over 6 A and vice versa.     

Modeling natural attenuation of benzene with analytical and numerical models

Natural attenuation of benzene is a much-accepted technology for remediating low risk sites. To date, numerous protocols have been developed for assessing natural attenuation and measuring indicator parameters. Many models have additionally been developed to describe the advection, dispersion, sorption and biodegradation processes involved. It is evident that while there is extensive guidance in natural attenuation protocols for field sampling methodologies, less emphasis is placed on analyzing natural attenuation data for supporting appropriate model development. This paper presents methodologies for data analysis and interpretation that may be undertaken to achieve data reduction for modeling purposes. A case study is presented to illustrate the use of an analytical and a numerical natural attenuation model at the same site for predicting the time required to achieve the remedial goal at the site.This paper was originally intended for the Special Issue on Natural Attenuation Volume I published in Biodegradation 15(6), 2004.     

Predicting human chronically paralyzed muscle force: a comparison of three mathematical models.

Chronic spinal cord injury (SCI) induces detrimental musculoskeletal adaptations that adversely affect health status, ranging from muscle paralysis and skin ulcerations to osteoporosis. SCI rehabilitative efforts may increasingly focus on preserving the integrity of paralyzed extremities to maximize health quality using electrical stimulation for isometric training and/or functional activities. Subject-specific mathematical muscle models could prove valuable for predicting the forces necessary to achieve therapeutic loading conditions in individuals with paralyzed limbs. Although numerous muscle models are available, three modeling approaches were chosen that can accommodate a variety of stimulation input patterns. To our knowledge, no direct comparisons between models using paralyzed muscle have been reported. The three models include 1) a simple second-order linear model with three parameters and 2) two six-parameter nonlinear models (a second-order nonlinear model and a Hill-derived nonlinear model). Soleus muscle forces from four individuals with complete, chronic SCI were used to optimize each model's parameters (using an increasing and decreasing frequency ramp) and to assess the models' predictive accuracies for constant and variable (doublet) stimulation trains at 5, 10, and 20 Hz in each individual. Despite the large differences in modeling approaches, the mean predicted force errors differed only moderately (8-15% error; P=0.0042), suggesting physiological force can be adequately represented by multiple mathematical constructs. The two nonlinear models predicted specific force characteristics better than the linear model in nearly all stimulation conditions, with minimal differences between the two nonlinear models. Either nonlinear mathematical model can provide reasonable force estimates; individual application needs may dictate the preferred modeling strategy.     

Comparative modeling of the conformational stability of chymotrypsin inhibitor 2 protein mutants using amino acid sequence autocorrelation (AASA) and amino acid 3D autocorrelation (AA3DA) vectors and ensembles of Bayesian-regularized genetic neural networks

Predicting protein stability changes upon point mutation is important for understanding protein structure and designing new proteins. Autocorrelation vector formalism was extended to amino acid sequences and 3D conformations for encoding protein structural information with modeling purpose. Protein autocorrelation vectors were weighted by 48 amino acid/residue properties selected from the AAindex database. Ensembles of Bayesian-regularized genetic neural networks (BRGNNs) trained with amino acid sequence autocorrelation (AASA) vectors and amino acid 3D autocorrelation (AA3DA) vectors yielded predictive models of the change of unfolding Gibbs free energy change (ΔΔG) of chymotrypsin Inhibitor 2 protein mutants. The ensemble predictor described about 58 and 72% of the data variances in test sets for AASA and AA3DA models, respectively. Optimum sequence and 3D-based ensembles exhibit high effects on relevant structural (volume, solvent-accessible surface area), physico-chemical (hydrophilicity/hydrophobicity-related) and thermodynamic (hydration parameters) properties.     

Cross‐scale predictive modeling of CHO cell culture growth and metabolites using Raman spectroscopy and multivariate analysis

Multi‐component, multi‐scale Raman spectroscopy modeling results from a monoclonal antibody producing CHO cell culture process including data from two development scales (3 L, 200 L) and a clinical manufacturing scale environment (2,000 L) are presented. Multivariate analysis principles are a critical component to partial least squares (PLS) modeling but can quickly turn into an overly iterative process, thus a simplified protocol is proposed for addressing necessary steps including spectral preprocessing, spectral region selection, and outlier removal to create models exclusively from cell culture process data without the inclusion of spectral data from chemically defined nutrient solutions or targeted component spiking studies. An array of single‐scale and combination‐scale modeling iterations were generated to evaluate technology capabilities and model scalability. Analysis of prediction errors across models suggests that glucose, lactate, and osmolality are well modeled. Model strength was confirmed via predictive validation and by examining performance similarity across single‐scale and combination‐scale models. Additionally, accurate predictive models were attained in most cases for viable cell density and total cell density; however, these components exhibited some scale‐dependencies that hindered model quality in cross‐scale predictions where only development data was used in calibration. Glutamate and ammonium models were also able to achieve accurate predictions in most cases. However, there are differences in the absolute concentration ranges of these components across the datasets of individual bioreactor scales. Thus, glutamate and ammonium PLS models were forced to extrapolate in cases where models were derived from small scale data only but used in cross‐scale applications predicting against manufacturing scale batches. © 2014 American Institute of Chemical Engineers Biotechnol. Prog., 31:566–577, 2015     

Predictive models in ecology: Comparison of performances and assessment of applicability

Ecological systems are governed by complex interactions which are mainly nonlinear. In order to capture the inherent complexity and nonlinearity of ecological, and in general biological systems, empirical models recently gained popularity. However, although these models, particularly connectionist approaches such as multilayered backpropagation networks, are commonly applied as predictive models in ecology to a wide variety of ecosystems and questions, there are no studies to date aiming to assess the performance, both in terms of data fitting and generalizability, and applicability of empirical models in ecology. Our aim is hence to provide an overview for nature of the wide range of the data sets and predictive variables, from both aquatic and terrestrial ecosystems with different scales of time-dependent dynamics, and the applicability and robustness of predictive modeling methods on such data sets by comparing different empirical modeling approaches. The models used in this study range from predicting the occurrence of submerged plants in shallow lakes to predicting nest occurrence of bird species from environmental variables and satellite images. The methods considered include k-nearest neighbor (k-NN), linear and quadratic discriminant analysis (LDA and QDA), generalized linear models (GLM) feedforward multilayer backpropagation networks and pseudo-supervised network ARTMAP.Our results show that the predictive performances of the models on training data could be misleading, and one should consider the predictive performance of a given model on an independent test set for assessing its predictive power. Moreover, our results suggest that for ecosystems involving time-dependent dynamics and periodicities whose frequency are possibly less than the time scale of the data considered, GLM and connectionist neural network models appear to be most suitable and robust, provided that a predictive variable reflecting these time-dependent dynamics included in the model either implicitly or explicitly. For spatial data, which does not include any time-dependence comparable to the time scale covered by the data, on the other hand, neighborhood based methods such as k-NN and ARTMAP proved to be more robust than other methods considered in this study. In addition, for predictive modeling purposes, first a suitable, computationally inexpensive method should be applied to the problem at hand a good predictive performance of which would render the computational cost and efforts associated with complex variants unnecessary.     

Diverse metabolic model parameters generate similar methionine cycle dynamics

Parameter estimation constitutes a major challenge in dynamic modeling of metabolic networks. Here we examine, via computational simulations, the influence of system nonlinearity and the nature of available data on the distribution and predictive capability of identified model parameters. Simulated methionine cycle metabolite concentration data (both with and without corresponding flux data) was inverted to identify model parameters consistent with it. Thousands of diverse parameter families were found to be consistent with the data to within moderate error, with most of the parameter values spanning over 1000-fold ranges irrespective of whether flux data was included. Due to strong correlations within the extracted parameter families, model predictions were generally reliable despite the broad ranges found for individual parameters. Inclusion of flux data, by strengthening these correlations, resulted in substantially more reliable flux predictions. These findings suggest that, despite the difficulty of extracting biochemically accurate model parameters from system level data, such data may nevertheless prove adequate for driving the development of predictive dynamic metabolic models.     

Estimation and Prediction With HIV-Treatment Interruption Data

We consider longitudinal clinical data for HIV patients undergoing treatment interruptions. We use a nonlinear dynamical mathematical model in attempts to fit individual patient data. A statistically-based censored data method is combined with inverse problem techniques to estimate dynamic parameters. The predictive capabilities of this approach are demonstrated by comparing simulations based on estimation of parameters using only half of the longitudinal observations to the full longitudinal data sets.     

Optimal estimation of ion-channel kinetics from macroscopic currents

Markov modeling provides an effective approach for modeling ion channel kinetics. There are several search algorithms for global fitting of macroscopic or single-channel currents across different experimental conditions. Here we present a particle swarm optimization(PSO)-based approach which, when used in combination with golden section search (GSS), can fit macroscopic voltage responses with a high degree of accuracy (errors within 1%) and reasonable amount of calculation time (less than 10 hours for 20 free parameters) on a desktop computer. We also describe a method for initial value estimation of the model parameters, which appears to favor identification of global optimum and can further reduce the computational cost. The PSO-GSS algorithm is applicable for kinetic models of arbitrary topology and size and compatible with common stimulation protocols, which provides a convenient approach for establishing kinetic models at the macroscopic level.