An analytical approach to the problem of inverse optimization with additive objective functions: an application to human prehension

We consider the problem of what is being optimized in human actions with respect to various aspects of human movements and different motor tasks. From the mathematical point of view this problem consists of finding an unknown objective function given the values at which it reaches its minimum. This problem is called the inverse optimization problem. Until now the main approach to this problems has been the cut-and-try method, which consists of introducing an objective function and checking how it reflects the experimental data. Using this approach, different objective functions have been proposed for the same motor action. In the current paper we focus on inverse optimization problems with additive objective functions and linear constraints. Such problems are typical in human movement science. The problem of muscle (or finger) force sharing is an example. For such problems we obtain sufficient conditions for uniqueness and propose a method for determining the objective functions. To illustrate our method we analyze the problem of force sharing among the fingers in a grasping task. We estimate the objective function from the experimental data and show that it can predict the force-sharing pattern for a vast range of external forces and torques applied to the grasped object. The resulting objective function is quadratic with essentially non-zero linear terms.     

A constitutive theory for biomembranes: application to epicardial mechanics.

We present a new theoretically motivated experimental approach for identifying the functional form of a constitutive relation for any nonlinear, anisotropic pseudoelastic biological membrane. The utility of this approach is illustrated by identifying, from biaxial data, a new constitutive relation for excised ventricular epicardium. Values of the associated material parameters are calculated and compared for right and left ventricular specimens. Based on our findings, we suggest that there are no significant differences in the biomechanical behavior of epicardium excised from the right and left ventricular free walls of canine hearts.     

A new method for regularization of the inverse problem of electrocardiography.

The inverse problem of electrocardiography (specifically, that part concerned with the computation of the ventricular surface activation isochrones) is shown to be formally equivalent to the problem of identification and measurement of discontinuities in derivatives of body surface potentials. This is based on the demonstration that such measurements allow localization of the relative extrema of the ventricular surface activation map (given a forward problem solution), which in turn restricts the space of admissible solution maps to a compact set. Although the inverse problem and the problem of identifying derivative discontinuities are both ill-posed, it is possible that the latter may be more easily or justifiably resolved with available information, particularly as current methods for regularizing the inverse problem typically rely on a regularization parameter chosen in an a posteriori fashion. An example of the power of the approach is the demonstration that a recent Uniform Dipole Layer Hypothesis-based method for producing the ventricular surface activation map is largely independent on that hypothesis and capable in principle of generating maps that are very similar in a precise sense to those that would result from the usual epicardial potential formulation (assuming the latter were capable of producing intrinsic deflections in computed epicardial electrograms sufficiently steep to accurately compute the activation map). This is consistent with the preliminary success of the former method, despite the significant inaccuracy of its underlying assumption.     

A new genetic distance with application to constrained variation at microsatellite loci.

Genetic variation at microsatellite loci is supposed to be constrained within some range in allele size. In this case, the average-square distance (delta mu)2 between two diverged populations moves asymptotically around and underestimates the time since the populations had split. A distance based on the between-locus correlation in the mean repeat scores, DR, is introduced. Numerical simulations show that DR is a linear function of time if the constraints are approximated by a linear centripetal force, which might be due to mutation bias toward a definite range or be caused both by directional mutation bias toward larger allele size and by selection against the greater number of repeats.     

Computational issues of importance to the inverse recovery of epicardial potentials in a realistic heart-torso geometry

In vitro data from a realistic-geometry electrolytic tank were used to demonstrate the consequences of computational issues critical to the ill-posed inverse problem in electrocardiography. The boundary element method was used to discretize the relationship between the body surface potentials and epicardial cage potentials. Variants of Tikhonov regularization were used to stabilize the inversion of the body surface potentials in order to reconstruct the epicardial surface potentials. The computational issues investigated were (1) computation of the regularization parameter; (2) effects of inaccuracy in locating the position of the heart; and (3) incorporation of a priori information on the properties of epicardial potentials into the regularization methodology. Two methods were suggested by which a priori information could be incorporated into the regularization formulation: (1) use of an estimate of the epicardial potential distribution everywhere on the surface and (2) use of regional bounds on the excursion of the potential. Results indicate that the a posteriori technique called CRESO, developed by Colli Franzone and coworkers, most consistently derives the regularization parameter closest to the optimal parameter for this experimental situation. The sensitivity of the inverse computation in a realistic-geometry torso to inaccuracies in estimating heart position are consistent with results from the eccentric spheres model; errors of 1 cm are well tolerated, but errors of 2 cm or greater result in a loss of position and amplitude information. Finally, estimates and bounds based on accurate, known information successfully lower the relative error associated with the inverse and have the potential to significantly enhance the amplitude and feature position information obtainable from the inverse-reconstructed epicardial potential map.     

Detection of potential enzyme targets by metabolic modelling and optimization: application to a simple enzymopathy

MOTIVATION: A very promising approach in drug discovery involves the integration of available biomedical data through mathematical modelling and data mining. We have developed a method called optimization program for drug discovery (OPDD) that allows new enzyme targets to be identified in enzymopathies through the integration of metabolic models and biomedical data in a mathematical optimization program. The method involves four steps: (i) collection of the necessary information about the metabolic system and disease; (ii) translation of the information into mathematical terms; (iii) computation of the optimization programs prioritizing the solutions that propose the inhibition of a reduced number of enzymes and (iv) application of additional biomedical criteria to select and classify the solutions. Each solution consists of a set of predicted values for metabolites, initial substrates and enzyme activities, which describe a biologically acceptable steady state of the system that shifts the pathologic state towards a healthy state. RESULTS: The OPDD was used to detect target enzymes in an enzymopathy, the human hyperuricemia. An existing S-system model and bibliographic information about the disease were used. The method detected six single-target enzyme solutions involving dietary modification, one of them coinciding with the conventional clinical treatment using allopurinol. The OPDD detected a large number of possible solutions involving two enzyme targets. All except one contained one of the previously detected six enzyme targets. The purpose of this work was not to obtain solutions for direct clinical implementation but to illustrate how increasing levels of biomedical information can be integrated together with mathematical models in drug discovery. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.     

Estimation of external contact loads using an inverse dynamics and optimization approach: General method and application to sit-to-stand maneuvers

This paper presents a general method to estimate unmeasured external contact loads (ECLs) acting on a system whose kinematics and inertial properties are known. This method is dedicated to underdetermined problems, e.g. when the system has two or more unmeasured external contact wrenches. It is based on inverse dynamics and a quadratic optimization, and is therefore relatively simple, computationally cost effective and robust. Net joint loads (NJLs) are included as variables of the problem, and thus could be estimated in the same procedure as the ECL and be used within the cost function.     

Michaelis-Menten kinetics under spatially constrained conditions: application to mibefradil pharmacokinetics

Two different approaches were used to study the kinetics of the enzymatic reaction under heterogeneous conditions to interpret the unusual nonlinear pharmacokinetics of mibefradil. Firstly, a detailed model based on the kinetic differential equations is proposed to study the enzymatic reaction under spatial constraints and in vivo conditions. Secondly, Monte Carlo simulations of the enzyme reaction in a two-dimensional square lattice, placing special emphasis on the input and output of the substrate were applied to mimic in vivo conditions. Both the mathematical model and the Monte Carlo simulations for the enzymatic reaction reproduced the classical Michaelis-Menten (MM) kinetics in homogeneous media and unusual kinetics in fractal media. Based on these findings, a time-dependent version of the classic MM equation was developed for the rate of change of the substrate concentration in disordered media and was successfully used to describe the experimental plasma concentration-time data of mibefradil and derive estimates for the model parameters. The unusual nonlinear pharmacokinetics of mibefradil originates from the heterogeneous conditions in the reaction space of the enzymatic reaction. The modified MM equation can describe the pharmacokinetics of mibefradil as it is able to capture the heterogeneity of the enzymatic reaction in disordered media.     

Improving the interpretation of fuzzy partitions in vegetation science with constrained ordinations

Classification and ordination techniques based in fuzzy set theory are now being commonly used in vegetation studies. However, several problems have been detected in spite of the significant theoretical advantages of the theory. In this paper we have improved the interpretability of fuzzy partitions by combining fuzzy partitions with correspondence analysis (CA) and detrended canonical correspondence analysis (DCCA) in an analysis of the beech forests of Basque Country, northern Spain. Our results seem to overcome difficulties in the interpretation of multi-group partitions.     

Hydrazine activation of guanylate cyclase: potential application to tobacco carcinogenesis.

Hydrazine, a chemical carcinogen in tobacco and tobacco smoke, has been shown to induce the production of a variety of tumors in rats. The present report demonstrates that hydrazine stimulates the enzyme guanylate cyclase (EC 4.6.1.2) which catalyzes the production of guanosine 3′,5′-monophosphate. At a maximal concentration of 100 mM, hydrazine activated guanylate cyclase 45-fold in liver, 39-fold in colon, 22-fold in stomach, 19-fold in heart, 18-fold in pancreas, 8-fold in lung and kidney, and 4-fold in spleen. Since recent evidence suggests a role for guanosine 3′,5′-monophosphate in malignant transformation, these data may help explain the tumor inducing capacity of this tobacco carcinogen.     

Clustering threshold gradient descent regularization: with applications to microarray studies

MOTIVATION: An important goal of microarray studies is to discover genes that are associated with clinical outcomes, such as disease status and patient survival. While a typical experiment surveys gene expressions on a global scale, there may be only a small number of genes that have significant influence on a clinical outcome. Moreover, expression data have cluster structures and the genes within a cluster have correlated expressions and coordinated functions, but the effects of individual genes in the same cluster may be different. Accordingly, we seek to build statistical models with the following properties. First, the model is sparse in the sense that only a subset of the parameter vector is non-zero. Second, the cluster structures of gene expressions are properly accounted for. RESULTS: For gene expression data without pathway information, we divide genes into clusters using commonly used methods, such as K-means or hierarchical approaches. The optimal number of clusters is determined using the Gap statistic. We propose a clustering threshold gradient descent regularization (CTGDR) method, for simultaneous cluster selection and within cluster gene selection. We apply this method to binary classification and censored survival analysis. Compared to the standard TGDR and other regularization methods, the CTGDR takes into account the cluster structure and carries out feature selection at both the cluster level and within-cluster gene level. We demonstrate the CTGDR on two studies of cancer classification and two studies correlating survival of lymphoma patients with microarray expressions. AVAILABILITY: R code is available upon request. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.     

Rhodopsin-transducin interface: studies with conformationally constrained peptides.

To probe the interaction between transducin (G(t)) and photoactivated rhodopsin (R*), 14 analog peptides were designed and synthesized restricting the backbone of the R*-bound structure of the C-terminal 11 residues of G(t)alpha derived by transferred nuclear Overhauser effect (TrNOE) NMR. Most of the analogs were able to bind R*, supporting the TrNOE structure. Improved affinities of constrained peptides indicated that preorganization of the bound conformation is beneficial. Cys347 was found to be a recognition site; particularly, the free sulfhydryl of the side chain seems to be critical for R* binding. Leu349 was another invariable residue. Both Ile and tert-leucine (Tle) mutations for Leu349 significantly reduced the activity, indicating that the Leu side chain is in intimate contact with R*. The structure of R* was computer generated by moving helix 6 from its position in the crystal structure of ground-state rhodopsin (R) based on various experimental data. Seven feasible complexes were found when docking the TrNOE structure with R* and none with R. The analog peptides were modeled into the complexes, and their binding affinities were calculated. The predicted affinities were compared with the measured affinities to evaluate the modeled structures. Three models of the R*/G(t)alpha complex showed strong correlation to the experimental data.     

Demecolcine-assisted enucleation of goat oocytes: protocol optimization, mechanism investigation, and application to improve the developmental potential of cloned embryos

Although demecolcine-assisted enucleation has been performed successfully in porcine and cattle, the mechanism and protocol optimization of chemically assisted enucleation need further investigation. The present study optimized the protocol for goat oocyte enucleation and demonstrated that a 30-min treatment with 0.8 ng/mL demecolcine-induced cytoplasmic protrusions in over 90% of the oocytes. Rates of enucleation, cell fusion, and blastocyst formation were significantly higher after demecolcine-assisted than after blind aspiration enucleation, although differences in rates of live births remain to be unequivocally determined between the two treatments. The ability to form protrusions decreased significantly as spindles became less organized in aged oocytes and the oocytes with a poor cumulus expansion. More than 93% of the demecolcine-induced protrusions persisted for 2 h in the absence of cytochalasin B (CB) but most disappeared within 30 min of CB treatment. The spindle disintegrated, an actin-rich ring formed around the chromosome mass and the MAP kinase activity increased significantly after demecolcine treatment. When oocytes with induced protrusions were treated with CB, however, the contractile ring disappeared, the spindle reintegrated, and both MPF and MAP kinase activities decreased significantly. It is concluded that (1) cytoplasmic protrusions can be induced in goat oocytes with a very low concentration of demecolcine; (2) oocyte selection and enucleation can be achieved simultaneously with demecolcine treatment; and (3) an interactive effect between the MAP kinase, MPF, microfilaments and microtubules might be implicated in the control of cytoplasmic protrusion formation after demecolcine treatment.     

Filtration capture immunoassay for bacteria: optimization and potential for urinalysis.

A novel assay utilizing immuno-labeling, filtration, and electrochemistry for the rapid detection of bacteria has been optimized for the detection of Escherichia coli O157:H7. Bacteria were specifically labeled with alkaline phosphatase conjugated polyclonal antibodies and captured on a polycarbonate track-etched membrane filter (0.2 microm pore size). The filter was then placed directly against a glassy carbon electrode, incubated with enzyme substrate, and the product detected by square wave voltammetry. The high speed and capture efficiency of membrane filtration and inherent sensitivity of electrochemical detection produced a 25-min assay with a detection limit of 5 x 10(3) E. coli O157:H7 per ml using a filtration volume of 100 microl (i.e. 500 cells filtered). The labeling, filtration, and electrochemical steps were optimized, and the assay performance using electrochemical and colorimetric detection methods was compared. The assay was used to detect E. coli O157:H7 that was spiked into filter-sterilized urine at clinically relevant concentrations.     

Ameboid cell motility: a model and inverse problem, with an application to live cell imaging data

In this article a mathematical model for ameboid cell movement is developed using a spring-dashpot system with Newtonian dynamics. The model is based on the facts that the cytoskeleton plays a primary role for cell motility and that the cytoplasm is viscoelastic. Based on the model, the inverse problem can be posed: if a structure like a spring-dashpot system is embedded into the living cell, what kind of characteristic properties must the structure have in order to reproduce a given movement of the cell? This inverse problem is the primary topic of this paper. On one side the model mimics some features of the movement, and on the other side, the solution to the inverse problem provides model parameters that give some insight, principally into the mechanical aspect, but also, through qualitative reasoning, into chemical and biophysical aspects of the cell. Moreover, this analysis can be done locally or globally and in different media by using the simplest possible information: positions of the cell and nuclear membranes. It is shown that the model and solution to the inverse problem for simulated data sets are highly accurate. An application to a set of live cell imaging data obtained from random movements of a human brain tumor cell (U87-MG human glioblastoma cell line) then provides an example of the efficiency of the model, through the solution of its inverse problem, as a way of understanding experimental data.     

Targeted proteomics for metabolic pathway optimization: application to terpene production

Successful metabolic engineering relies on methodologies that aid assembly and optimization of novel pathways in microbes. Many different factors may contribute to pathway performance, and problems due to mRNA abundance, protein abundance, or enzymatic activity may not be evident by monitoring product titers. To this end, synthetic biologists and metabolic engineers utilize a variety of analytical methods to identify the parts of the pathway that limit production. In this study, targeted proteomics, via selected-reaction monitoring (SRM) mass spectrometry, was used to measure protein levels in Escherichia coli strains engineered to produce the sesquiterpene, amorpha-4,11-diene. From this analysis, two mevalonate pathway proteins, mevalonate kinase (MK) and phosphomevalonate kinase (PMK) from Saccharomyces cerevisiae, were identified as potential bottlenecks. Codon-optimization of the genes encoding MK and PMK and expression from a stronger promoter led to significantly improved MK and PMK protein levels and over three-fold improved final amorpha-4,11-diene titer (>500 mg/L).     

A general approach to the optimization of the conformation of ring molecules with an application to valinomycin

A general and efficient methodology is presented which allows molecules containing one or many rings of any size to be manipulated within energy minimization procedures. Variables describing the conformation of the molecules concerned are limited to dihedral and ring valence angles and the ring closure conditions are treated as equality constraints. An application is made to the ion transporter valinomycin and its complexes with K+ and Na+ which illustrates the possibilities of the approach and leads to results which allow a better understanding of the conformational mechanics of this important ionophore.     

Microbial degradation of trichloroethylene in the rhizosphere: potential application to biological remediation of waste sites.

The possibility that vegetation may be used to actively promote microbial restoration of chemically contaminated soils was tested by using rhizosphere and nonvegetated soils collected from a trichloroethylene (TCE)-contaminated field site. Biomass determinations, disappearance of TCE from the headspace of spiked soil slurries, and mineralization of [14C]TCE to 14CO2 all showed that microbial activity is greater in rhizosphere soils and that TCE degradation occurs faster in the rhizosphere than in the edaphosphere. Thus, vegetation may be an important variable in the biological restoration of surface and near-surface soils.     

Spring-mass running: simple approximate solution and application to gait stability

The planar spring-mass model is frequently used to describe bouncing gaits (running, hopping, trotting, galloping) in animal and human locomotion and robotics. Although this model represents a rather simple mechanical system, an analytical solution predicting the center of mass trajectory during stance remains open. We derive an approximate solution in elementary functions assuming a small angular sweep and a small spring compression during stance. The predictive power and quality of this solution is investigated for model parameters relevant to human locomotion. The analysis shows that (i), for spring compressions of up to 20% (angle of attack > or = 60 degree, angular sweep < or = 60 degree) the approximate solution describes the stance dynamics of the center of mass within a 1% tolerance of spring compression and 0.6 degree tolerance of angular motion compared to numerical calculations, and (ii), despite its relative simplicity, the approximate solution accurately predicts stable locomotion well extending into the physiologically reasonable parameter domain. (iii) Furthermore, in a particular case, an explicit parametric dependency required for gait stability can be revealed extending an earlier, empirically found relationship. It is suggested that this approximation of the planar spring-mass dynamics may serve as an analytical tool for application in robotics and further research on legged locomotion.