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.     

Single-cell behavior and population heterogeneity: solving an inverse problem to compute the intrinsic physiological state functions

The dynamics of isogenic cell populations can be described by cell population balance models that account for phenotypic heterogeneity. To utilize the predictive power of these models, however, we must know the rates of single-cell reaction and division and the bivariate partition probability density function. These three intrinsic physiological state (IPS) functions can be obtained by solving an inverse problem that requires knowledge of the phenotypic distributions for the overall cell population, the dividing cell subpopulation and the newborn cell subpopulation. We present here a robust computational procedure that can accurately estimate the IPS functions for heterogeneous cell populations. A detailed parametric analysis shows how the accuracy of the inverse solution is affected by discretization parameters, the type of non-parametric estimators used, the qualitative characteristics of phenotypic distributions and the unknown partitioning probability density function. The effect of finite sampling and measurement errors on the accuracy of the recovered IPS functions is also assessed. Finally, we apply the procedure to estimate the IPS functions of an E. coli population carrying an IPTG-inducible genetic toggle network. This study completes the development of an integrated experimental and computational framework that can become a powerful tool for quantifying single-cell behavior using measurements from heterogeneous cell populations.     

Parameter optimization by using differential elimination: a general approach for introducing constraints into objective functions

Background

The investigation of network dynamics is a major issue in systems and synthetic biology. One of the essential steps in a dynamics investigation is the parameter estimation in the model that expresses biological phenomena. Indeed, various techniques for parameter optimization have been devised and implemented in both free and commercial software. While the computational time for parameter estimation has been greatly reduced, due to improvements in calculation algorithms and the advent of high performance computers, the accuracy of parameter estimation has not been addressed.

Results

We propose a new approach for parameter optimization by using differential elimination, to estimate kinetic parameter values with a high degree of accuracy. First, we utilize differential elimination, which is an algebraic approach for rewriting a system of differential equations into another equivalent system, to derive the constraints between kinetic parameters from differential equations. Second, we estimate the kinetic parameters introducing these constraints into an objective function, in addition to the error function of the square difference between the measured and estimated data, in the standard parameter optimization method. To evaluate the ability of our method, we performed a simulation study by using the objective function with and without the newly developed constraints: the parameters in two models of linear and non-linear equations, under the assumption that only one molecule in each model can be measured, were estimated by using a genetic algorithm (GA) and particle swarm optimization (PSO). As a result, the introduction of new constraints was dramatically effective: the GA and PSO with new constraints could successfully estimate the kinetic parameters in the simulated models, with a high degree of accuracy, while the conventional GA and PSO methods without them frequently failed.

Conclusions

The introduction of new constraints in an objective function by using differential elimination resulted in the drastic improvement of the estimation accuracy in parameter optimization methods. The performance of our approach was illustrated by simulations of the parameter optimization for two models of linear and non-linear equations, which included unmeasured molecules, by two types of optimization techniques. As a result, our method is a promising development in parameter optimization.

     

Topology fingerprint approach to the inverse protein folding problem.

We describe the most general solution to date of the problem of matching globular protein sequences to the appropriate three-dimensional structures. The screening template, against which sequences are tested, is provided by a protein "structural fingerprint" library based on the contact map and the buried/exposed pattern of residues. Then, a lattice Monte Carlo algorithm validates or dismisses the stability of the proposed fold. Examples of known structural similarities between proteins having weakly or unrelated sequences such as the globins and phycocyanins, the eight-member alpha/beta fold of triose phosphate isomerase and even a close structural equivalence between azurin and immunoglobulins are found.     

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.     

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.     

Towards a biomechanics-based technique for assessing myocardial contractility: an inverse problem approach

This work presents the initial development and implementation of a novel 3D biomechanics-based approach to measure the mechanical activity of myocardial tissue, as a potential non-invasive tool to assess myocardial function. This technique quantifies the myocardial contraction forces developed within the ventricular myofibers in response to electro-physiological stimuli. We provide a 3D finite element formulation of a contraction force reconstruction algorithm, along with its implementation using magnetic resonance (MR) data. Our algorithm is based on an inverse problem solution governed by the fundamental continuum mechanics principle of conservation of linear momentum, under a first-order approximation of elastic and isotropic material conditions. We implemented our technique using a subject-specific ventricle model obtained by extracting the left ventricular anatomical features from a set of high-resolution cardiac MR images acquired throughout the cardiac cycle using prospective electrocardiographic gating. Cardiac motion information was extracted by non-rigid registration of the mid-diastole reference image to the remaining images of a 4D dataset. Using our technique, we reconstructed dynamic maps that show the contraction force distribution superimposed onto the deformed ventricle model at each acquired frame in the cardiac cycle. Our next objective will consist of validating this technique by showing the correlation between the presence of low contraction force patterns and poor myocardial functionality.     

Differences among the polyadenylated RNA sequences of human leucocyte populations: an approach to the objective classification of human leukaemias

We have constructed a complementary DNA (cDNA) library representing expressed sequences of the white blood cells from a patient with chronic granulocytic leukaemia. The library was screened by colony hybridization of 32P-labelled cDNAs synthesized from the polyadenylated RNAs of the white blood cells from patients with chronic granulocytic or chronic lymphocytic leukaemia. The autoradiographic patterns were compared and 70 recombinants were selected to comprise a panel which distinguished between these two types of leukaemia. Hybridization of this panel with complementary DNAs transcribed from the polyadenylated RNAs of a variety of normal and neoplastic leucocyte populations showed that the RNA sequences in high abundance in leucocytes from chronic granulocytic leukaemias differ quite radically from those in other leucocytes. The patterns of hybridization seen when this panel was challenged with cDNAs representing the RNAs of normal and leukaemic leucocyte populations were sufficiently different to distinguish clearly the peripheral blood leucocytes of chronic granulocytic leukaemias from other populations of white blood cells, both normal and leukaemic. We suggest that this approach might provide additional markers useful in the classification of the acute leukaemias, especially the undifferentiated leukaemias whose identification by conventional methods is uncertain.     

An integrated inverse model-experimental approach to determine soft tissue three-dimensional constitutive parameters: application to post-infarcted myocardium

Knowledge of the complete three-dimensional (3D) mechanical behavior of soft tissues is essential in understanding their pathophysiology and in developing novel therapies. Despite significant progress made in experimentation and modeling, a complete approach for the full characterization of soft tissue 3D behavior remains elusive. A major challenge is the complex architecture of soft tissues, such as myocardium, which endows them with strongly anisotropic and heterogeneous mechanical properties. Available experimental approaches for quantifying the 3D mechanical behavior of myocardium are limited to preselected planar biaxial and 3D cuboidal shear tests. These approaches fall short in pursuing a model-driven approach that operates over the full kinematic space. To address these limitations, we took the following approach. First, based on a kinematical analysis and using a given strain energy density function (SEDF), we obtained an optimal set of displacement paths based on the full 3D deformation gradient tensor. We then applied this optimal set to obtain novel experimental data from a 1-cm cube of post-infarcted left ventricular myocardium. Next, we developed an inverse finite element (FE) simulation of the experimental configuration embedded in a parameter optimization scheme for estimation of the SEDF parameters. Notable features of this approach include: (i) enhanced determinability and predictive capability of the estimated parameters following an optimal design of experiments, (ii) accurate simulation of the experimental setup and transmural variation of local fiber directions in the FE environment, and (iii) application of all displacement paths to a single specimen to minimize testing time so that tissue viability could be maintained. Our results indicated that, in contrast to the common approach of conducting preselected tests and choosing an SEDF a posteriori, the optimal design of experiments, integrated with a chosen SEDF and full 3D kinematics, leads to a more robust characterization of the mechanical behavior of myocardium and higher predictive capabilities of the SEDF. The methodology proposed and demonstrated herein will ultimately provide a means to reliably predict tissue-level behaviors, thus facilitating organ-level simulations for efficient diagnosis and evaluation of potential treatments. While applied to myocardium, such developments are also applicable to characterization of other types of soft tissues.     

Improving Tikhonov regularization with linearly constrained optimization: application to the inverse epicardial potential solution.

Two methods to improve on the accuracy of the Tikhonov regularization technique commonly used for the stable recovery of solutions to ill-posed problems are presented. These methods do not require a priori knowledge of the properties of the solution or of the error. Rather they exploit the observed properties of overregularized and underregularized Tikhonov solutions so as to impose linear constraints on the sought-after solution. The two methods were applied to the inverse problem of electrocardiography using a spherical heart-torso model and simulated inner-sphere (epicardial) and outer-sphere (body) potential distributions. It is shown that if the overregularized and underregularized Tikhonov solutions are chosen properly, the two methods yield epicardial solutions that are not only more accurate than the optimal Tikhonov solution but also provide other qualitative information, such as correct position of the extrema, not obtainable using ordinary Tikhonov regularization. A heuristic method to select the overregularized and underregularized solutions is discussed.     

An iterative approach from the standpoint of the additive hypothesis to the dendrogram problem posed by molecular data sets

The problem of constructing a dendrogram depicting phylogenetic relationships for a collection of contemporary species is considered. An approach was developed based on the additive hypothesis in which each “length” between two species can be described by the shortest sum of lengths for the individual links on the dendrogram topology which connect the two species. The additive hypothesis holds equally well if the dendro gram is replaced by its corresponding (rootless) network. Network topologies are defined set theoretically in terms of the initial, contemporary species, and a coefficient is defined for each point of any conceivable network. It is proved mathematically that each point of an additive network gives a coefficient value of zero, whereas each point not belonging to an additive network gives a coefficient value greater than zero. This suggests an iterative procedure in which “false” network points are replaced by “true” ones, or more generally in which “very false” network points are replaced by “nearly true” ones. The first procedure follows from the mathematical proof and the second is confirmed by simulation. Since most real data sets are not additive in the strict sense, a real data example was presented in which the iterative procedure produced a plausible network topology.     

Non-linear global optimization via parameterization and inverse function approximation: an artificial neural networks approach

In this article, a novel technique for non-linear global optimization is presented. The main goal is to find the optimal global solution of non-linear problems avoiding sub-optimal local solutions or inflection points. The proposed technique is based on a two steps concept: properly keep decreasing the value of the objective function, and calculating the corresponding independent variables by approximating its inverse function. The decreasing process can continue even after reaching local minima and, in general, the algorithm stops when converging to solutions near the global minimum. The implementation of the proposed technique by conventional numerical methods may require a considerable computational effort on the approximation of the inverse function. Thus, here a novel Artificial Neural Network (ANN) approach is implemented to reduce the computational requirements of the proposed optimization technique. This approach is successfully tested on some highly non-linear functions possessing several local minima. The results obtained demonstrate that the proposed approach compares favorably over some current conventional numerical (Matlab functions) methods, and other non-conventional (Evolutionary Algorithms, Simulated Annealing) optimization methods.     

Evidence for composite cost functions in arm movement planning: an inverse optimal control approach

An important issue in motor control is understanding the basic principles underlying the accomplishment of natural movements. According to optimal control theory, the problem can be stated in these terms: what cost function do we optimize to coordinate the many more degrees of freedom than necessary to fulfill a specific motor goal? This question has not received a final answer yet, since what is optimized partly depends on the requirements of the task. Many cost functions were proposed in the past, and most of them were found to be in agreement with experimental data. Therefore, the actual principles on which the brain relies to achieve a certain motor behavior are still unclear. Existing results might suggest that movements are not the results of the minimization of single but rather of composite cost functions. In order to better clarify this last point, we consider an innovative experimental paradigm characterized by arm reaching with target redundancy. Within this framework, we make use of an inverse optimal control technique to automatically infer the (combination of) optimality criteria that best fit the experimental data. Results show that the subjects exhibited a consistent behavior during each experimental condition, even though the target point was not prescribed in advance. Inverse and direct optimal control together reveal that the average arm trajectories were best replicated when optimizing the combination of two cost functions, nominally a mix between the absolute work of torques and the integrated squared joint acceleration. Our results thus support the cost combination hypothesis and demonstrate that the recorded movements were closely linked to the combination of two complementary functions related to mechanical energy expenditure and joint-level smoothness.     

An analytical approach to the implementation of genetically modified crops

Public scepticism towards genetically modified (GM) crops is increasing. To address this, the risks and benefits of GM crops must be examined across scientific disciplines, and be discussed with the authorities, the agricultural industry and the consumers. In a feasibility study we have systematically analysed the challenges of the development and marketing of GM crops in Europe. A life-cycle inventory was used together with established technology foresight techniques in an interdisciplinary and empirical framework. The approach taken in this study established a dialogue between stakeholders and provided a framework for discussions about the future direction of GM crops.     

A modified approach to the measurement problem: objective reduction in the retinal molecule prior to conformational change

A new analysis of the measurement problem reveals the possibility that collapse of the wavefunction may now take place just before photoisomerization of the rhodopsin molecule in the retinal rods. It is known that when a photon is initially absorbed by the retinal molecule which, along with opsin comprises the rhodopsin molecule, an electron in the highest pi orbital is immediately excited to a pi* orbital. This means that a measurement or transfer of information takes place at the quantum level before the retinal molecule commences the conformational change from cis to trans. This could have profound implications for resolving some of the foundational issues confronting quantum mechanics.     

An evolutionary approach to the traveling salesman problem

Evolutionary optimization has been proposed as a method to generate machine learning through automated discovery. A simulation of natural evolution is conducted using the traveling salesman problem as an artificial environment. For an exact solution of a traveling salesman problem, the only known algorithms require the number of steps to grow at least exponentially with the number of elements in the problem. Three adaptive techniques are described and analyzed. Evolutionary adaptation is demonstrated to be worthwhile in a variety of contexts. Local stagnation is prevented by allowing for the probabilistic survival of the simulated organisms. In complex problems, the final routing is estimated to be better than 99.99999999999% of all possible tours, even though only a small fraction (8.58 × 10^–151) of the total number of tours are examined.     

Invited contribution: An objective approach to the development of short-term tests predictive of carcinogenicity

The Carcinogenicity Prediction and Battery Selection procedure was developed to address two problems: (1) the identification of highly predictive, yet cost-effective, batteries of short-term tests and (2) the objective prediction of the potential carcinogenicity of chemicals based upon the results of short-term tests even when a mixture of positive and negative results is obtained. In the present report the usefulness of the Carcinogenicity Prediction and Battery Selection procedure is demonstrated using benzo[a]pyrene, benzoin and diethylstilbestrol as examples. In addition, its applicability in the analysis of all the possible outcomes of a battery is illustrated together with an analysis of the worth of additional testing.Abbreviations B[a]P benzo[a]pyrene - CASE Computer-Automated Structure Evaluation - CPBS Carcinogenicity Prediction and Battery Selection - DEHP diethylhexylphthalate - DES diethylstilbestrol - NTA nitrilotriacetate - TCDD 2,3,7,8-tetrachlorodibenzo-p-dioxin