The Obstacle-Set Method for Representing Muscle Paths in Musculoskeletal Models

A computational method is introduced for modeling the paths of muscles in the human body. The method is based on the premise that the resultant muscle force acts along the locus of the transverse cross-sectional centroids of the muscle. The path of the muscle is calculated by idealizing its centroid path as a frictionless elastic band, which moves freely over neighboring anatomical constraints such as bones and other muscles. The anatomical constraints, referred to as obstacles, are represented in the model by regular-shaped, rigid bodies such as spheres and cylinders. The obstacles, together with the muscle path, define an obstacle set. It is proposed that the path of any muscle can be modeled using one or more of the following four obstacle sets: single sphere, single cylinder, double cylinder, and sphere-capped cylinder. Assuming that the locus of the muscle centroids is known for an arbitrary joint configuration, the obstacle-set method can be used to calculate the path of the muscle for all other joint configurations. The obstacle-set method accounts not only for the interaction between a muscle and a neighboring anatomical constraint, but also for the way in which this interaction changes with joint configuration. Consequently, it is the only feasible method for representing the paths of muscles which cross joints with multiple degrees of freedom such as the deltoid at the shoulder.     

How to reliably estimate the tortuosity of an animal's path: straightness, sinuosity, or fractal dimension?

The tortuosity of an animal's path is a key parameter in orientation and searching behaviours. The tortuosity of an oriented path is inversely related to the efficiency of the orientation mechanism involved, the best mechanism being assumed to allow the animal to reach its goal along a straight line movement. The tortuosity of a random search path controls the local searching intensity, allowing the animal to adjust its search effort to the local profitability of the environment. This paper shows that (1) the efficiency of an oriented path can be reliably estimated by a straightness index computed as the ratio between the distance from the starting point to the goal and the path length travelled to reach the goal, but such a simple index, ranging between 0 and 1, cannot be applied to random search paths; (2) the tortuosity of a random search path, ranging between straight line movement and Brownian motion, can be reliably estimated by a sinuosity index which combines the mean cosine of changes of direction with the mean step length; and (3) in the current state of the art, the fractal analysis of animals' paths, which may appear as an alternative and promising way to measure the tortuosity of a random search path as a fractal dimension ranging between 1 (straight line movement) and 2 (Brownian motion), is only liable to generate artifactual results. This paper also provides some help for distinguishing between oriented and random search paths, and depicts a general, comprehensive framework for analysing individual animals' paths in a two-dimensional space.     

A copula method for modeling directional dependence of genes

Background  

Genes interact with each other as basic building blocks of life, forming a complicated network. The relationship between groups of genes with different functions can be represented as gene networks. With the deposition of huge microarray data sets in public domains, study on gene networking is now possible. In recent years, there has been an increasing interest in the reconstruction of gene networks from gene expression data. Recent work includes linear models, Boolean network models, and Bayesian networks. Among them, Bayesian networks seem to be the most effective in constructing gene networks. A major problem with the Bayesian network approach is the excessive computational time. This problem is due to the interactive feature of the method that requires large search space. Since fitting a model by using the copulas does not require iterations, elicitation of the priors, and complicated calculations of posterior distributions, the need for reference to extensive search spaces can be eliminated leading to manageable computational affords. Bayesian network approach produces a discretely expression of conditional probabilities. Discreteness of the characteristics is not required in the copula approach which involves use of uniform representation of the continuous random variables. Our method is able to overcome the limitation of Bayesian network method for gene-gene interaction, i.e. information loss due to binary transformation.     

Modularization of biochemical networks based on classification of Petri net t-invariants

Background  

Structural analysis of biochemical networks is a growing field in bioinformatics and systems biology. The availability of an increasing amount of biological data from molecular biological networks promises a deeper understanding but confronts researchers with the problem of combinatorial explosion. The amount of qualitative network data is growing much faster than the amount of quantitative data, such as enzyme kinetics. In many cases it is even impossible to measure quantitative data because of limitations of experimental methods, or for ethical reasons. Thus, a huge amount of qualitative data, such as interaction data, is available, but it was not sufficiently used for modeling purposes, until now. New approaches have been developed, but the complexity of data often limits the application of many of the methods. Biochemical Petri nets make it possible to explore static and dynamic qualitative system properties. One Petri net approach is model validation based on the computation of the system's invariant properties, focusing on t-invariants. T-invariants correspond to subnetworks, which describe the basic system behavior.     

Path matching and graph matching in biological networks.

We develop algorithms for the following path matching and graph matching problems: (i) given a query path p and a graph G, find a path p' that is most similar to p in G; (ii) given a query graph G (0) and a graph G, find a graph G (0)' that is most similar to G (0) in G. In these problems, p and G (0) represent a given substructure of interest to a biologist, and G represents a large network in which the biologist desires to find a related substructure. These algorithms allow the study of common substructures in biological networks in order to understand how these networks evolve both within and between organisms. We reduce the path matching problem to finding a longest weighted path in a directed acyclic graph and show that the problem of finding top k suboptimal paths can be solved in polynomial time. This is in contrast with most previous approaches that used exponential time algorithms to find simple paths which are practical only when the paths are short. We reduce the graph matching problem to finding highest scoring subgraphs in a graph and give an exact algorithm to solve the problem when the query graph G (0) is of moderate size. This eliminates the need for less accurate heuristic or randomized algorithms.We show that our algorithms are able to extract biologically meaningful pathways from protein interaction networks in the DIP database and metabolic networks in the KEGG database. Software programs implementing these techniques (PathMatch and GraphMatch) are available at http://faculty.cs.tamu.edu/shsze/pathmatch and http://faculty.cs.tamu.edu/shsze/graphmatch.     

Thermodynamic calculations for biochemical transport and reaction processes in metabolic networks

Thermodynamic analysis of metabolic networks has recently generated increasing interest for its ability to add constraints on metabolic network operation, and to combine metabolic fluxes and metabolite measurements in a mechanistic manner. Concepts for the calculation of the change in Gibbs energy of biochemical reactions have long been established. However, a concept for incorporation of cross-membrane transport in these calculations is still missing, although the theory for calculating thermodynamic properties of transport processes is long known. Here, we have developed two equivalent equations to calculate the change in Gibbs energy of combined transport and reaction processes based on two different ways of treating biochemical thermodynamics. We illustrate the need for these equations by showing that in some cases there is a significant difference between the proposed correct calculation and using an approximative method. With the developed equations, thermodynamic analysis of metabolic networks spanning over multiple physical compartments can now be correctly described.     

Comparing mutational pathways to lopinavir resistance in HIV-1 subtypes B versus C

Although combination antiretroviral therapies seem to be effective at controlling HIV-1 infections regardless of the viral subtype, there is increasing evidence for subtype-specific drug resistance mutations. The order and rates at which resistance mutations accumulate in different subtypes also remain poorly understood. Most of this knowledge is derived from studies of subtype B genotypes, despite not being the most abundant subtype worldwide. Here, we present a methodology for the comparison of mutational networks in different HIV-1 subtypes, based on Hidden Conjunctive Bayesian Networks (H-CBN), a probabilistic model for inferring mutational networks from cross-sectional genotype data. We introduce a Monte Carlo sampling scheme for learning H-CBN models for a larger number of resistance mutations and develop a statistical test to assess differences in the inferred mutational networks between two groups. We apply this method to infer the temporal progression of mutations conferring resistance to the protease inhibitor lopinavir in a large cross-sectional cohort of HIV-1 subtype C genotypes from South Africa, as well as to a data set of subtype B genotypes obtained from the Stanford HIV Drug Resistance Database and the Swiss HIV Cohort Study. We find strong support for different initial mutational events in the protease, namely at residue 46 in subtype B and at residue 82 in subtype C. The inferred mutational networks for subtype B versus C are significantly different sharing only five constraints on the order of accumulating mutations with mutation at residue 54 as the parental event. The results also suggest that mutations can accumulate along various alternative paths within subtypes, as opposed to a unique total temporal ordering. Beyond HIV drug resistance, the statistical methodology is applicable more generally for the comparison of inferred mutational networks between any two groups.     

The convex wrapping algorithm: A method for identifying muscle paths using the underlying bone mesh

Associating musculoskeletal models to motion analysis data enables the determination of the muscular lengths, lengthening rates and moment arms of the muscles during the studied movement. Therefore, those models must be anatomically personalized and able to identify realistic muscular paths. Different kinds of algorithms exist to achieve this last issue, such as the wired models and the finite elements ones. After having studied the advantages and drawbacks of each one, we present the convex wrapping algorithm. Its purpose is to identify the shortest path from the origin to the insertion of a muscle wrapping over the underlying skeleton mesh while respecting possible non-sliding constraints. After the presentation of the algorithm, the results obtained are compared to a classically used wrapping surface algorithm (obstacle set method) by measuring the length and moment arm of the semitendinosus muscle during an asymptomatic gait. The convex wrapping algorithm gives an efficient and realistic way of identifying the muscular paths with respect to the underlying bones mesh without the need to define simplified geometric forms. It also enables the identification of the centroid path of the muscles if their thickness evolution function is known. All this presents a particular interest when studying populations presenting noticeable bone deformations, such as those observed in cerebral palsy or rheumatic pathologies.     

Kinetic constraints for formation of steady states in biochemical networks

The constraint-based analysis has emerged as a useful tool for analysis of biochemical networks. This work introduces the concept of kinetic constraints. It is shown that maximal reaction rates are appropriate constraints only for isolated enzymatic reactions. For biochemical networks, it is revealed that constraints for formation of a steady state require specific relationships between maximal reaction rates of all enzymes. The constraints for a branched network are significantly different from those for a cyclic network. Moreover, the constraints do not require Michaelis-Menten constants for most enzymes, and they only require the constants for the enzymes at the branching or cyclic point. Reversibility of reactions at system boundary or branching point may significantly impact on kinetic constraints. When enzymes are regulated, regulations may impose severe kinetic constraints for the formation of steady states. As the complexity of a network increases, kinetic constraints become more severe. In addition, it is demonstrated that kinetic constraints for networks with co-regulation can be analyzed using the approach. In general, co-regulation enhances the constraints and therefore larger fluctuations in fluxes can be accommodated in the networks with co-regulation. As a first example of the application, we derive the kinetic constraints for an actual network that describes sucrose accumulation in the sugar cane culm, and confirm their validity using numerical simulations.     

Adjusting for founder relatedness in a linkage analysis using prior information

In genetic linkage studies, while the pedigrees are generally known, background relatedness between the founding individuals, assumed by definition to be unrelated, can seriously affect the results of the analysis. Likelihood approaches to relationship estimation from genetic marker data can all be expressed in terms of finding the most likely pedigree connecting the individuals of interest. When the true relationship is the main focus, the set of all possible alternative pedigrees can be too large to consider. However, prior information is often available which, when incorporated in a formal and structured way, can restrict this set to a manageable size thus enabling the calculation of a posterior distribution from which inferences can be drawn. Here, the unknown relationships are more of a nuisance factor than of interest in their own right, so the focus is on adjusting the results of the analysis rather than on direct estimation. In this paper, we show how prior information on founder relationships can be exploited in some applications to generate a set of candidate extended pedigrees. We then weight the relevant pedigree-specific likelihoods by their posterior probabilities to adjust the lod score statistics.     

Efficient algorithms for detecting signaling pathways in protein interaction networks.

The interpretation of large-scale protein network data depends on our ability to identify significant substructures in the data, a computationally intensive task. Here we adapt and extend efficient techniques for finding paths and trees in graphs to the problem of identifying pathways in protein interaction networks. We present linear-time algorithms for finding paths and trees in networks under several biologically motivated constraints. We apply our methodology to search for protein pathways in the yeast protein-protein interaction network. We demonstrate that our algorithm is capable of reconstructing known signaling pathways and identifying functionally enriched paths and trees in an unsupervised manner. The algorithm is very efficient, computing optimal paths of length 8 within minutes and paths of length 10 in about three hours.     

Designing metabolism: Alternative connectivities for the pentose phosphate pathway

We present a method for generating alternative biochemical pathways between specified compounds. We systematically generated diverse alternatives to the nonoxidative stage of the pentose phosphate pathway, by first finding pathways between 5-carbon and 6-carbon skeletons. Each solution of the equations for the stoichiometric coefficients of skeleton-changing reactions defines a set of networks. Within each set we selected networks with modules; a module is a coupled set of reactions that occurs more than one in a network. The networks can be classified into at least 53 families in at least seven superfamilies, according to the number, the input-output relations, and the internal structure of their modules. We then assigned classes of enzymes to mediate transformations of carbon skeletons and modifications of functional groups. The ensemble of candidate networks was too large to allow complete determination of the optimal network. However, among the networks we studied the real pathway is especially favorable in several respects. It has few steps, uses no reducing or oxidizing compounds, requires only one ATP in one direction of flux, and does not depend on recurrent inputs.     

Biological adaptations for functional features of language in the face of cultural evolution

Although there may be no true language universals, it is nonetheless possible to discern several family resemblance patterns across the languages of the world. Recent work on the cultural evolution of language indicates the source of these patterns is unlikely to be an innate universal grammar evolved through biological adaptations for arbitrary linguistic features. Instead, it has been suggested that the patterns of resemblance emerge because language has been shaped by the brain, with individual languages representing different but partially overlapping solutions to the same set of nonlinguistic constraints. Here, we use computational simulations to investigate whether biological adaptation for functional features of language, deriving from cognitive and communicative constraints, may nonetheless be possible alongside rapid cultural evolution. Specifically, we focus on the Baldwin effect as an evolutionary mechanism by which previously learned linguistic features might become innate through natural selection across many generations of language users. The results indicate that cultural evolution of language does not necessarily prevent functional features of language from becoming genetically fixed, thus potentially providing a particularly informative source of constraints on cross-linguistic resemblance patterns.     

An overview of data models for the analysis of biochemical pathways

Biochemical pathways such as metabolic, regulatory or signal transduction pathways can be viewed as interconnected processes forming an intricate network of functional and physical interactions between molecular species in the cell. The amount of information available on such pathways for different organisms is increasing very rapidly. This is offering the possibility of performing various analyses on the structure of the full network of pathways for one organism as well as across different organisms, and has therefore generated interest in developing databases for storing and managing this information. Analysing these networks remains far from straightforward owing to the nature of the databases, which are often heterogeneous, incomplete or inconsistent. Pathway analysis is hence a challenging problem in systems biology and in bioinformatics. Various forms of data models have been devised for the analysis of biochemical pathways. This paper presents an overview of the types of models used for this purpose, concentrating on those concerned with the structural aspects of biochemical networks. In particular, the different types of data models found in the literature are classified using a unified framework. In addition, how these models have been used in the analysis of biochemical networks is described. This enables us to underline the strengths and weaknesses of the different approaches, as well as to highlight relevant future research directions.     

Assessing larval rootworm behaviour after contacting maize roots: impact of germplasm,rootworm species and diapause status

Current methods of screening maize (Zea mays L.) germplasm for susceptibility or resistance to corn rootworms (Coleoptera: Chrysomelidae) rely primarily on information from large‐scale field experiments. Due to labour and cost constraints associated with field trials, alternative evaluation methods are desirable. We used a previously developed behavioural bioassay to: (1) investigate the host search behaviour of rootworm larvae after contact with 14 maize genotypes, (2) compare the behaviour of non‐diapausing Diabrotica virgifera virgifera LeConte, diapausing D. v. virgifera, and diapausing D. barberi Smith & Lawrence and (3) determine if this technique can be used to separate susceptible vs. resistant maize genotypes. The majority of rootworm larvae engaged in intensive (local search) behaviour after exposure to maize roots, whereas larvae continued to exhibit extensive (ranging) behaviour after contact with negative controls. Even though a transgenic hybrid with resistance to D. v. virgifera was included in analyses, quantitative path measurements were similar among genotypes and only differed between specific maize lines and controls. Notably, there were differences in host search behaviour among rootworm groups, with non‐diapausing D. v. virgifera having more convoluted paths and engaging in intensive search more frequently than diapausing rootworms. Correlations between larval path measurements and historic root damage ratings were not significant, although there were weak positive correlations between historic adult emergence densities and measures of path linearity. However, due to the lack of significant behavioural differences among maize lines with a range of susceptibility levels, we concluded that this bioassay is not useful in screening maize germplasm for rootworm resistance.