Muscle mass in musculoskeletal models

Most current models of musculoskeletal dynamics lump a muscle's mass with its body segment, and then simulate the dynamics of these body segments connected by joints. As shown here, this popular approach leads to errors in the system's inertia matrix and hence in all aspects of the dynamics. Two simplified mathematical models were created to capture the relevant features of monoarticular and biarticular muscles, and the errors were analyzed. The models were also applied to two physiological examples: the triceps surae muscles that plantar flex the human ankle and the biceps femoris posterior muscle of the rat hind limb. The analysis of errors due to lumping showed that these errors can be large. Although the errors can be reduced in some postures, they cannot be easily eliminated in models that use segment lumping. Some options for addressing these errors are discussed.     

Extended foot-ankle musculoskeletal models for application in movement analysis

Multibody simulations of human motion require representative models of the anatomical structures. A model that captures the complexity of the foot is still lacking. In the present work, two detailed 3D multibody foot-ankle models generated based on CT scans using a semi-automatic tool are described. The proposed models consists of five rigid segments (talus, calcaneus, midfoot, forefoot and toes), connected by five joints (ankle, subtalar, midtarsal, tarsometatarsal and metatarsophalangeal), one with 15DOF and the other with 8DOF. The calculated kinematics of both models were evaluated using gait trials and compared against literature, both presenting realistic results. An inverse dynamic analysis was performed for the 8DOF model, again presenting feasible dynamic results.     

Computational analysis of models for cotransport

A well-characterized crude peroxisomal fraction from brown adipose tissue was used to compare peroxisomal beta-oxidation with beta-oxidation in isolated mitochondria. The apparent Km and chain-length specificity for peroxisomal (acyl-CoA) and mitochondrial (acyl-carnitine) beta-oxidation were determined with saturated C4-C22 fatty acyls and some unsaturated fatty acyls. Peroxisomes showed the lowest Km for medium-chain (9:0-10:0) and mono-unsaturated long-chain (16:1-22:1) fatty acids, and highest oxidation rates with lauroyl-CoA (12:0). Mitochondria showed the lowest Km for long-chain fatty acids (16:0-18:0) and highest oxidation rates with 12:0-16:0 and with 18:2. These in vitro results offer an explanation of previous results obtained in situ by Foerster et al. (Foerster, E.-C., F?hrenkemper, T., Rabo, U., Graf, P. and Sies, H. (1981) Biochem. J. 196, 705-712) and indicate a role for peroxisomes in degradation of medium-chain and mono-unsaturated long-chain fatty acids. It is concluded that no mechanism, other than relative preferences, needs to be suggested for channelling of fatty acids between the two subcellular organelles.     

Computational models for mechanics of morphogenesis

In the developing embryo, tissues differentiate, deform, and move in an orchestrated manner to generate various biological shapes driven by the complex interplay between genetic, epigenetic, and environmental factors. Mechanics plays a key role in regulating and controlling morphogenesis, and quantitative models help us understand how various mechanical forces combine to shape the embryo. Models allow for the quantitative, unbiased testing of physical mechanisms, and when used appropriately, can motivate new experimentaldirections. This knowledge benefits biomedical researchers who aim to prevent and treat congenital malformations, as well as engineers working to create replacement tissues in the laboratory. In this review, we first give an overview of fundamental mechanical theories for morphogenesis, and then focus on models for specific processes, including pattern formation, gastrulation, neurulation, organogenesis, and wound healing. The role of mechanical feedback in development is also discussed. Finally, some perspectives aregiven on the emerging challenges in morphomechanics and mechanobiology. Birth Defects Research (Part C) 96:132–152, 2012. © 2012 Wiley Periodicals, Inc.     

Computational models in systems biology

A report of the 6th International Conference on Computational Methods in Systems Biology, Rostock, Germany, 12-15 October 2008.One of the chief goals of systems biology is to build mechanistic mathematical models of biological systems to further the understanding of biological detail. Such models often aim at predicting the outcome of potentially interesting biological experiments, and if such predictions are confirmed by wet-lab observations, an important step forward is made. How exactly such models are constructed and how predictions are computed were at the core of a recent conference on Computational Methods in Systems Biology that brought 80 participants to Rostock, Germany (for conference proceedings see volume 5307 of Lecture Notes in Bioinformatics http://dx.doi.org/10.1007/978-3-540-88562-7).A simplistic approach to model construction might be to capture everything that is known about a system and simulate it in supercomputers. While this is appropriate for some systems, it is impossible or highly impracticable for many others. This is mostly due to the complexity of biological systems, which demand simplification to make them amenable to modeling. Such simplifications have to capture the essence of the processes of interest, while neglecting as many of the less important details as possible. Thus, one can consider model building in systems biology as the art of building caricatures of life: capture the essence, ignore the rest.     

Computational models in systems biology

A report of the 6th International Conference on Computational Methods in Systems Biology, Rostock, Germany, 12-15 October 2008.     

A Volterra representation for some neuron models

A Volterra-like polynomial representation is derived and its convergence discussed for two neuronal models in which subthreshold inputs are integrated either without loss (integrate and fire) or with a decay which follows an exponential time course (leaky integrator). This polynomial representation provides a kind of nonlinear transfer function for the nonlinear encoding process. Standard formulae are used to derive explicitely the output for various inputs as in linear system theory. Moreover, the nonlinear transfer function associated with cascades or networks of neurons can be also obtained. Finally, extensions and implications of these results are discussed.     

Biglycan knockout mice: new models for musculoskeletal diseases

Biglycan is a Class I Small Leucine Rich Proteoglycans (SLRP) that is localized on human chromosome Xq28-ter. The conserved nature of its intron-exon structure and protein coding sequence compared to decorin (another Class I SLRP) indicates the two genes may have arisen from gene duplication. Biglycan contains two chondroitin sulfate glycosaminoglycan (GAG) chains attached near its NH₂ terminus making it different from decorin that has only one GAG chain. To determine the functions of biglycan in vivo, transgenic mice were developed that were deficient in the production of the protein (knockout). These mice acquire diminished bone mass progressively with age. Double tetracycline-calcein labeling revealed that the biglycan deficient mice are defective in their capacity to form bone. Based on this observation, we tested the hypothesis that the osteoporosis-like phenotype is due to defects in cells critical to the process of bone formation. Our data shows that biglycan deficient mice have diminished capacity to produce marrow stromal cells, the bone cell precursors, and that this deficiency increases with age. The cells also have reduced response to tranforming growth factor- (TGF-), reduced collagen synthesis and relatively more apoptosis than cells from normal littermates. In addition, calvaria cells isolated from biglycan deficient mice have reduced expression of late differentiation markers such as bone sialoprotein and osteocalcin and diminished ability to accumulate calcium judged by alizerin red staining. We propose that any one of these defects in osteogenic cells alone, or in combination, could contribute to the osteoporosis observed in the biglycan knockout mice. Other data suggests there is a functional relationship between biglycan and bone morphogenic protein-2/4 (BMP 2/4) action in controlling skeletal cell differentiation. In order to test the hypothesis that functional compensation can occur between SLRPs, we created mice deficient in biglycan and decorin. Decorin deficient mice have normal bone mass while the double biglycan/decorin knockout mice have more severe osteopenia than the single biglycan indicating redundancy in SLRP function in bone tissue. To further determine whether compensation could occur between different classes of SLRPs, mice were generated that are deficient in both biglycan (class I) and fibromodulin, a class II SLRP highly expressed in mineralizing tissue. These doubly deficient mice had an impaired gait, ectopic calcification of tendons and premature osteoarthritis. Transmission electron microscopy analysis showed that like the decorin and biglycan knockouts, they have severely disturbed collagen fibril structures. Biomechanical analysis of the affected tendons showed they were weaker compared to control animals leading to the conclusion that instability of the joints could be the primary cause of all the skeletal defects observed in the fibromodulin/biglycan knockout mice. These studies present important new animal models for musculoskeletal diseases and provide the opportunity to characterize the network of signals that control tissue integrity and function through SLRP activity. Published in 2003.     

On evaluating models in Computational Morphodynamics

Recent advances in experimental plant biology have led to an increased potential to investigate plant development at a systems level. The emerging research field of Computational Morphodynamics has the aim to lead this development by combining dynamic spatial experimental data with computational models of molecular networks, growth, and mechanics in a multicellular context. The increased number of published models may lead to a diversification of our understanding of the systems, and methods for evaluating, comparing, and sharing models are main challenges for the future. We will discuss this problem using ideas originating from physics and use recent computational models of plant development as examples.     

Alternative time representation in dopamine models

Dopaminergic neuron activity has been modeled during learning and appetitive behavior, most commonly using the temporal-difference (TD) algorithm. However, a proper representation of elapsed time and of the exact task is usually required for the model to work. Most models use timing elements such as delay-line representations of time that are not biologically realistic for intervals in the range of seconds. The interval-timing literature provides several alternatives. One of them is that timing could emerge from general network dynamics, instead of coming from a dedicated circuit. Here, we present a general rate-based learning model based on long short-term memory (LSTM) networks that learns a time representation when needed. Using a naïve network learning its environment in conjunction with TD, we reproduce dopamine activity in appetitive trace conditioning with a constant CS-US interval, including probe trials with unexpected delays. The proposed model learns a representation of the environment dynamics in an adaptive biologically plausible framework, without recourse to delay lines or other special-purpose circuits. Instead, the model predicts that the task-dependent representation of time is learned by experience, is encoded in ramp-like changes in single-neuron activity distributed across small neural networks, and reflects a temporal integration mechanism resulting from the inherent dynamics of recurrent loops within the network. The model also reproduces the known finding that trace conditioning is more difficult than delay conditioning and that the learned representation of the task can be highly dependent on the types of trials experienced during training. Finally, it suggests that the phasic dopaminergic signal could facilitate learning in the cortex.     

Computational models of signalling networks for non-linear control

Artificial signalling networks (ASNs) are a computational approach inspired by the signalling processes inside cells that decode outside environmental information. Using evolutionary algorithms to induce complex behaviours, we show how chaotic dynamics in a conservative dynamical system can be controlled. Such dynamics are of particular interest as they mimic the inherent complexity of non-linear physical systems in the real world. Considering the main biological interpretations of cellular signalling, in which complex behaviours and robust cellular responses emerge from the interaction of multiple pathways, we introduce two ASN representations: a stand-alone ASN and a coupled ASN. In particular we note how sophisticated cellular communication mechanisms can lead to effective controllers, where complicated problems can be divided into smaller and independent tasks.     

Interpolation coding: A representation for numbers in neural models

A central task of perception can be defined as one of computing hierarchies of invariants. One way of representing such invariants in intermediate levels of abstraction in this hierarchy is to use discrete units. These have been termed value units. A problem with such an encoding is that there has not been a good way to represent accurate numerical quantities using these units. This paper remedies the deficiency by describing a scheme that interpolates values between units representing fixed numerical quantities. The scheme has nice properties: it extends across functional mappings and it allows different sources of evidence to be combined.This work was supported in part by the National Science Foundation under Grant DCR-8405720 and the National Institutes of Health under Public Health Service Grant 1R01NS22407-01     

Computational models for neurogenic gene expression in the Drosophila embryo

The early Drosophila embryo is emerging as a premiere model system for the computational analysis of gene regulation in development because most of the genes, and many of the associated regulatory DNAs, that control segmentation and gastrulation are known. The comprehensive elucidation of Drosophila gene networks provides an unprecedented opportunity to apply quantitative models to metazoan enhancers that govern complex patterns of gene expression during development. Models based on the fractional occupancy of defined DNA binding sites have been used to describe the regulation of the lac operon in E. coli and the lysis/lysogeny switch of phage lambda. Here, we apply similar models to enhancers regulated by the Dorsal gradient in the ventral neurogenic ectoderm (vNE) of the early Drosophila embryo. Quantitative models based on the fractional occupancy of Dorsal, Twist, and Snail binding sites raise the possibility that cooperative interactions among these regulatory proteins mediate subtle differences in the vNE expression patterns. Variations in cooperativity may be attributed to differences in the detailed linkage of Dorsal, Twist, and Snail binding sites in vNE enhancers. We propose that binding site occupancy is the key rate-limiting step for establishing localized patterns of gene expression in the early Drosophila embryo.     

Computational models of grid cells

Grid cells are space-modulated neurons with periodic firing fields. In moving animals, the multiple firing fields of an individual grid cell form a triangular pattern tiling the entire space available to the animal. Collectively, grid cells are thought to provide a context-independent metric representation of the local environment. Since the discovery of grid cells in 2005, a number of models have been proposed to explain the formation of spatially repetitive firing patterns as well as the conversion of these signals to place signals one synapse downstream in the hippocampus. The present article reviews the most recent developments in our understanding of how grid patterns are generated, maintained, and transformed, with particular emphasis on second-generation computational models that have emerged during the past 2-3 years in response to criticism and new data.     

Computational models of association cortex

Recent computational models, or mathematical realizations of neurobiological theories, are providing insights into the organization and workings of the association cortex. Such models concern the construction of cortical maps, the neural basis of cognitive functions such as visual perception, reward-motivated learning and some aspects of consciousness.     

Computational models in genetics at BGRS-2018

Background

Ticks are a problem for cattle production mainly in tropical and subtropical regions, because they generate great economic losses. Acaricides and vaccines have been used to try to keep tick populations under control. This has been proven difficult given the resistance to acaricides and vaccines observed in ticks. Resistance to protein rBm86-based vaccines has been associated with the genetic diversity of Bm86 among the ectoparasite’s populations. So far, neither genetic diversity, nor spatial distribution of circulating Bm86 haplotypes, have been studied within the Mexican territory. Here, we explored the genetic diversity of 125 Bm86 cDNA gene sequences from R. microplus from 10 endemic areas of Mexico by analyzing haplotype distribution patterns to help in understanding the population genetic structure of Mexican ticks.

Results

Our results showed an average nucleotide identity among the Mexican isolates of 98.3%, ranging from 91.1 to 100%. Divergence between the Mexican and Yeerongpilly (the Bm86 reference vaccine antigen) sequences ranged from 3.1 to 7.4%. Based on the geographic distribution of Bm86 haplotypes in Mexico, our results suggest gene flow occurrence within different regions of the Mexican territory, and even the USA.

Conclusions

The polymorphism of Bm86 found in the populations included in this study, could account for the poor efficacy of the current Bm86 antigen based commercial vaccine in many regions of Mexico. Our data may contribute towards designing new, highly-specific, Bm86 antigen vaccine candidates against R. microplus circulating in Mexico.

     

Computational models for the prediction of polypeptide aggregation propensity

In amyloid fibrils, beta-strand conformations of polypeptide chains, or segments thereof, are perpendicular to the fibril axis, but knowledge of their three dimensional structure at atomic level of detail is scarce. Two types of computational approaches have been developed recently for investigating the aggregation propensity of peptides and proteins and identifying the segments most prone to form fibrils (hot spots). The physicochemical properties of the natural amino acids (e.g. beta-propensity, hydrophobicity, aromatic content and charge) have been used to derive phenomenological models able to predict changes in aggregation rate upon mutation, as well as absolute rates and hot spots. Applications of these models to entire proteomes have provided evidence that intrinsically disordered proteins are less amyloidogenic than globular proteins. In the second type of approach, amyloidogenic polypeptides have been decomposed into overlapping segments, and atomistic simulations of three or more copies of each segment have been performed to obtain insights into aggregation propensity and structural details of the ordered aggregates (e.g. turn regions).