Mechanochemical Symmetry Breaking in Hydra Aggregates

Tissue morphogenesis comprises the self-organized creation of various patterns and shapes. Although detailed underlying mechanisms are still elusive in many cases, an increasing amount of experimental data suggests that chemical morphogen and mechanical processes are strongly coupled. Here, we develop and test a minimal model of the axis-defining step (i.e., symmetry breaking) in aggregates of the Hydra polyp. Based on previous findings, we combine osmotically driven shape oscillations with tissue mechanics and morphogen dynamics. We show that the model incorporating a simple feedback loop between morphogen patterning and tissue stretch reproduces a wide range of experimental data. Finally, we compare different hypothetical morphogen patterning mechanisms (Turing, tissue-curvature, and self-organized criticality). Our results suggest the experimental investigation of bigger (i.e., multiple head) aggregates as a key step for a deeper understanding of mechanochemical symmetry breaking in Hydra.     

Ovoid geometry of the Pacinian corpuscle is not the determining factor for mechanical excitation

Static displacements in Pacinian corpuscles (PCs) were measured using video microscopy. Mechanical stimuli of 10-40 microm steps were applied to the PC capsule surfaces using cylindrical contacts with different diameters. Displacements parallel to the stimulation axis were measured at various locations in the focal plane of the optical setup. In contrast to previous data in the literature, the displacements within the corpuscle were found to be linearly related to the indentation amplitude. Displacements decreased as a function of lamella depth, with a more negative slope close to the surface and less negative slope at deeper locations. The experimental data were compared to the predictions of a previous mechanical model, and to the results of two new models: (1) elastic semi-infinite continuum model; (2) ovoid isotropic finite-element model. Although the previous model did not specify displacement boundary conditions, it predicted the current experimental results well. On the other hand, the experimental displacements were found to be smaller than those predicted by the semi-infinite continuum and finite-element models. However, both semi-infinite continuum and finite-element models yielded close results, which show that the three-dimensional ovoid geometry of the corpuscle is not the primary factor for determining the displacements in physiological conditions. Furthermore, simulations with the finite-element model using a wide range of material properties yielded similar results. This supports the hypothesis that a homogeneous isotropic model for the PC cannot predict experimental results. The modeling analyses suggest that the experimental results are largely affected by the displacement of the incompressible interlamellar fluid and the layered structure of the corpuscle.     

Development of a novel MATLAB-based framework for implementing mechanical joint stability constraints within OpenSim musculoskeletal models

The Static Optimization (SO) solver in OpenSim estimates muscle activations and forces that only equilibrate applied moments. In this study, SO was enhanced through an open-access MATLAB interface, where calculated muscle activations can additionally satisfy crucial mechanical stability requirements. This Stability-Constrained SO (SCSO) is applicable to many OpenSim models and can potentially produce more biofidelic results than SO alone, especially when antagonistic muscle co-contraction is required to stabilize body joints. This hypothesis was tested using existing models and experimental data in the literature. Muscle activations were calculated by SO and SCSO for a spine model during two series of static trials (i.e. simulation 1 and 2), and also for a lower limb model (supplementary material 2). In simulation 1, symmetric and asymmetric flexion postures were compared, while in simulation 2, various external load heights were compared, where increases in load height did not change the external lumbar flexion moment, but necessitated higher EMG activations. During the tasks in simulation 1, the predicted muscle activations by SCSO demonstrated less average deviation from the EMG data (6.8% −7.5%) compared to those from SO (10.2%). In simulation 2, SO predicts constant muscle activations and forces, while SCSO predicts increases in the average activations of back and abdominal muscles that better match experimental data. Although the SCSO results are sensitive to some parameters (e.g. musculotendon stiffness), when considering the strategy of the central nervous system in distributing muscle forces and in activating antagonistic muscles, the assigned activations by SCSO are more biofidelic than SO.     

Ovoid geometry of the Pacinian corpuscle is not the determining factor for mechanical excitation

Static displacements in Pacinian corpuscles (PCs) were measured using video microscopy. Mechanical stimuli of 10–40?µm steps were applied to the PC capsule surfaces using cylindrical contactors with different diameters. Displacements parallel to the stimulation axis were measured at various locations in the focal plane of the optical setup. In contrast to previous data in the literature, the displacements within the corpuscle were found to be linearly related to the indentation amplitude. Displacements decreased as a function of lamella depth, with a more negative slope close to the surface and less negative slope at deeper locations. The experimental data were compared to the predictions of a previous mechanical model, and to the results of two new models: () elastic semi-infinite continuum model; () ovoid isotropic finite-element model. Although the previous model did not specify displacement boundary conditions, it predicted the current experimental results well. On the other hand, the experimental displacements were found to be smaller than those predicted by the semi-infinite continuum and finite-element models. However, both semi-infinite continuum and finite-element models yielded close results, which show that the three-dimensional ovoid geometry of the corpuscle is not the primary factor for determining the displacements in physiological conditions. Furthermore, simulations with the finite-element model using a wide range of material properties yielded similar results. This supports the hypothesis that a homogeneous isotropic model for the PC cannot predict experimental results. The modeling analyses suggest that the experimental results are largely affected by the displacement of the incompressible interlamellar fluid and the layered structure of the corpuscle.     

A computational model of limb impedance control based on principles of internal model uncertainty

Efficient human motor control is characterized by an extensive use of joint impedance modulation, which is achieved by co-contracting antagonistic muscles in a way that is beneficial to the specific task. While there is much experimental evidence available that the nervous system employs such strategies, no generally-valid computational model of impedance control derived from first principles has been proposed so far. Here we develop a new impedance control model for antagonistic limb systems which is based on a minimization of uncertainties in the internal model predictions. In contrast to previously proposed models, our framework predicts a wide range of impedance control patterns, during stationary and adaptive tasks. This indicates that many well-known impedance control phenomena naturally emerge from the first principles of a stochastic optimization process that minimizes for internal model prediction uncertainties, along with energy and accuracy demands. The insights from this computational model could be used to interpret existing experimental impedance control data from the viewpoint of optimality or could even govern the design of future experiments based on principles of internal model uncertainty.     

A minimal mathematical model of human periodic breathing

Numerous mathematical models of periodic breathing (PB) currently exist. These models suggest mechanisms that may underlie many known causes of PB. However, each model that has been shown to simulate PB under reasonable conditions contains greater than 15 physiological parameters. Because some parameters exhibit a wide range of values in a population, such simulations cannot test a model's ability to account for the breathing patterns of individuals. Furthermore it is impractical to perform a direct experimental validation study that would require the estimation of each of 15 or more parameters for each subject. A minimal model of PB is presented that is suitable for direct validation. Analytic expressions are given that define the conditions for PB in terms of the following: 1) CO2 sensitivity, 2) Cardiac output, 3) Mixed venous CO2, 4) Circulation time, and 5) Mean lung volume for CO2. This model is shown to be consistent with previous models and experimental data regarding the degree of hypoxia or congestive heart failure required to produce PB. A quantitative measure of relative stability is defined as a metric of comparison to the human studies described in the accompanying paper (J. Appl. Physiol. 65: 1389-1399, 1988).     

Universal scaling of species‐abundance distributions across multiple scales

The scale‐dependent species abundance distribution (SAD) is fundamental in ecology, but few spatially explicit models of this pattern have thus far been studied. Here we show spatially explicit neutral model predictions for SADs over a wide range of spatial scales, which appear to match empirical patterns qualitatively. We find that the assumption of a log‐series SAD in the metacommunity made by spatially implicit neutral models can be justified with a spatially explicit model in the large area limit. Furthermore, our model predicts that SADs on multiple scales are characterized by a single, compound parameter that represents the ratio of the survey area to the species’ average biogeographic range (which is in turn set by the speciation rate and the dispersal distance). This intriguing prediction is in line with recent empirical evidence for a universal scaling of the species‐area curve. Hence we hypothesize that empirical SAD patterns will show a similar universal scaling for many different taxa and across multiple spatial scales.     

Expanded thermodynamic true yield prediction model: adjustments and limitations

Bacterial yield prediction is critical for bioprocess optimization and modeling of natural biological systems. In previous work, an expanded thermodynamic true yield prediction model was developed through incorporating carbon balance and nitrogen balance along with electron balance and energy balance. In the present work, the application of the expanded model is demonstrated in multiple growth situations (aerobic heterotrophs, anoxic, anaerobic heterotrophs, and autolithotrophs). Two adjustments are presented that enable improved prediction when additional information regarding the environmental conditions (pH) or degradation pathway (requirement for oxygenase- or oxidase-catalyzed reactions) is known. A large data set of reported yields is presented and considered for suitability in model validation. Significant uncertainties of literature-reported yield values are described. Evaluation of the model with experimental yield values shows good predictive ability. However, the wide range in reported yields and the variability introduced into the prediction by uncertainty in model parameters, limits comprehensive validation. Our results suggest that the uncertainty of the experimental data used for validation limits further improvement of thermodynamic prediction models.     

Influence of dominance, leptokurtosis and pleiotropy of deleterious mutations on quantitative genetic variation at mutation-selection balance

In models of maintenance of genetic variance (V (G)) it has often been assumed that mutant alleles act additively. However, experimental data show that the dominance coefficient varies among mutant alleles and those of large effect tend to be recessive. On the basis of empirical knowledge of mutations, a joint-effect model of pleiotropic and real stabilizing selection that includes dominance is constructed and analyzed. It is shown that dominance can dramatically alter the prediction of equilibrium V (G). Analysis indicates that for the situations where mutations are more recessive for fitness than for a quantitative trait, as supported by the available data, the joint-effect model predicts a significantly higher V (G) than does an additive model. Importantly, for what seem to be realistic distributions of mutational effects (i.e., many mutants may not affect the quantitative trait substantially but are likely to affect fitness), the observed high levels of genetic variation in the quantitative trait under strong apparent stabilizing selection can be generated. This investigation supports the hypothesis that most V (G) comes from the alleles nearly neutral for fitness in heterozygotes while apparent stabilizing selection is contributed mainly by the alleles of large effect on the quantitative trait. Thus considerations of dominance coefficients of mutations lend further support to our previous conclusion that mutation-selection balance is a plausible mechanism of the maintenance of the genetic variance in natural populations.     

The scaling or ontogeny of human gait kinetics and walk-run transition: The implications of work vs. peak power minimization

A simple model is developed to find vertical force profiles and stance durations that minimize either limb mechanical work or peak power demands during bipedal locomotion. The model predicts that work minimization is achieved with a symmetrical vertical force profile, consistent with previous models and observations of adult humans, and data for 487 participants (predominantly 11–18 years old) required to walk at a range of speeds at a Science Fair. Work minimization also predicts the discrete walk-run transition, familiar for adult humans. In contrast, modeled peak limb mechanical power demands are minimized with an early skew in vertical ground reaction force that increases with speed, and stance durations that decrease steadily with speed across the work minimizing walk-run transition speed. The peak power minimization model therefore predicts a continuous walk-run gait transition that is quantitatively consistent with measurements of younger children (1.1–4.7 years) required to locomote at a range of speeds but free to select their own gaits.     

Stabilization of Structured Populations via Vector Target-Oriented Control

In contrast with unstructured models, structured discrete population models have been able to fit and predict chaotic experimental data. However, most of the chaos control techniques in the literature have been designed and analyzed in a one-dimensional setting. Here, by introducing target-oriented control for discrete dynamical systems, we prove the possibility to stabilize a chosen state for a wide range of structured population models. The results are illustrated with introducing a control in the celebrated LPA model describing a flour beetle dynamics. Moreover, we show that the new control allows to stabilize periodic solutions for higher-order difference equations, such as the delayed Ricker model, for which previous target-oriented methods were not designed.     

Geometric peculiarities of intestinal surface and efficiency of coupling between membrane hydrolysis and transport of nutrients

Kinetics of the membrane hydrolysis of maltose and of the absorption of the released glucose in the isolated loop of rat small intestine has been examined in a wide range of maltose concentrations (25–200 mM) under the conditions of chronic experiments. The processes studied were simulated by means of mathematical models using two approximations of the villous surface of intestinal epithelium: (i) smooth flat surface with adjoining pre-epithelial (“unstirred”) layer and (ii) folded surface with “unstirred” layer between the folds and partly above them. The results of modeling matched well the experimental data in the whole range of maltose concentrations only in the case of the folded surface. A model with this approximation predicts a closer coupling between maltose hydrolysis and absorption of released glucose as well as a lower glucose concentration in the intestinal lumen than in the case of a flat surface. We conclude that in order to evaluate correctly a relative role of various mechanisms of glucose transport across intestinal epithelium under normal conditions, one should take into account the pre-epithelial layer of the small intestine and geometric peculiarities of its epithelial surface.     

cgDNA: a software package for the prediction of sequence-dependent coarse-grain free energies of B-form DNA

cgDNA is a package for the prediction of sequence-dependent configuration-space free energies for B-form DNA at the coarse-grain level of rigid bases. For a fragment of any given length and sequence, cgDNA calculates the configuration of the associated free energy minimizer, i.e. the relative positions and orientations of each base, along with a stiffness matrix, which together govern differences in free energies. The model predicts non-local (i.e. beyond base-pair step) sequence dependence of the free energy minimizer. Configurations can be input or output in either the Curves+ definition of the usual helical DNA structural variables, or as a PDB file of coordinates of base atoms. We illustrate the cgDNA package by comparing predictions of free energy minimizers from (a) the cgDNA model, (b) time-averaged atomistic molecular dynamics (or MD) simulations, and (c) NMR or X-ray experimental observation, for (i) the Dickerson–Drew dodecamer and (ii) three oligomers containing A-tracts. The cgDNA predictions are rather close to those of the MD simulations, but many orders of magnitude faster to compute. Both the cgDNA and MD predictions are in reasonable agreement with the available experimental data. Our conclusion is that cgDNA can serve as a highly efficient tool for studying structural variations in B-form DNA over a wide range of sequences.     

A computational model of dendrite elongation and branching based on MAP2 phosphorylation

We introduce a new computational model of dendritic development in neurons. In contrast to previous models, our model explicitly includes cellular mechanisms involved in dendritic development. It is based on recent experimental data which indicates that the phosphorylation state of microtubule-associated protein 2 (MAP2) may play a key role in controlling dendritic elongation and branching (Audesirk et al., 1997). Dephosphorylated MAP2 favours elongation by promoting microtubule polymerization and bundling, whilst branching is more likely to occur when MAP2 is phosphorylated and microtubules are spaced apart. In the model, the rate of elongation and branching is directly determined by the ratio of phosphorylated to dephosphorylated MAP2. This is regulated by calmodulin-dependent protein kinase II (CaMKII) and calcineurin, which are both dependent on the intracellular calcium concentration. Results from computer simulations of the model suggest that the wide variety of branching patterns observed among different cell types may be generated by the same underlying mechanisms and that elongation and branching are not necessarily independent processes. The model predicts how the branching pattern will change following manipulations with calcium, CaMKII and MAP2 phosphorylation.     

Intra‐specific variability and plasticity influence potential tree species distributions under climate change

Aim To assess the effect of local adaptation and phenotypic plasticity on the potential distribution of species under future climate changes. Trees may be adapted to specific climatic conditions; however, species range predictions have classically been assessed by species distribution models (SDMs) that do not account for intra‐specific genetic variability and phenotypic plasticity, because SDMs rely on the assumption that species respond homogeneously to climate change across their range, i.e. a species is equally adapted throughout its range, and all species are equally plastic. These assumptions could cause SDMs to exaggerate or underestimate species at risk under future climate change. Location The Iberian Peninsula. Methods Species distributions are predicted by integrating experimental data and modelling techniques. We incorporate plasticity and local adaptation into a SDM by calibrating models of tree survivorship with adaptive traits in provenance trials. Phenotypic plasticity was incorporated by calibrating our model with a climatic index that provides a measure of the differences between sites and provenances. Results We present a new modelling approach that is easy to implement and makes use of existing tree provenance trials to predict species distribution models under global warming. Our results indicate that the incorporation of intra‐population genetic diversity and phenotypic plasticity in SDMs significantly altered their outcome. In comparing species range predictions, the decrease in area occupancy under global warming conditions is smaller when considering our survival–adaptation model than that predicted by a ‘classical SDM’ calibrated with presence–absence data. These differences in survivorship are due to both local adaptation and plasticity. Differences due to the use of experimental data in the model calibration are also expressed in our results: we incorporate a null model that uses survival data from all provenances together. This model always predicts less reduction in area occupancy for both species than the SDM calibrated with presence–absence. Main conclusions We reaffirm the importance of considering adaptive traits when predicting species distributions and avoiding the use of occurrence data as a predictive variable. In light of these recommendations, we advise that existing predictions of future species distributions and their component populations must be reconsidered.     

Proactive interference, retroactive interference--what about self-interference? A new interpretation of the recency-primacy shift

The recency-primacy shift (RPS) indicates that memory for early list items improves and memory for later items becomes worse as the retention interval between study and test increases. In this contribution, this puzzling experimental finding--memory improving with time--is found to be consistent with a model in which recognition is temporarily interfered with by its own storage process (self-interference). I show that this interpretation can qualitatively better account for the RPS experimental data than can the dimensional distinctiveness model, the only other outstanding explanation of the RPS. Two experimental predictions separate the 2 models: The dimensional distinctiveness model predicts no RPS for 2-item lists, in contrast to self-interference, and as the overall timescale is changed, the dimensional distinctiveness model predicts no difference in the RPS whereas self-interference predicts significant changes.     

Biological assessment of robust noise models in microarray data analysis

MOTIVATION: Although several recently proposed analysis packages for microarray data can cope with heavy-tailed noise, many applications rely on Gaussian assumptions. Gaussian noise models foster computational efficiency. This comes, however, at the expense of increased sensitivity to outlying observations. Assessing potential insufficiencies of Gaussian noise in microarray data analysis is thus important and of general interest. RESULTS: We propose to this end assessing different noise models on a large number of microarray experiments. The goodness of fit of noise models is quantified by a hierarchical Bayesian analysis of variance model, which predicts normalized expression values as a mixture of a Gaussian density and t-distributions with adjustable degrees of freedom. Inference of differentially expressed genes is taken into consideration at a second mixing level. For attaining far reaching validity, our investigations cover a wide range of analysis platforms and experimental settings. As the most striking result, we find irrespective of the chosen preprocessing and normalization method in all experiments that a heavy-tailed noise model is a better fit than a simple Gaussian. Further investigations revealed that an appropriate choice of noise model has a considerable influence on biological interpretations drawn at the level of inferred genes and gene ontology terms. We conclude from our investigation that neglecting the over dispersed noise in microarray data can mislead scientific discovery and suggest that the convenience of Gaussian-based modelling should be replaced by non-parametric approaches or other methods that account for heavy-tailed noise.     

The Hill model for binding myosin S1 to regulated actin is not equivalent to the McKillop-Geeves model

The Hill two-state cooperativity model and the McKillop-Geeves (McK-G) three-state model predict very similar binding traces of myosin subfragment 1 (S1) binding to regulated actin filaments in the presence and absence of calcium, and both fit the experimental data reasonably well [Chen et al., Biophys. J., 80, 2338-2349]. Here, we compared the Hill model and the McK-G model for binding myosin S1 to regulated actin against three sets of experimental data: the titration of regulated actin with S1 and the kinetics of S1 binding of regulated actin with either excess S1 to actin or excess actin to S1. Each data set was collected for a wide range of specified calcium concentrations. Both models were able to generate reasonable fits to the time course data and to titration data. The McK-G model can fit all three data sets with the same calcium-concentration-sensitive parameters. Only K(B) and K(T) show significant calcium dependence, and the parameters have a classic pCa curve. A unique set of the Hill model parameters was extremely difficult to estimate from the best fits of multiple sets of data. In summary, the McK-G cooperativity model more uniquely resolves parameters estimated from kinetic and titration data than the Hill model, predicts a sigmoidal dependence of key parameters with calcium concentration, and is simpler and more suitable for practical use.     

Experiments on movement of DNA regions in Escherichia coli evaluated by computer simulation

During the cell cycle of Escherichia coli DNA is replicated and segregated over two prospective daughter cells. Nucleoids as a whole separate gradually in line with cell elongation, but sub-nucleoid DNA regions may behave differently, separating non-gradually. We tested the ability of three models to predict the outcome of a fluorescent in situ hybridisation (FISH) experiment. We did this by comparing computer-simulated data with experimental data. The first model predicts gradual separation in line with cell elongation. The second model predicts that origins stick together for some time after duplication before one copy jumps to the other side of the cell (non-gradual separation). The simulated data of these models are very similar, indicating that FISH is not a suitable method to distinguish between these two models. The third model predicts that origins may be anywhere within the nucleoid(s). We found that simulated data using the third model resemble the experimental data most. However, DNA regions are not randomly localised in the cell, although their localisation is fuzzy. We propose that movement of DNA regions is the result of a combination of factors. Nucleoid segregation (or the forces behind it) dictates the overall direction of movement. Other factors, of which we show that diffusion could be an important one, move DNA in other directions giving rise to non-gradual movement in individual cells and contributing to variation in intracellular position per cell length in a population of cells.