Interaction between muscle cell and external mechanical field: a model study

We have suggested a mathematical model of the muscle cell membrane on the basis of the thin elastic rods theory which takes external mechanic effects into account. We have also performed a quantitative analysis of deformation of rodent shin muscles when exposed to hindlimb suspension. Maximal deformation is shown to be typical for soleus muscle fibers and their magnitude is connected with stiffness of the cortical cytoskeleton.     

Mechanisms of cardiac cell excitation with premature monophasic and biphasic field stimuli: a model study.

The mechanisms by which extracellular electric field stimuli induce the (re)excitation of cardiac cells in various stages of refractoriness are still not well understood. We modeled the interactions between an isolated cardiac cell and imposed extracellular electric fields to determine the mechanisms by which relatively low-strength uniform monophasic and biphasic field stimuli induce premature reexcitations. An idealized ventricular cell was simulated with 11 subcellular membrane patches, each of which obeyed Luo-Rudy (phase 1) kinetics. Implementing a standard S1-S2 pulse protocol, strength-interval maps of the cellular excitatory responses were generated for rectangular monophasic and symmetric biphasic field stimuli of 2, 5, 10, and 20 ms total duration. In contrast to previously documented current injection studies, our results demonstrate that a cardiac cell exhibits a significantly nonmonotonic excitatory response to premature monophasic and, to a much lesser degree, biphasic field stimuli. Furthermore, for monophasic stimuli at low field strengths, the cell is exquisitely sensitive to the timing of the shock, demonstrating a classic all-or-none depolarizing response. However, at higher field strengths this all-or-none sensitivity reverts to a more gradual transition of excitatory responses with respect to stimulus prematurity. In contrast, biphasic stimuli produce such graded responses at all suprathreshold stimulus strengths. Similar behaviors are demonstrated at all S2 stimulus durations tested. The generation of depolarizing (sodium) currents is triggered by one or more of the sharp field gradient changes produced at the stimulus edges-i.e., make, break, and transphasic (for biphasic stimuli)-with the magnitude of these edge-induced current contributions dependent on both the prematurity and the strength of the applied field. In all cases, however, depolarizing current arises from the partial removal of sodium inactivation from at least part of the cell, because of either the natural process of repolarization or a localized acceleration of this process by the impressed field.     

Surfing on the seascape: Adaptation in a changing environment

The environment changes constantly at various time scales and, in order to survive, species need to keep adapting. Whether these species succeed in avoiding extinction is a major evolutionary question. Using a multilocus evolutionary model of a mutation‐limited population adapting under strong selection, we investigate the effects of the frequency of environmental fluctuations on adaptation. Our results rely on an “adaptive‐walk” approximation and use mathematical methods from evolutionary computation theory to investigate the interplay between fluctuation frequency, the similarity of environments, and the number of loci contributing to adaptation. First, we assume a linear additive fitness function, but later generalize our results to include several types of epistasis. We show that frequent environmental changes prevent populations from reaching a fitness peak, but they may also prevent the large fitness loss that occurs after a single environmental change. Thus, the population can survive, although not thrive, in a wide range of conditions. Furthermore, we show that in a frequently changing environment, the similarity of threats that a population faces affects the level of adaptation that it is able to achieve. We check and supplement our analytical results with simulations.     

Repetitive firing: a quantitative study of feedback in model encoders

Recognition of nonlinearities in the neuronal encoding of repetitive spike trains has generated a number of models to explain this behavior. Here we develop the mathematics and a set of tests for two such models: the leaky integrator and the variable-gamma model. Both of these are nearly sufficient to explain the dynamic behavior of a number of repetitively firing, sensory neurons. Model parameters can be related to possible underlying basic mechanisms. Summed and nonsummed, spike- locked negative feedback are examined in conjunction with the models. Transfer functions are formulated to predict responses to steady state, steps, and sinusoidally varying stimuli in which output data are the times of spike-train events only. An electrical analog model for the leaky integrator is tested to verify predicted responses. Curve fitting and parameter variation techniques are explored for the purpose of extracting basic model parameters from spike train data. Sinusoidal analysis of spike trains appear to be a very accurate method for determining spike-locked feedback parameters, and it is to a large extent a model independent method that may also be applied to neuronal responses.     

Regulation of plant cell wall stiffness by mechanical stress: a mesoscale physical model

Journal of Mathematical Biology - A crucial question in developmental biology is how cell growth is coordinated in living tissue to generate complex and reproducible shapes. We address this issue...     

Engineered heart tissue enables study of residual undifferentiated embryonic stem cell activity in a cardiac environment

Embryonic stem cell (ESC) derivatives are a promising cell source for cardiac cell therapy. Mechanistic studies upon cell injection in conventional animal models are limited by inefficient delivery and poor cell survival. As an alternative, we have used an engineered heart tissue (EHT) based on neonatal rat cardiomyocytes (CMs) cultivated with electrical field stimulation as an in vitro model to study cell injection. We injected (0.001, 0.01, and 0.1 million) and tracked (by qPCR and histology) undifferentiated yellow‐fluorescent protein transgenic mouse ESCs and Flk1 + /PDGFRα+ cardiac progenitor (CPs) cells, to investigate the effect of the cardiac environment on cell differentiation, as well as to test whether our in vitro model system could recapitulate the formation of teratoma‐like structures commonly observed upon in vivo ESC injection. By 8 days post‐injection, ESCs were spatially segregated from the cardiac cell population; however, ESC injection increased survival of CMs. The presence of ESCs blocked electrical conduction through the tissue, resulting in a 46% increase in the excitation threshold. Expression of mouse cardiac troponin I, was markedly increased in CP injected constructs compared to ESC injected constructs at all time points and cell doses tested. As early as 2 weeks, epithelial and ganglion‐like structures were observed in ESC injected constructs. By 4 weeks of ESC injection, teratoma‐like structures containing neural, epithelial, and connective tissue were observed in the constructs. Non‐cardiac structures were observed in the CP injected constructs only after extended culture (4 weeks) and only at high cell doses, suggesting that these cells require further enrichment or differentiation prior to transplantation. Our data indicate that the cardiac environment of host tissue and electrical field stimulation did not preferentially guide the differentiation of ESCs towards the cardiac lineage. In the same environment, injection of CP resulted in a more robust cardiac differentiation than injection of ESC. Our data demonstrate that the model‐system developed herein can be used to study the functional effects of candidate stem cells on the host myocardium, as well as to measure the residual activity of undifferentiated cells present in the mixture. Biotechnol. Bioeng. 2011; 108:704–719. © 2010 Wiley Periodicals, Inc.     

Streptomycetes: a new model to study cell death.

Colonies of streptomycetes are now viewed as multicellular entities containing morphologically and biochemically differentiated cell types which have specific functions and precise spatial relationships to one another. Like multicellular organisms, colony development in streptomycetes is also maintained by a tight balance between cell proliferation and cell death processes. This review describes the current state of knowledge concerning cell death in streptomycetes.     

The mechanical environment of the chondrocyte: a biphasic finite element model of cell-matrix interactions in articular cartilage

Mechanical compression of the cartilage extracellular matrix has a significant effect on the metabolic activity of the chondrocytes. However, the relationship between the stress–strain and fluid-flow fields at the macroscopic “tissue” level and those at the microscopic “cellular” level are not fully understood. Based on the existing experimental data on the deformation behavior and biomechanical properties of articular cartilage and chondrocytes, a multi-scale biphasic finite element model was developed of the chondrocyte as a spheroidal inclusion embedded within the extracellular matrix of a cartilage explant. The mechanical environment at the cellular level was found to be time-varying and inhomogeneous, and the large difference (3 orders of magnitude) in the elastic properties of the chondrocyte and those of the extracellular matrix results in stress concentrations at the cell–matrix border and a nearly two-fold increase in strain and dilatation (volume change) at the cellular level, as compared to the macroscopic level. The presence of a narrow “pericellular matrix” with different properties than that of the chondrocyte or extracellular matrix significantly altered the principal stress and strain magnitudes within the chondrocyte, suggesting a functional biomechanical role for the pericellular matrix. These findings suggest that even under simple compressive loading conditions, chondrocytes are subjected to a complex local mechanical environment consisting of tension, compression, shear, and fluid pressure. Knowledge of the local stress and strain fields in the extracellular matrix is an important step in the interpretation of studies of mechanical signal transduction in cartilage explant culture models.     

A Leydig cell tumour: a model for the study of lutropin action.

The properties of cells isolated from a Leydig cell tumour have been compared with normal rat testis Leydig cells. These cells were found to be similar in the following respects: 1. Lutropin-stimulated cyclic AMP and testosterone production. 2. Lutropin-activated protein kinase activity followed by phosphorylation of endogenous proteins of mol. wts. 57,000and 14,000. 3. Parallel lutropin dose vs. response curves for phosphorylation of the endogenous proteins and for testosterone production. 4. Two forms of isoenzyme, cyclic AMP dependent protein kinase, present. They differed mainly with respect to the lutropin-stimulated testosterone production, which was much lower in the tumour cells compared with the normal adult testis Leydig cells (4.6 +/- 1.1 and 114 +/- 16 ng testosterone/10(6) cells per 2 h, respectively). However, the lutropin-stimulated steroid production in the tumour cells was quantitatively comparable with the normal rat Leydig cell when the metabolism of pregnenolone in intact cells and mitochondria was inhibited by addition of SU-10603 and/or cyanoketone. It is concluded that the Leydig cell tumour used in this study can be used to investigate certain aspects of lutropin action where large quantities of cells are required.     

SER-HIS-ASP catalytic triad in model non-aqueous solvent environment: a computational study

Emerging new properties and applications of enzymes in organic solvents and ionic liquids are unabating. By applying a combined Quantum Mechanics/Continuum Mechanics computation on a prototypical catalytic triad serine-histidine-aspartate (SER-HIS-ASP) interacting with ethanol or acetonitrile molecules, the major difference between protic and aprotic solvents in effecting transition-state stabilization has been analyzed. Moderately polar aprotic solvent acetonitrile is predicted to be unable to stabilize the transition state in replacing the role of the oxyanion-hole environment, whereas protic ethanol solvent molecules of similar polarity to acetonitrile are adequate in re-gaining the enzymatic activities.     

Sink feedback regulation of photosynthesis in vines: measurements and a model.

An experimental and modelling study of source-sink interactions in Vitis vinifera L., cv. Cabernet Sauvignon, rooted cuttings under non-limiting environmental conditions with a 12 h photoperiod is presented here. After 4 h, measured photosynthesis, stomatal conductance and leaf carbohydrate content reached maximum values. Over the remainder of the photoperiod, photosynthesis and stomatal conductance decreased continuously, whereas leaf carbohydrate content remained relatively constant. Because the experiment took place in a non-limiting environment, the results suggest that stomatal regulation of photosynthesis was mediated by an internal factor, possibly related to sink activity. A simple 1-source, 2-sink model was developed to examine the extent to which the data could be explained by a hypothetical sink-to-source feedback mechanism mediated by carbohydrate levels in either the mesophyll, the source phloem or the phloem of one of the two sinks. Model simulations reproduced the data well under the hypothesis of a phloem-based feedback signal, although the data were insufficient to elucidate the detailed nature of such a signal. In a sensitivity analysis, the steady-state response of photosynthesis to sink activity was explored and predictions made for the partitioning of photosynthate between the two sinks. The analysis highlights the effectiveness of a phloem-based feedback signal in regulating the balance between source and sink activities. However, other mechanisms for the observed decline in photosynthesis, such as photoinhibition, endogenous circadian rhythms or hydraulic signals in the leaf cannot be excluded. Nevertheless, it is concluded that the phloem-based feedback model developed here may provide a useful working hypothesis for incorporation into plant growth models and for further development and testing.     

Adaptation to mechanical load determines shape and properties of heart and circulation: the CircAdapt model

With circulatory pathology, patient-specific simulation of hemodynamics is required to minimize invasiveness for diagnosis, treatment planning, and followup. We investigated the advantages of a smart combination of often already known hemodynamic principles. The CircAdapt model was designed to simulate beat-to-beat dynamics of the four-chamber heart with systemic and pulmonary circulation while incorporating a realistic relation between pressure-volume load and tissue mechanics and adaptation of tissues to mechanical load. Adaptation was modeled by rules, where a locally sensed signal results in a local action of the tissue. The applied rules were as follows: For blood vessel walls, 1) flow shear stress dilates the wall and 2) tensile stress thickens the wall; for myocardial tissue, 3) strain dilates the wall material, 4) larger maximum sarcomere length increases contractility, and 5) contractility increases wall mass. The circulation was composed of active and passive compliances and inertias. A realistic circulation developed by self-structuring through adaptation provided mean levels of systemic pressure and flow. Ability to simulate a wide variety of patient-specific circumstances was demonstrated by application of the same adaptation rules to the conditions of fetal circulation followed by a switch to the newborn circulation around birth. It was concluded that a few adaptation rules, directed to normalize mechanical load of the tissue, were sufficient to develop and maintain a realistic circulation automatically. Adaptation rules appear to be the key to reduce dramatically the number of input parameters for simulating circulation dynamics. The model may be used to simulate circulation pathology and to predict effects of treatment.     

Adaptation to a limiting environment: the phosphorus content of terrestrial cave arthropods

Stoichiometric imbalances (mismatches between elemental ratios of consumers and their food) are expected to be especially important in detritus-based systems because poor resource quality may impose severe growth constraints. Such imbalances have been highlighted in producer-based food webs and detritus-based aquatic systems, but similar investigations of detritus-based terrestrial ecosystems are absent. Cave animals are dependent on detrital subsidies from the surface and display adaptations to caves (e.g., decreased growth and metabolic rates). Here we examined how nutrient quality may constrain consumer strategies in caves. We found that the quality of cave resources was comparable to resources on the surface, but there was some evidence that cave animals may face nutritional constraints for at least a part of the year. Such constraints may be especially important for millipedes, whose C:P was particularly low (i.e., nutrient-demanding) relative to cave detritus. Based on the growth rate hypothesis, we predicted that cave-adapted species would have lower %P, lower %RNA, and a lower RNA/DNA ratio relative to surface-dwelling counterparts; however, the differences we discovered between congeneric millipedes may not necessarily be due to P scarcity. Consistent with stoichiometric theory, we found significant negative %P allometry across phylogenetic groupings of 17 cave arthropods. We did not see this allometric relationship in millipedes, perhaps because of the lowered P content of the cave-obligate species. Our results highlight the potential for stoichiometric challenges of caves to influence the adaptations of terrestrial cave animals. This novel explanation for cave adaptation may yield insights into cave biodiversity and biogeography.     

Dimorphism in Histoplasma capsulatum: a model for the study of cell differentiation in pathogenic fungi.

Several fungi can assume either a filamentous or a unicellular morphology in response to changes in environmental conditions. This process, known as dimorphism, is a characteristic of several pathogenic fungi, e.g., Histoplasma capsulatum, Blastomyces dermatitidis, and Paracoccidioides brasiliensis, and appears to be directly related to adaptation from a saprobic to a parasitic existence. H. capsulatum is the most extensively studied of the dimorphic fungi, with a parasitic phase consisting of yeast cells and a saprobic mycelial phase. In culture, the transition of H. capsulatum from one phase to the other can be triggered reversibly by shifting the temperature of incubation between 25 degrees C (mycelia) and 37 degrees C (yeast phase). Mycelia are found in soil and never in infected tissue, in contrast to the yeast phase, which is the only form present in patients. The temperature-induced phase transition and the events in establishment of the disease state are very likely to be intimately related. Furthermore, the temperature-induced phase transition implies that each growth phase is an adaptation to two critically different environments. A fundamental question concerning dimorphism is the nature of the signal(s) that responds to temperature shifts. So far, both the responding cell component(s) and the mechanism(s) remain unclear. This review describes the work done in the last several years at the biochemical and molecular levels on the mechanisms involved in the mycelium to yeast phase transition and speculates on possible models of regulation of morphogenesis in dimorphic pathogenic fungi.     

Heterogeneous cell mechanical properties: an atomic force microscopy study.

Atomic force microscopy (AFM) is a non-invasive microscopy to explore living biological systems like cells in liquid environment. Thus AFM is an appropriate tool to investigate surface chemical modification and its influence on biological systems. In particular, control over biomaterial surface chemistry can result in a regulated cell response. This report investigates the influence of adhesive and non-adhesive surfaces on the cell morphology and the influence of the cytoskeleton structure on the local mechanical properties. In this study, the main work concerns a thorough investigation of the height images obtained with an AFM as therecorded images provide the evolution of the mechanical properties of the cell as function of its local structure. Information on the cell elasticity due to the cytoskeleton organization is deduced when comparing the AFM tip indentation depth versus the distance between the cytoskeleton bundles for the different samples.     

The elliptocyte: a study of the relationship between cell shape and membrane structure using the camelid erythrocyte as a model

1. The elliptocytic shape of the camelid erythrocyte is very stable and has a high resistance to modification by drugs and treatment which alter the shape of the discocytic erythrocytes of scimitar-horned oryx and man. 2. Differences in the erythrocyte membrane proteins have been found which indicate that proteins play an important role in stabilisation of the camelid elliptocyte. 3. The organisation of the cytoskeletal network in camelid elliptocytes differs from that established for human discocytes.     

Toward a generalised tensegrity model describing the mechanical behaviour of the cytoskeleton structure

The control of many cell functions including growth, migration and mechanotransduction, depends crucially on stress-induced mechanical changes in cell shape and cytoskeleton (CSK) structure. Quantitative studies have been carried out on 6-bar tensegrity models to analyse several mechanical parameters involved in the mechanical responses of adherent cells (i.e. strain hardening, internal stress and scale effects). In the present study, we attempt to generalize some characteristic mechanical laws governing spherical tensegrity structures, with a view of evaluating the mechanical behaviour of the hierarchical multi-modular CSK-structure. The numerical results obtained by studying four different tensegrity models are presented in terms of power laws and point to the existence of unique and constant relationships between the overall structural stiffness and the local properties (length, number and internal stress) of the constitutive components.