The effect of resistance level and stability demands on recruitment patterns and internal loading of spine in dynamic flexion and extension using a simple trunk model

The effects of external resistance on the recruitment of trunk muscles in sagittal movements and the coactivation mechanism to maintain spinal stability were investigated using a simple computational model of iso-resistive spine sagittal movements. Neural excitation of muscles was attained based on inverse dynamics approach along with a stability-based optimisation. The trunk flexion and extension movements between 60° flexion and the upright posture against various resistance levels were simulated. Incorporation of the stability constraint in the optimisation algorithm required higher antagonistic activities for all resistance levels mostly close to the upright position. Extension movements showed higher coactivation with higher resistance, whereas flexion movements demonstrated lower coactivation indicating a greater stability demand in backward extension movements against higher resistance at the neighbourhood of the upright posture. Optimal extension profiles based on minimum jerk, work and power had distinct kinematics profiles which led to recruitment patterns with different timing and amplitude of activation.     

The effect of resistance level and stability demands on recruitment patterns and internal loading of spine in dynamic flexion and extension using a simple trunk model

The effects of external resistance on the recruitment of trunk muscles in sagittal movements and the coactivation mechanism to maintain spinal stability were investigated using a simple computational model of iso-resistive spine sagittal movements. Neural excitation of muscles was attained based on inverse dynamics approach along with a stability-based optimisation. The trunk flexion and extension movements between 60° flexion and the upright posture against various resistance levels were simulated. Incorporation of the stability constraint in the optimisation algorithm required higher antagonistic activities for all resistance levels mostly close to the upright position. Extension movements showed higher coactivation with higher resistance, whereas flexion movements demonstrated lower coactivation indicating a greater stability demand in backward extension movements against higher resistance at the neighbourhood of the upright posture. Optimal extension profiles based on minimum jerk, work and power had distinct kinematics profiles which led to recruitment patterns with different timing and amplitude of activation.     

The extracellular potential field of the single active nerve fiber in a volume conductor

The potential field of an active fiber in a uniform medium of infinite extent and within a nerve trunk is calculated from transmembrane potential data. The resulting distributions are given quantitatively. A comparison of both magnitude and field pattern in the nerve trunk and infinite medium environments is made and the effect of interstitial conductivity and nerve trunk diameter on potential magnitudes is considered.     

Extracellular potentials of a single myelinated nerve fiber in an unbounded volume conductor

The extracellular potentials of a single myelinated nerve fiber in an unbounded volume conductor were studied. The spatial distribution of the transmembrane potential was obtained by integrating the system of partial differential equations characterizing the electric processes in the active myelinated nerve fiber. The spatial distribution of the extracellular potentials at various radial distances in the volume conductor were calculated using the line source model. Up to a certain radial distance (500 m) the discontinuity of the action potential propagation is reflected in the extracellular potentials, while further in the volume conductor the potentials are smooth. The effect of the fiber diameter and the internodal distance on the volume conductor potentials as well as the changes in the magnitude of the extracellular potential (in the time domain) between two adjacent nodes at various radial distances were studied. The radial decline of the peak-to-peak amplitude of the extracellular potential depends on the radial coordinater of the field point and increases with the increase ofr.     

Yearly variation in recruitment and its effect on population dynamics inYoldia notabilis (Mollusca: Bivalvia), analyzed using projection matrix model

Long-term variation in recruitment was estimated by constructing projection matrices for a marine bivalve, Yoldia notabilis, at two stations in Otsuchi Bay, northeastern Japan, and the effects of its variation on population dynamics were examined using a simple matrix model. The matrix model was developed from the Leslie matrix, in which the population growth rate λ was expressed as a function of recruitment rate r₀. The equilibrium recruitment rate r_s, or the recruitment rate required to maintain population at constant size (λ=1), was expressed by the reciprocal of the reproductive value of a newly recruited individual. The estimates of r_s for the field population were lower at the shallower station than at the deeper station, reflecting higher survivorship and fecundity. Past recruitment rate estimated both by the field samplings for 3 years and by the back-calculation from the current age structure for over 10 years showed large yearly variation, ranging between 0 and 58.6×10⁻⁴. The estimates were larger than r_s, and hence, large enough to increase population size (λ>1) only in approximately one-third of the estimated years. This suggests that the population has been maintained by occasional successful recruitment occurring once every few years.     

A simple theory of peptide interactions on a membrane surface: excluded volume and entropic order

A simple theory of the interactions of peptides bound onto a lipid membrane is developed, modeling the peptides as rods on a surface. At low peptide surface-concentration, excluded volume dominates the peptide-peptide interactions and the orientation of the peptides is random, resulting in an isotropic configuration. However, at high peptide density on the membrane, the peptides become orientationally ordered, resulting in an anisotropic configuration. This effect is entirely entropic in origin, and simply reflects the fact that peptides can be exchanged more easily on the surface if they are equally aligned, resulting in a larger number of possible configurations. In three dimensions, this phenomenon corresponds to the well-known isotropic-nematic phase transition. In two dimensions, the problem is not as well understood. The theoretical treatment presented here yields a simple, manageable expression which can be compared with experimental data. Two-dimensional ordering results in an increase in the apparent binding constant of peptides to membranes at high concentration of peptides relative to what is expected from the effect of excluded volume alone. The possible implications of side-by-side alignment for several biological processes, such as peptide translocation across membranes and plaque formation in Alzheimer's disease, are discussed.     

Myelin as longitudinal conductor: a multi-layered model of the myelinated human motor nerve fibre

 The myelin sheath is normally regarded as an electrical insulator. Low values of radial conductance and capacitance have been measured, and in electrical models of myelinated axons the contribution of longitudinal conduction within the sheath has been ignored. According to X-ray diffraction studies, however, myelin sheaths comprise alternate lipid and aqueous layers, and the latter may be expected to have a low resistivity. We propose a new model of myelinated axons in which the aqueous layers within the myelin provide appreciable longitudinal and radial conductance, the latter via a spiral pathway. We have investigated the likely contribution of these conductive paths within the myelin to the electrical properties of a human motor nerve fibre by computer simulation, representing the myelin sheath as a series of interconnecting parallel lamellae. With this new model, action potential conduction has been simulated along a 20-node cable, and the electrotonic responses to 100-ms depolarizing and hyperpolarizing current pulses have been simulated for a uniformly polarized fibre. We have found that the hypothesis of a longitudinally conducting myelin sheath improves our previous model in two ways: it is no longer necessary to make implausible assumptions about the resistivity or width of the periaxonal space to simulate realistic electrotonus, and the conduction velocity is appreciably faster (by 8.6%). Received: 19 April 1999 / Accepted in revised form: 11 September 2000     

Chaos and order in plankton dynamics. Complex behavior of a simple model

The role of the diffusive interaction between fish-populated and fish-free habitats in a patchy environment in plankton pattern formation is studied by means of a minimal reaction-diffusion model of the nutrient-plankton-fish food chain. It is shown that such interaction can give rise to spatio-temporal plankton patterns. The fractal dimension of the patterns is shown dependent on the fish predation rate. The spatially averaged plankton dynamics depending on both fish predation rate and distance between fish-populated habitats can exhibit chaotic and regular behavior. The chaotic plankton dynamics is characteristic of a wide parameter range.     

The effect of denaturants on protein thermal stability analyzed through a theoretical model considering multiple binding sites

A novel mathematical development applied to protein ligand binding thermodynamics is proposed, which allows the simulation, and therefore the analysis of the effects of multiple and independent binding sites to the Native and/or Unfolded protein conformations, with different binding constant values. Protein stability is affected when it binds to a small number of high affinity ligands or to a high number of low affinity ligands. Differential scanning calorimetry (DSC) measures released or absorbed energy of thermally induced structural transitions of biomolecules. This paper presents the general theoretical development for the analysis of thermograms of proteins obtained for n-ligands bound to the native protein and m-ligands bound to their unfolded form. In particular, the effect of ligands with low affinity and with a high number of binding sites (n and/or m > 50) is analyzed. If the interaction with the native form of the protein is the one that predominates, they are considered stabilizers and if the binding with the unfolded species predominates, it is expected a destabilizing effect. The formalism presented here can be adapted to fitting routines in order to simultaneously obtain the unfolding energy and ligand binding energy of the protein. The effect of guanidinium chloride on bovine serum albumin thermal stability, was successfully analyzed with the model considering low number of middle affinity binding sites to the native state and a high number of weak binding sites to the unfolded state.     

The complex effect of granulocyte colony-stimulating factor on human granulopoiesis analyzed by a new physiologically-based mathematical model

Neutropenia, frequently a side effect of chemo- and radiotherapy, increases susceptibility to microbial infections and is a life-threatening condition. For realistically predicting drug treatment effects on granulopoiesis, we have constructed a new mathematical model of granulopoiesis in the bone marrow and in the peripheral blood, featuring cell cycle phase transition and detailed granulocyte-colony stimulating factor (G-CSF) pharmacokinetics (PK) and pharmacodynamics (PD), including intracellular second messenger. Using this model, in conjunction with clinical results, we evaluated the system parameters, implemented those in the model and successfully retrieved the results of several independent clinical experiments under a wide range of G-CSF regimens. Our results show that the introduction of G-CSF-controlled intracellular second messenger is indispensable for precise retrieval of the clinical results, and suggest that the half-life of this messenger varies between a single and multiple G-CSF administration schedules. In addition, our model provided reliable steady-state, as well as dynamic, estimations of human granulopoiesis parameters. These included an estimation of apoptosis index in the post-mitotic compartment, which corroborates previous results. At present the model is used for suggesting improved drug regimens.     

The protective effect of the vagus nerve in a murine model of chronic relapsing colitis

The vagus nerve inhibits the response to systemic administration of endotoxin, and we have recently extended this observation to show that the vagus attenuates acute experimental colitis in mice. The purpose of the present study was to determine whether there is a tonic counterinflammatory influence of the vagus on colitis maintained over several weeks. We assessed disease activity index, macroscopic and histological damage, myeloperoxidase (MPO) activity, and Th1 and Th2 cytokine profiles in chronic colitis induced by administration of dextran sodium sulfate (DSS) in drinking water for three cycles during 5 days with 11 days of rest between each cycle (DSS 3, 2, 2%) in healthy and vagotomized C57BL/6 mice and in mice deficient in macrophage-colony stimulating factor (M-CSF). A pyloroplasty was performed in vagotomized mice. Vagotomy accelerated the onset and the severity of inflammation during the first and second but not the third cycle. Although macroscopic scores were not significantly changed, histological scores as well as MPO activity and colonic tissue levels of IL-1alpha, TNF-alpha, IFN-gamma, and IL-18 but not IL-4 were significantly increased in vagotomized mice compared with sham-operated mice that received DSS. In control mice (without colitis), vagotomy per se did not affect any inflammatory marker. Vagotomy had no effect on the colitis in M-CSF-derived macrophage-deficient mice. These results indicate that the vagus protects against acute relapses on a background of chronic inflammation. Identification of the molecular mechanisms underlying the protective role of parasympathetic nerves opens a new therapeutic avenue for the treatment of acute relapses of chronic inflammatory bowel disease.     

A biomechanical model to simulate the effect of a high vertical loading on trunk flexural stiffness

A human trunk model was developed to simulate the effect of a high vertical loading on trunk flexural stiffness. A force–length relationship is attributed to each muscle of the multi-body model. Trunk stiffness and muscle forces were evaluated experimentally and numerically for various applied loads. Experimental evaluation of trunk stiffness was carried out by measuring changes in reaction force following a sudden horizontal displacement at the T10 level prior to paraspinal reflexes induction. Results showed that the trunk stiffness increases under small applied loads, peaks when the loads were further increased and decreases when higher loads are applied. A sensitivity analysis to muscle force–length relationship is provided to determine the model's limitations. This model pointed out the importance of taking into account the changes in muscle length to evaluate the effect of spinal loads beyond the safe limit that cannot be evaluated experimentally and to predict the trunk instability under vertical load.