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PubMed1987

Mathematical modeling of the effects of the signal recognition particle on translation and translocation of proteins across the endoplasmic reticulum membrane.

The kinetics of the signal recognition particle(SRP)-mediated process of protein translocation across the endoplasmic reticulum membrane was studied by mathematical modeling and complementary experiments. The following results were obtained. (1) A model according to which SRP directs the ribosome, rather than the mRNA, to the membrane is supported by experiments designed to discriminate between the two alternatives. (2) This model describes both steady-state and synchronized translation experiments and makes a number of predictions. (3) The interaction between a nascent protein and SRP may be described by two parameters: (i) a binding constant which can be attributed to the structure of the signal peptide, and (ii) the size of the "SRP-window", i.e. the distance between the first and the last site on the polypeptide chain that can interact with SRP. For preprolactin a binding constant of 1 to 2.5 nmol-1l was estimated. Modeling of the synchronized synthesis of ovalbumin indicates that it has a much weaker binding constant than preprolactin (approximately 0.25 nmol-1l) although we cannot exclude the possibility that the SRP-window may be also smaller. (4) A better understanding of the molecular effects of SRP on translation and translocation through the rough endoplasmic reticulum membrane has been achieved. Inhibition of the steady-state rate of translation by SRP requires a stoichiometric interaction of SRP with ribosomes carrying nascent polypeptide chains and will occur only when ribosomes are piled up back to the initiation site. Translocation, on the other hand, requires only the catalytic action of SRP and is determined by the local concentration of protein-synthesizing ribosomes accumulated at the site(s) of SRP interaction. As a consequence, translational inhibition by SRP may sometimes fail to occur, depending either on the type of protein or on experimental conditions, such as a high mRNA concentration, even if translocation can be demonstrated. (5) A rough extrapolation to the conditions in vivo indicates that all synthesized polypeptide chains destined for translocation across or integration into the endoplasmic reticulum membrane are indeed quantitatively translocated and that no translational inhibition occurs.

Endoplasmic Reticulum↗
PubMed2001

Mathematical modelling of the formation of rennet-induced gels by plant coagulants and chymosin.

Rheological properties of reconstituted skim milk coagulated with plant coagulants Cynara cardunculus L., Cynara humilis L. and chymosin was monitored by dynamic low amplitude oscillation. There are no published reports on the modelling of the gelation behaviour of milk by plant coagulants. Three mathematical models, Scott Blair. Douillard and Carlson, were fitted to the storage modulus (G') as function of time curves. For all coagulants. Scott Blair model was the most efficient in modelling the gelation process, and gave both the smallest residuals and standard error of residuals, Se (P < 0.0001). Douillard model gave the poorest fit and in particular it was not able to predict the initial part of the gelation curves. Carlson model had an intermediate behaviour and, in the case of chymosin, it gave results that were quite comparable to Scott Blair model. The parameters of the Scott Blair model were different for plant coagulants and chymosin. Chymosin had the longest rate constant (tau) and the time shift coefficient (t8) was also different between vegetable coagulants and chymosin (P < 0.0005). These results are in agreement with the overall trends for gelation profiles obtained for vegetable coagulants and chymosin. In the beginning of gelation both plant coagulants produced gels with slightly higher G' values than chymosin, but after longer incubation times chymosin gels had higher G' values. It was concluded that the Scott Blair model was the best equation to follow the gelation of milk induced by both plant coagulants as well as chymosin. Modelling is an important and useful method for comparing the gelation process in gels formed by different types of coagulants.

Animals↗
PubMed1986

Dynamic interactions and mutual synchronization of sinoatrial node pacemaker cells. A mathematical model.

Dynamic interactions and mutual entrainment of coupled sinoatrial pacemaker cells with different intrinsic frequencies were investigated using a computerized mathematical model. Transmembrane potentials were simulated using equations of individual membrane currents based on voltage clamp data for the sinoatrial node. The intrinsic frequency of a given cell was altered by applying bias hyperpolarizing current, or by changing the amount of slow inward current. Cells were coupled through simple ohmic resistances to form linear arrays of two or more cells. Simulations closely reproduced previous experimental work showing that the mutual interactions between pacemakers are mediated electrotonically and show phase dependence. Results from the present simulations provide an explanation for the ionic basis of these phase-dependent interactions. In addition, it is demonstrated that the mutual entrainment of coupled pacemakers can lead to their coordinated behavior (synchronization). Two pacemaker cells can synchronize at simple harmonic (i.e., 1:1, 2:1, etc.) or more complex ratios (3:2, 5:3, etc.), depending on the differences in intrinsic frequencies and the degree of electrical coupling between cells. Simulations using larger numbers of linearly connected cells yielded various patterns of pacemaker activity including 2:1 sinoatrial block and complex dysrhythmic activity. The overall results may be used to predict higher order interactions of thousands of cells comprising the sinus node. Under such a scheme, synchronization occurs not by the conducted influence of a dominant pacemaker cell, but by the mutual "democratic" interaction of individual pacemaker cells.

Action Potentials↗
PubMed2006

Mathematical models and lymphatic filariasis control: endpoints and optimal interventions.

The current global initiative to eliminate lymphatic filariasis is a major renewed commitment to reduce or eliminate the burden of one of the major helminth infections from resource-poor communities of the world. Mathematical models of filariasis transmission can serve as an effective tool for guiding the scientific development and management of successful community-level intervention programmes by acting as analytical frameworks for integrating knowledge regarding parasite transmission dynamics with programmatic factors. However, the power of these tools for supporting control interventions will be realized fully only if researchers address the current uncertainties and gaps in data and knowledge of filarial population dynamics and the effectiveness of currently proposed filariasis intervention options.

Animals↗
PubMed1996

A mathematical model of activity-dependent, anatomical segregation induced by competition for neurotrophic support.

Mathematical or computational models of activity-dependent neural competition typically impose competition in anatomically fixed networks by the use of synaptic normalisation, for which there is very little experimental support. Recent experimental evidence, however, strongly implicates neurotrophic factors in neural plasticity and competition, in addition to their well-known potent effects on neurite outgrowth and synaptogenesis. We therefore present a simple, mathematical model of anatomical segregation induces by activity-dependent competition for a limited supply of a neurotrophic factor provided by target cells to afferents. We extract the behaviour of the model in various regimes, in which the neurotrophic factor is either in critical supply or in abundant supply, by a combination of analytical and numerical methods, and study the effects of correlations in afferent inputs on competition. We apply the model to three different systems: ocular dominance column formation; elimination of polyneuronal innervation at the vertebrate neuromuscular junction; trigeminal brain stem whisker-related structure formation. Several classes of related predictions emerge, including the prediction that kittens reared with strabismus should require a higher concentration of neurotrophic factor infusion into their primary visual cortex than normally reared cats in order to induce the anatomical desegregation of ocular dominance columns. We also speculate on the mechanisms of support of inhibitory rather than excitatory neurons, and suggest the existence of a separate, (Cl-)-mediated activity-dependent pathway for their neurotrophic support.

Animals↗
PubMed1986

Oscillatory response of photosynthesis in leaves to environmental perturbations: a mathematical model.

Oscillations in the yield of chlorophyll fluorescence, in oxygen evolution, and in CO2 uptake observed with leaves upon perturbation of steady-state conditions are suggested to be due to the interdependence of turnover of adenylates and Calvin cycle intermediates. This suggestion is quantified in a mathematical model; the behavior of the model system in the neighborhood of the singular point of the system is analyzed. The linearized system is solved analytically, a condition for the occurrence of oscillations is given, and explicit expressions for the oscillation period and the damping constant are derived. The model is shown to be capable of exhibiting oscillations with the period observed with algae or leaves, whereas calculated values of the damping constant are higher than those measured for leaves or algae.

Adenosine Triphosphate↗
PubMed2004

Use of a mathematical model to study the dynamics of Ctenocephalides felis populations in the home environment and the impact of various control measures.

The biology of fleas has been studied by a number of authors, as has the impact of various types of control measures. However, there are no mathematical models simulating the dynamics of a population of Ctenocephalides felis felis fleas on their host (the cat) and in their close environment (apartment). The model presented in this paper allows for integration of the numerous biological and behavioural parameters of the parasites and their hosts and for the variation of these same parameters. The various types of control measures can be programmed so that their impact over time can be studied. The model confirms the key role played by adult fleas, or emerged fleas contained in the cocoon. Only regular applications of persistent insecticides to the host animal will enable control of the parasite population. A combination of these insecticides with an IGR (Insect Growth Regulator) will accelerate decontamination of the home environment and see the disappearance of the parasites altogether if they are not reintroduced. The association of additional measures such as vacuum cleaning will accelerate the process of decontamination but will have no impact if carried out in isolation. One-off treatment with insecticide will not enable a reduction in the parasite population, even if carried out frequently. Use of insecticides on the home environment premises alone does not appear to be an adequate means of control. The present model can be used to test various integrated control measures which take into account different factors such as the number of host animals, the frequency of movement outdoors, the impact of the seasons.

Animals↗
PubMed1976

[Dynamics of the process of gas transport into the body using a mathematical model].

Dynamics of mass-transport of oxygen, carbon dioxide, and inert gases in lungs, blood, and tissues, as well as gas transport through alveolar capillary and erythrocyte membranes at rest and during exercise under normal and increased ambient pressures, were studied on a mathematical model. The model consists of 34 differential and 58 algebraic equations and makes it possible to estimate the dynamics of changes of over 90 parameters. The effect of various factors: duration of the respiratory cycle, tidal volume, airways resistance, the surface of diffusion, the resistance of alveolar-capillary wall, erythrocyte membrane, ventilation-perfusion relations, pulmonary blood shunts, blood supply to the tissues, Haldane and Verigo-Bohr effect, buffer capacity of the blood, and others) on the mass-transport of gases were quantitatively estimated.

Biological Transport↗
PubMed1992

Epidermal wound healing: the clinical implications of a simple mathematical model.

The role of biochemical regulation in the healing of epidermal wounds remains the subject of much biological debate. We have previously developed a mathematical model which focuses on the role of mitogenic autoregulation in reepithelialization (23-25). Here, we discuss some predictions of our model and their clinical relevance. We investigate both the effects of adding mitotic regulators to healing wounds and the dependence of healing time on wound shape. The latter study suggests a possible mechanism for the control of changes in wound shape during healing. The predictions we make are amenable to experimental verification, and suggest new ideas for experimental research.

Animals↗
PubMed2005

Mathematical modeling and in vitro study of controlled drug release via a highly swellable and dissoluble polymer matrix: polyethylene oxide with high molecular weights.

A mathematical model is developed to describe the transport phenomena of a water-soluble small molecular drug (caffeine) from highly swellable and dissoluble polyethylene oxide (PEO) cylindrical tablets. Several important aspects in drug release kinetics were taken into account simultaneously in this theoretical model: swelling of the hydrophilic matrix and water penetration, three-dimensional and concentration-dependent diffusion of drug and water, and polymer dissolution. The moving boundary conditions are explicitly derived, and the resulting coupled partial differential equations are solved numerically. In vitro study of swelling, dissolution behavior of PEOs with different molecular weights and drug release are also carried out. When compared with experimental results, this theoretical model agrees with the water uptake, dimensional change and polymer dissolution profiles very well for pure PEO tablets with two different molecular weights. Drug release profiles using this model are predicted with a very good agreement with experimental data at different initial loadings. The overall drug release process is found to be highly dependent on the matrix swelling, drug and water diffusion, polymer dissolution and initial dimensions of the tablets. Their influences on drug release kinetics from PEO with two different molecular weights are also investigated.

Delayed-Action Preparations↗
PubMed1995

Modal and temporal analysis of head mathematical models.

The basic hypotheses used during these investigations were based on the vibration analysis of the head, which demonstrated that the head is not a solid nondeformable body, but a complex structure including deformable elements. Laboratoire des Systemes Biomecanique (LSBM) has recently proposed three mathematical models: a lumped model, a finite element model of the head in its sagittal plane, and a three-dimensional finite element model. These models were validated by their modal behavior and enabled the lesion mechanisms to be distinguished as a function of the spectral characteristics of the shock. The objective of this study is to complete these modal results by temporal analysis of the models by calculating the evolution of the intracranian mechanical parameters under shock conditions. To describe the head's dynamic behavior in the temporal domain, constant energy shocks of variable duration were simulated to evaluate their influence on different quantities as the intracerebral stresses in terms of compression, tensile, and shearing stresses, the relative brain-skull displacement, and the skull deformation. The importance of modal behavior of the head is illustrated by analyzing its temporal response to variable duration impacts, thus exciting very different frequencies. For a triangular shock, the critical duration times are between 10 and 15 x 10(-3) s, which correspond to impacts that excite the first resonance frequency of the head. Taking modal behavior into consideration in developing the finite element model leads to a harmonization of the calculated intracerebral stresses, even for short duration shocks. So, when the head is considered as a complex structure made up of several deformable elements, risk limitation is conditioned by an impact energy reduction for frequencies close to the natural frequencies of the structure. In the time field, the objective will be to avoid a number of impact shapes and durations. Therefore, the aim will not be to dampen the impact at any cost, but to damper it in an "intelligent" manner. In the future, this will allow the reduction of an injury mechanism-related risk, without increasing the risk of an injury generated by another mechanism.

Biomechanical Phenomena↗
PubMed1990

[A mathematical model of age distribution of malignant tumours mortality].

There was a tendency that the mortality of malignant tumours increased with age. In order to explore the law of this tendency, the data of malignant tumours mortality from disease monitoring points in Shandong Province were mathematically analogized, and the mathematical model of age distribution of malignant tumours mortality was established by using the exponential curve, y = 10a + bx. The model was also tested and verified by using national data, to observe the universal significance of the model. The model gave a theoretical account of the law of age distribution of malignant tumours mortality from a population, and provided an initial method to predict malignant tumours mortality. The increment quantity of malignant tumours mortality in various age groups when age increased one year could be calculated by using the differential equation from the exponential curve equation, y = 10a + bx. Further, "an increment multiple constant" of the increment quantity of malignant tumours mortality could be calculated. The constant could be used as an Index for comparison in risk degree and age distribution law of malignant tumours mortality among various age groups and the same age group in different periods, and provided leads for further research of the causes of malignant tumours.

Age Factors↗
PubMed1994

Externally driven countercurrent multiplication in a mathematical model of the urinary concentrating mechanism of the renal inner medulla.

Substitution of measured permeabilities into mathematical models of the concentrating mechanism of the renal inner medulla yields less than the known urine osmolalities. To gain a better understanding of the mechanism we analyse a model in which a force of unspecified origin [expressed as fraction, epsilon, of entering descending thin limb (DTL) concentration] drives fluid from DTL to interstitial vascular space (CORE), thus concentrating the solution in DTL. When flow in the DTL reverses at the hairpin bend of the loop of Henle, the high solute permeability of ascending thin limb (ATL) permits solute to diffuse into the CORE thus permitting epsilon to be multiplied many-fold. Behavior of the model is described by two non-linear differential equations. In the limit for infinite salt permeability of ATL the two equations reduce to a single equation that is formally identical with that for the Hargitay and Kuhn multiplier, which assumes fluid transport directly from DTL to ATL (Z. Electrochem. Angew. Phys. Chem. 55, 539, 1951). Solutions of the equations describing the model with parameters taken from perfused thin limbs show that urine osmolalities of the order of 5000 mosm L-1 can be generated by forces of the order of 20 mosm L-1. It seems probable that mammals including desert rodents use some variant of this basic mechanism for inner medullary concentration.

Animals↗
PubMed2006

A process-based mathematical model on methane production with emission indices for control.

In this paper, a process-based mathematical model is developed for the production of methane through biodegradation. It is a three-dimensional model given by ordinary differential equations. The results of the analysis of the model are interpreted through three emission indices, which are introduced for the first time. The estimation of either one or all of them can interpret the feasibility of the equilibrium and the long-term emission tendency of methane. The vulnerability of the methane production process with respect to soil temperature effects in methanogenic phase has been discussed and a feasible condition within a specified temperature range has defined for the nonvulnerability of the methane production process and also it has shown that under the same condition, zero-emission process of methane will be nonvulnerable with respect to the soil temperature effects in methanogenic phase. Lastly, condition for zero emission of methane is also obtained and it is interpreted through the emission indices.

Biomass↗
PubMed1988

A personal computer-based arrhythmia generator based on mathematical models of cardiac arrhythmia.

A personal computer-based arrhythmia generator has been developed based upon mathematical models of modulated parasystole and the related equations. A system of nonlinear difference equations is used to generate the time series of RR intervals of ECG that contain normal as well as ectopic QRS waves. The ECG waveform is synthesized according to the computed RR interval and the type of QRS wave and output via DA converter in a real-time base. Various types of ECGs with ventricular ectopic beats and those with very long periods were generated by selecting values for a small number of model parameters. This method requires neither large RAM nor external memory for storing a library of arrhythmic ECGs. The theory, hardware design, software implementation on a personal computer, and experimental reconstruction of clinical ECGs based on the model are discussed.

Arrhythmias, Cardiac↗
PubMed2005

On a mathematical model of a human root dentin.

OBJECTIVE: On the basis of recent experimental data, a new mathematical model that predicts creep in human root dentin has been developed. METHOD: The chosen constitutive model comprises fractional derivatives of stress and strain and the restrictions on the coefficients that follow from the Clausius-Duhem inequality. RESULTS: The four constants describing mechanical properties of the human dentin at constant temperature are calculated from a highly non-linear system involving Mittag-Leffler-type functions. Special attention is paid to thermodynamical restrictions that should be observed in determining parameters of the model from experimental results. SIGNIFICANCE: The proposed model allows us to predict behavior of a human dentin in different load situations. Also it could be used for describing mechanical properties of dentin that are important in the development of 'dentin-like' restorative materials.

Algorithms↗
PubMed2004

A mathematical model for Chagas disease with infection-age-dependent infectivity.

In this paper we develop a mathematical model for Chagas disease with infection-age-dependent infectivity. The effects of vector and blood transfusion transmission are considered, and the infected population is structured by the infection age (the time elapsed from infection). The authors identify the basic reproduction ratio R0 and show that the disease can invade into the susceptible population and unique endemic steady state exists if R0 > 1, whereas the disease dies out if R0 is small enough. We show that depending on parameters, backward bifurcation of endemic steady state can occur, so even if R0 < 1, there could exist endemic steady states. We also discuss local and global stability of steady states.

Age Factors↗