Search PubMed⌕ Search

SEARCH · Search PubMed

Results for “Stability analysis”

Search indexed PubMed citations on genomics, clinical trials, systematic reviews and public health. Explore titles, authors and supplied subject terms, then open the PubMed record.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 595 records · Page 33Linked to original sources
PubMed2002

Peptide investigations of pairwise interactions in the collagen triple-helix.

Pairwise interactions have been studied for the major secondary structures in proteins. The present work extends the characterization of interactions between side-chains to the context of a collagen triple-helix. In this study, the most frequent Gly-X-Y tripeptide sequences in collagen are characterized in terms of interchain interactions between non-imino acid X and Y residues, through the use of host-guest peptides and statistical frequency analysis. Stabilities predicted on the basis of additivity show good agreement with experimental values for almost half of the peptides, indicating a lack of interaction. A small number of peptides have a stability lower than predicted, while a larger number are more stable than expected. Of all triplets containing residues of opposite charge, only Gly-Lys-Asp and Gly-Arg-Asp exhibit stabilizing electrostatic interactions, and these pairs are found together preferentially in collagens. Repulsion of like charges is observed in Gly-Arg-Lys, Gly-Lys-Arg, and Gly-Glu-Asp sequences, and a small degree of hydrophobic stabilization was observed for the Gly-Leu-Leu guest triplet. The data reported here help clarify basic principles of triple-helix stability. In addition, the experimentally determined stabilities of the tripeptide units found most frequently in collagens constitute a database useful for predicting triple-helix stability in peptides, collagens and other triple-helix-containing proteins.

Amino Acid Sequence↗
PubMed1995

The structural stability of a three-species food chain model.

A three-species food-chain model which was previously shown to exhibit chaotic dynamics was revisited. By exploring the sensitivity of that result this study found that complex behavior depended on the functional form chosen to model the interaction between the two highest species in the food chain. Two separate scenarios were explored: the gradual addition of refugia modeling the escape from predation at low prey densities; and the gradual addition of predator interference modeling territorial behavior. The addition of even a small amount of refugia provided a stabilizing influence as the chaotic dynamics collapsed to stable limit cycles. The results of adding interference to the model were more complex. Although the numerical simulations indicated that a low level of interference provided a stabilizing influence, the analytical results suggest that complex dynamics are possible for a range of parameter values that are biologically relevant. The sensitivity of the stability profile to functional changes in the model suggests two important ecological motivations for structural stability analysis. First, in ecological systems, environmental fluctuations cause continuous changes in the functional relationships between and within species, resulting in potential changes in the complexity of the dynamics over time. Second, slight changes in ecological structure may cause significant bifurcations; however, most ecological data are inadequate to distinguish such phenomena.

Animals↗
PubMed1998

Lyme disease: self-regulation and pathogen invasion.

Ecological interactions underlying the epidemic of Lyme disease involve a spirochete, a tick (with larval, nymph and adult stages), and two (or more) vertebrate hosts. Juvenile ticks ordinarily feed on mice; adult ticks feed on deer. Mice acquire the spirochete from infected nymphs and then pass the infection to larvae of the next tick generation. Lyme disease may result when a human is inadvertently bitten by an infectious nymph. Our model of the Lyme phenomenon counts the total number of ticks in each stage, the numbers of infected ticks by stage, and the number of infected mice. We fix the total population sizes of deer and mice, assume the ticks self-regulate, and solve the homogeneous-mixing case for equilibrium abundances. A local stability analysis identifies a condition where extinction of the spirochete is stable. Reversing this condition implies that the spirochete can invade the system of ticks and vertebrate hosts. When the spirochete can invade, a positive equilibrium number of infected organisms is locally stable. Spirochete invasion is promoted by a sufficient density of mice suffering low mortality, high susceptibility to infection in both mice and ticks, a high attack rate of ticks on mice, a high density of larval ticks, and low mortality among tick nymphs. Low mouse mortality allows the frequency of infection among nymphs to approach an individual tick's susceptibility when feeding on an infected mouse.

Animals↗
PubMed2002

The fertilization dance: a mechanical view of the egg rotation during the initial spermatozoa-ovum interaction.

The motion of the ovum and the spermatozoa toward each other in the oviduct culminates in a meeting that ultimately results in fertilization. This encounter is characterized by a slow rotation of the sperms-egg cluster while the sperms attempt a penetration. The mysterious rotation was observed in vivo and in vitro for homologous and heterologous systems. It lacks a satisfactory biological explanation while it seems to be correlated with the efficiency of fertilization. A simple bio-mechanical model presented here predicts that the slow rotation of the sperms-egg cluster is a natural consequence of the encounter in most cases. A linear stability analysis of the system suggests a quantitative explanation of the rotation causes, its intensity and its direction. The entire encounter seems as a micro-scale process of courting of the ovum by the spermatozoa, which is expressed as circular dance.

Biomechanical Phenomena↗
PubMed2002

Stochastic vs. deterministic modeling of intracellular viral kinetics.

Within its host cell, a complex coupling of transcription, translation, genome replication, assembly, and virus release processes determines the growth rate of a virus. Mathematical models that account for these processes can provide insights into the understanding as to how the overall growth cycle depends on its constituent reactions. Deterministic models based on ordinary differential equations can capture essential relationships among virus constituents. However, an infection may be initiated by a single virus particle that delivers its genome, a single molecule of DNA or RNA, to its host cell. Under such conditions, a stochastic model that allows for inherent fluctuations in the levels of viral constituents may yield qualitatively different behavior. To compare modeling approaches, we developed a simple model of the intracellular kinetics of a generic virus, which could be implemented deterministically or stochastically. The model accounted for reactions that synthesized and depleted viral nucleic acids and structural proteins. Linear stability analysis of the deterministic model showed the existence of two nodes, one stable and one unstable. Individual stochastic simulation runs could access and remain at the unstable node. In addition, deterministic and averaged stochastic simulations yielded different transient kinetics and different steady-state levels of viral components, particularly for low multiplicities of infection (MOI), where few virus particles initiate the infection. Furthermore, a bimodal population distribution of viral components was observed for low MOI stochastic simulations. The existence of a low-level infected subpopulation of cells, which could act as a viral reservoir, suggested a potential mechanism of viral persistence.

Animals↗
PubMed1996

Differential binding of HMG1, HMG2, and a single HMG box to cisplatin-damaged DNA.

The HMG box domain is a DNA binding domain present in the nonhistone chromosomal proteins HMG1 and HMG2 and in other proteins involved in the regulation of gene expression. Previous studies have demonstrated that HMG1 and HMG2 bind with high affinity to DNA modified with the cancer chemotherapeutic drug cisplatin (CDDP). In this report, we compare the binding of full-length HMG1 and HMG2 and the HMG boxes present in these proteins to that of CDDP-DNA. Complexes between HMG1, HMG2, or HMG Box A + B and CDDP-DNA were stable at > or = 500 mM salt, while complexes between a single HMG box and CDDP-DNA exhibited decreased stability. Analysis of a series of HMG1 Box A mutant constructs revealed different affinities for CDDP-DNA. Two constructs containing a Phe to Ala substitution at position 19 and a Tyr to Gly substitution at position 71, are noteworthy; these peptides exhibited reduced affinity for CDDP-DNA. We have generated a structure of HMG1 Box A and used it, along with the results of our binding studies, to model its interaction with CDDP-DNA. HMG1 Box A binds in the minor groove of CDDP-DNA, in agreement with earlier studies. Our model predicts that Tyr71 partially intercalates and forms an H bond with the sugar-phosphate backbone. The model also suggests that Phe 19 does not directly interact with DNA, and hence an Ala substitution at position 19 may alter protein structure. This model should provide a framework for future studies examining HMG Box-DNA interactions.

Amino Acid Sequence↗
PubMed1994

Translating stochastic density-dependent individual behavior with sensory constraints to an Eulerian model of animal swarming.

Density-dependent social behaviors such as swarming and schooling determine spatial distribution and patterns of resource use in many species. Lagrangian (individual-based) models have been used to investigate social groups arising from hypothetical algorithms for behavioral interactions, but the Lagrangian approach is limited by computational and analytical constraints to relatively small numbers of individuals and relatively short times. The dynamics of "group properties", such as population density, are often more ecologically useful descriptions of aggregated spatial distributions than individual movements and positions. Eulerian (partial differential equation) models directly predict these group properties; however, such models have been inadequately tied to specific individual behaviors. In this paper, I present an Eulerian model of density-dependent swarming which is derived directly from a Lagrangian model in which individuals with limited sensing distances seek a target density of neighbors. The essential step in the derivation is the interpretation of the density distribution as governing the occurrence of animals as Poisson points; thus the number of individuals observed in any spatial interval is a Poisson-distributed random variable. This interpretation appears to be appropriate whenever a high degree of randomness in individual positions is present. The Eulerian model takes the form of a nonlinear partial integro-differential equation (PIDE); this equation accurately predicts statistically stationary swarm characteristics, such as expected expected density distribution. Stability analysis of the PIDE correctly predicts transients in the stochastic form of the aggregation model. The model is presented in one-dimensional form; however, it illustrates an approach that can be equally well applied in higher dimensions, and for more sophisticated behavioral algorithms.

Algorithms↗
PubMed1980

The effect of integral conditions in certain equations modelling epidemics and population growth.

Models of epidemics that lead to delay differential equations often have subsidiary integral conditions that are imposed by the interpretation of these models. The neglect of these conditions may lead to solutions that behave in a radically different manner from solutions restricted to obey them. Examples are given of such behavior, including cases where periodic solutions may occur off the natural set defined by these conditions but not on it. A complete stability analysis is also given of a new model of a disease propagated by a vector where these integral conditions play an important role.

Disease Outbreaks↗
PubMed1984

The role of convection in the standard fluid-mechanical model for morphogenesis.

The effect of convection on reaction-diffusion instabilities in a visco-elastic medium is studied by using the standard continuum theory of a fluid mixture. The medium is assumed to be in local mechanical equilibrium, and convection is generated by pressure forces which arise if the equilibrium density of the medium changes with its composition. A linear stability analysis shows that reaction-diffusion instabilities proceeding from homogeneous steady states at rest are unmodified by induced convection to first order in concentration changes. We suggest that a non-linear analysis would show convection produces no new instabilities, as a linear analysis of inhomogeneous non-convecting stationary states shows that reaction-diffusion growth rates are reduced by convection at long wavelengths and are otherwise unchanged. For applications in embryology, numerical estimates suggest that convection can be ignored in reaction-diffusion mechanisms for pattern formation, and this conclusion is supported by a dimensional analysis.

Animals↗
PubMed1988

Transformation of Neurospora crassa with the trp-1 gene and the effect of host strain upon the fate of the transforming DNA.

Neurospora trp-1+ transformants, obtained by transforming a trp-1 inl strain with plasmid DNA containing the wild type trp1+ gene, were characterized by genetic and Southern blot analyses. The transforming trp-1 gene integrated at or near the resident site in all of the trp-1+ transformants obtained with circular DNA or DNA cut within the trp-1 coding region. The frequency of homologous integration decreased substantially when the donor DNA was cleaved outside the trp-1 coding region. The transformants were very stable mitotically and, in general, also showed meiotic stability. Analysis of trp-1+ transformants obtained with another recipient strain, trp-1+ ga-2 aro-9 inl, showed that homologous integration of donor DNA occurred in only 20% of the transformants, whether circular or linear DNA was used. Thus, the host strain employed for transformation appears to be a major factor in determining the fate of transforming DNA. Southern blot analysis of transformants showed that integration of the transforming DNA at the homologous site occurred by double crossover or gene conversion events rather than by insertion of the entire plasmid DNA. Multiple and apparently non functional integration events were observed in some transformants.

DNA Restriction Enzymes↗
PubMedDate not supplied

Stability of source estimates in rolandic spikes.

The interictal spike discharges present in rolandic epilepsy has a dominant horizontal dipolar topography, centered near the rolandic area. In order to examine the generator configuration of this focus, we investigated the variation of spike topography in 20 children with rolandic epilepsy of childhood by the dipole localization method (DLM). A quantitative measure ("stability index" or SI) of the degree of source fluctuation was devised, based on the consistency of the source parameters (location, direction and magnitude) over contiguous time points. A high SI was associated with overlapping source locations and parallel directions over many time points, while a low SI was seen with poor and variable solutions. At the peak and trough of the spike, the corresponding sources were found to have different locations. If the patients were separated into those with and without neurological findings, the mean times at which stable sources existed were significantly different: 35 and 150 ms respectively after the spike apex. Further, the group without abnormal neurological findings tended to have higher values of SI. These results suggest that such stability analysis allows measurement of the spatial and temporal extents of source estimates. These results further support the hypothesis that the topographic behaviour of a spike focus is closely associated with its clinical characteristics.

Brain Mapping↗
PubMed1982

Pattern formation in morphogenesis. Analytical treatment of the Gierer-Meinhardt model on a sphere.

We first treat the Gierer-Meinhardt equations by linear stability analysis to determine the critical parameter, at which the homogeneous distributions of activator and inhibitor concentrations become unstable. We find two types of instabilities: one leading to spatial pattern formation and another one leading to temporal oscillations. We consider the case where two instabilities are present. Using the method of generalized Ginzburg-Landau equations introduced earlier we then analyze the nonlinear equations. As we are mainly interested in spatial pattern formation on a sphere we consider the problem under an appropriate constraint. Combining the two occurring solutions we find patterns well-known in biology, such as a gradient system and temporal oscillations.

Animals↗
PubMed1996

Evolutionary dynamics of predator-prey systems: an ecological perspective.

Evolution takes place in an ecological setting that typically involves interactions with other organisms. To describe such evolution, a structure is needed which incorporates the simultaneous evolution of interacting species. Here a formal framework for this purpose is suggested, extending from the microscopic interactions between individuals--the immediate cause of natural selection, through the mesoscopic population dynamics responsible for driving the replacement of one mutant phenotype by another, to the macroscopic process of phenotypic evolution arising from many such substitutions. The process of coevolution that results from this is illustrated in the context of predator-prey systems. With no more than qualitative information about the evolutionary dynamics, some basic properties of predator-prey coevolution become evident. More detailed understanding requires specification of an evolutionary dynamic; two models for this purpose are outlined, one from our own research on a stochastic process of mutation and selection and the other from quantitative genetics. Much of the interest in coevolution has been to characterize the properties of fixed points at which there is no further phenotypic evolution. Stability analysis of the fixed points of evolutionary dynamical systems is reviewed and leads to conclusions about the asymptotic states of evolution rather different from those of game-theoretic methods. These differences become especially important when evolution involves more than one species.

Animals↗
PubMed1992

A mathematical model of the P-glycoprotein pump as a mediator of multidrug resistance.

Cells displaying the classic multidrug resistant (MDR) phenotype possess a transmembrane protein (p170 or P-glycoprotein) which can actively extrude cytotoxic agents from the cytoplasm. A mathematical model of this drug efflux pump has been developed. Outward transport is modeled as a facilitated diffusion process. Since energy-dependent efflux of cytotoxic agents requires that ATP also bind to p170, the model includes a dynamic calculation for efflux rate which considers Michaelis-Menten kinetics for both the substrate agent and ATP. The final system consists of one partial differential equation (PDE) for the facilitated diffusion of substrate agents out of the cell, a 2 x 2 ordinary differential equation (ODE) system for the dynamic calculation of the ATP-ADP pool, and a dynamic algebraic calculation of the efflux rate given substrate levels at the interior cell membrane interface and ATP levels in the cell. A stability analysis of the ATP-ADP pool distribution and a simplistic closed form solution of the linearized PDE are included. Numerical simulations are also provided.

ATP Binding Cassette Transporter, Subfamily B, Mem↗
PubMed1994

Modelling the dynamics of F-actin in the cell.

The regulation of the interactions between the actin binding proteins and the actin filaments are known to affect the cytoskeletal structure of F-actin. We develop a model depicting the formation of actin cytoskeleton, bundles and orthogonal networks, via activation or inactivation of different types of actin binding proteins. It is found that as the actin filament density increases in the cell, a spontaneous tendency to organize into bundles or networks occurs depending on the active actin binding protein concentration. Also, a minute change in the relative binding affinity of the actin binding proteins in the cell may lead to a major change in the actin cytoskeleton. Both the linear stability analysis and the numerical results indicate that the structures formed are highly sensitive to changes in the parameters, in particular to changes in the parameter phi, denoting the relative binding affinity and concentration of the actin binding proteins.

Actins↗
PubMed2005

Eye movement instabilities and nystagmus can be predicted by a nonlinear dynamics model of the saccadic system.

The study of eye movements and oculomotor disorders has, for four decades, greatly benefitted from the application of control theoretic concepts. This paper is an example of a complementary approach based on the theory of nonlinear dynamical systems. Recently, a nonlinear dynamics model of the saccadic system was developed, comprising a symmetric piecewise-smooth system of six first-order autonomous ordinary differential equations. A preliminary numerical investigation of the model revealed that in addition to generating normal saccades, it could also simulate inaccurate saccades, and the oscillatory instability known as congenital nystagmus (CN). By varying the parameters of the model, several types of CN oscillations were produced, including jerk, bidirectional jerk and pendular nystagmus. The aim of this study was to investigate the bifurcations and attractors of the model, in order to obtain a classification of the simulated oculomotor behaviours. The application of standard stability analysis techniques, together with numerical work, revealed that the equations have a rich bifurcation structure. In addition to Hopf, homoclinic and saddlenode bifurcations organised by a Takens-Bogdanov point, the equations can undergo nonsmooth pitchfork bifurcations and nonsmooth gluing bifurcations. Evidence was also found for the existence of Hopf-initiated canards. The simulated jerk CN waveforms were found to correspond to a pair of post-canard symmetry-related limit cycles, which exist in regions of parameter space where the equations are a slow-fast system. The slow and fast phases of the simulated oscillations were attributed to the geometry of the corresponding slow manifold. The simulated bidirectional jerk and pendular waveforms were attributed to a symmetry invariant limit cycle produced by the gluing of the asymmetric cycles. In contrast to control models of the oculomotor system, the bifurcation analysis places clear restrictions on which kinds of behaviour are likely to be associated with each other in parameter space, enabling predictions to be made regarding the possible changes in the oscillation type that may be observed upon changing the model parameters. The analysis suggests that CN is one of a range of oculomotor disorders associated with a pathological saccadic braking signal, and that jerk and pendular nystagmus are the most probable oscillatory instabilities. Additionally, the transition from jerk CN to bidirectional jerk and pendular nystagmus observed experimentally when the gaze angle or attention level is changed is attributed to a gluing bifurcation. This suggests the possibility of manipulating the waveforms of subjects with jerk CN experimentally to produce waveforms with an extended foveation period, thereby improving visual resolution.

Humans↗
PubMed2006

Mathematical modelling of engineered tissue growth using a multiphase porous flow mixture theory.

This paper outlines the framework of a porous flow mixture theory for the mathematical modelling of in vitro tissue growth, and gives an application of this theory to an aspect of tissue engineering. The problem is formulated as a set of partial differential equations governing the space and time dependence of the amounts of each component of the tissue (phase), together with the physical stresses in each component. The theory requires constitutive relations to specify the material properties of each phase, and also requires relations to specify the stresses developed due to mechanical interactions, both within each phase and between different phases. An application of the theory is given to the study of the mobility and aggregation of a population of cells seeded into an artificial polymeric scaffold. Stability analysis techniques show that the interplay of the forces between the tissue constituents results in two different regimes: either the cells form aggregates or disperse through the scaffold.

Algorithms↗
PubMed2006

An age-structured epidemic model of rotavirus with vaccination.

The recent approval of a rotavirus vaccine in Mexico motivates this study on the potential impact of the use of such a vaccine on rotavirus prevention and control. An age-structured model that describes the rotavirus transmission dynamics of infections is introduced. Conditions that guarantee the local and global stability analysis of the disease-free steady state distribution as well as the existence of an endemic steady state distribution are established. The impact of maternal antibodies on the implementation of vaccine is evaluated. Model results are used to identify optimal age-dependent vaccination strategies. A convergent numerical scheme for the model is introduced but not implemented. This paper is dedicated to Prof. K. P. Hadeler, who continues to push the frontier of knowledge in mathematical biology.

Age Factors↗