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PubMed1999

Population dynamics and the evolution of virulence in epidemiological models with discrete host generations

Chaos is the likely outcome of the interaction between a parasite and a host with discrete generations, if the parasite's virulence is high and if transmission from one generation to the next is held constant. We studied two alternative routes of transmission-vertical transmission from infecteds to their offspring, and transmission via long-lasting spores produced in those individuals that were killed by the infection-to investigate the influence of the transmission route on the system's evolution and population dynamics. The major results are: (1) vertical transmission often leads to low virulence, thus confirming most epidemiological models. However, if hosts can become super-infected, the evolutionary dynamics of virulence can have several equilibrium points, including 100% disease-induced mortality; (2) when parasites are transmitted with long-lasting spores, the evolutionary dynamics of virulence can become unstable, leading to the repeated bifurcation of two sub-populations with high and low virulence or to punctuated equilibria with sudden changes in the average level of virulence; (3) in general, the evolution of virulence moves the system to an area where the population dynamics are stable. When evolution leads to chaos, the system most often becomes extinct. Only for a restricted parameter space in the system where transmission from one generation to the next is via long-lasting spores do the dynamics become chaotic without extinction of the system. Copyright 1999 Academic Press.

Journal Article↗
PubMed1999

Simplified dynamics of human and mammalian neocortical neurons.

The behavior of human and mammalian neocortical neurons is governed by the interplay of approximately a dozen ion currents. Due to the complexity of the resulting dynamics, it is sometimes advantageous to resort to simpler systems in order to gain insight into the relationship between underlying dynamical principles and biophysics. This paper presents a new and extremely simple approximation to the dynamics of neocortical neurons based on just four simulated ion currents: I(Na), I(K), I(T), and I(AHP). The formulation incorporates Ohm's law plus explicit representation of Na(+), K(+), and Ca(2+)equilibrium potentials, yet mathematical simplicity is retained by restriction of the dynamics to cubic nonlinearities. The resulting equations produce a good approximation to spike shapes, firing rates, and bursting behavior throughout the physiological range. Analysis of the equations suggests that four unique dynamical regimes form the basis for different categories of neocortical neurons. Synaptic coupling between these model neurons demonstrates their potential utility in simulations by producing network models of bursting and of short-term memory function.

Animals↗
PubMed2002

Dynamics of Boolean networks controlled by biologically meaningful functions.

The remarkably stable dynamics displayed by randomly constructed Boolean networks is one of the most striking examples of the spontaneous emergence of self-organization in model systems composed of many interacting elements (Kauffman, S., J. theor. Biol.22, 437-467, 1969; The Origins of Order, Oxford University Press, Oxford, 1993). The dynamics of such networks is most stable for a connectivity of two inputs per element, and decreases dramatically with increasing number of connections. Whereas the simplicity of this model system allows the tracing of the dynamical trajectories, it leaves out many features of real biological connections. For instance, the dynamics has been studied in detail only for networks constructed by allowing all theoretically possible Boolean rules, whereas only a subset of them make sense in the material world. This paper analyses the effect on the dynamics of using only Boolean functions which are meaningful in a biological sense. This analysis is particularly relevant for nets with more than two inputs per element because biological networks generally appear to be more extensively interconnected. Sets of the meaningful functions were assembled for up to four inputs per element. The use of these rules results in a smaller number of distinct attractors which have a shorter length, with relatively little sensitivity to the size of the network and to the number of inputs per element. Forcing away the activator/inhibitor ratio from the expected value of 50% further enhances the stability. This effect is more pronounced for networks consisting of a majority of activators than for networks with a corresponding majority of inhibitors, indicating that the former allow the evolution of larger genetic networks. The data further support the idea of the usefulness of logical networks as a conceptual framework for the understanding of real-world phenomena.

Algorithms↗
PubMed1998

Effects of Optimal Antipredator Behavior of Prey on Predator-Prey Dynamics: The Role of Refuges.

The influence of optimal antipredator behavior of prey on predator-prey dynamics in a two-patch environment is studied. One patch represents an open habitat while the other is a refuge for prey. It is assumed that prey maximize their fitness measured by the instantaneous per capita growth rate. In each patch population dynamics is described by the Lotka-Volterra time continuous model. The refuge is characterized by its protectiveness which is inversely related to the predation risk for prey, and the dependence of population dynamics on protectiveness is studied. It is shown that adaptive behavior of prey changes qualitative properties of the underlying Lotka-Volterra model due to the appearance of a bounded attractor. Adaptive prey behavior does not lead to a stable equilibrium but to the reduction of population fluctuations. Dynamic consequences of a limited carrying capacity of the refuge are also considered. Low refuge carrying capacity leads to stability of predator-prey dynamics while stability is lost when the carrying capacity of the refuge is high. Lastly, it is shown that optimal antipredator behavior of prey leads to persistence and reduction of oscillations in population densities. Copyright 1998 Academic Press.

Journal Article↗
PubMed1999

The dynamics of infinitesimally rare alleles, applied to the evolution of mutation rates and the expression of deleterious mutations.

A new method is presented for analysing the dynamics of a classical model where infinitesimally rare alleles segregate at an infinite number of unlinked loci, and where the alleles at different loci have equivalent effects. The dynamics of the distribution of the number of rare alleles per individual (the "phenotypic distribution") can be followed without knowing the frequencies of individual genotypes. Meiosis and random union of gametes have a very simple effect on the factorial cumulants of the phenotypic distribution which are consequently the natural set of variables to follow. An exact solution is presented for the dynamics of rare alleles under mutation and multiplicative selection. This solution has a simple representation in terms of the factorial cumulants. Unlike the QLE (quasi-linkage equilibrium) solution, this solution applies even when the population is far from linkage equilibrium. This approach is extended to analyse the joint dynamics of infinitesimally rare alleles at an infinite number of unlinked loci, together with a locus (with arbitrary allele frequencies) with which they interact. This more general method is used to investigate (1) the joint dynamics of a modifier of the mutation rate, together with deleterious alleles under mutation and multiplicative selection, and (2) the fate of an allele that ameliorates or exacerbates the fitness effects of deleterious alleles. When a new modifier allele causes a large change in the mutation rate, strong linkage disequilibrium is generated during its progress. However, using this new approach based on factorial cumulants, it is found that a remarkably simple invasion condition applies to alleles at the modifier locus, even when strong linkage disequilibrium is generated.

Alleles↗
PubMed2025

Microfluidics to Follow Spatiotemporal Dynamics at the Nucleo-Cytoplasmic Interface During Plant Root Growth.

Nuclear dynamics refers to global/local changes in the molecular and spatial organization of genomic DNA that can occur during development or in response to environmental stress signals and eventually impact genomic functions. In plants, nuclear dynamics relies notably on the connection of the nucleus with the cytoskeleton during development. It orchestrates genomic functions in response to developmental and environmental cues. This is particularly true in the plant root system, which is constantly exposed to a wide range of internal and external stimuli. Currently, studying nuclear dynamics in a growing root is challenging due to limitations regarding real-time imaging for quantitative analyses under controlled conditions. Microfluidic systems for plant cell studies are valuable analytical tools that provide precise control of culture conditions together with live-imaging capabilities at high temporal and spatial resolutions. Herein, we describe a microfluidic platform to unravel dynamically and noninvasively nuclear organization in the seedling root system exposed to various treatments. As exemplified here, our microfluidic platform can be conveniently used for real-time microscopy imaging and quantitative analysis of fine nuclear morphological changes upon modifying cytoskeleton dynamics. Importantly, our system can be applied to a wide variety of microscopic means including high-resolution microscopy to investigate diverse subcellular compartments or nuclear domains in Arabidopsis thaliana roots.

Plant Roots↗
PubMed1996

Dynamics control of semantic processes in a hierarchical associative memory.

A neural mechanism for control of dynamics and function of associative processes in a hierarchical memory system is demonstrated. For the representation and processing of abstract knowledge, the semantic declarative memory system of the human brain is considered. The dynamics control mechanism is based on the influence of neuronal adaptation on the complexity of neural network dynamics. Different dynamical modes correspond to different levels of the ultrametric structure of the hierarchical memory being invoked during an associative process. The mechanism is deterministic but may also underlie free associative thought processes. The formulation of an abstract neural network model of hierarchical associative memory utilizes a recent approach to incorporate neuronal adaptation. It includes a generalized neuronal activation function recently derived by a Hodgkin-Huxley-type model. It is shown that the extent to which a hierarchically organized memory structure is searched is controlled by the neuronal adaptability, i.e. the strength of coupling between neuronal activity and excitability. In the brain, the concentration of various neuromodulators in turn can regulate the adaptability. An autonomously controlled sequence of bifurcations, from an initial exploratory to a final retrieval phase, of an associative process is shown to result from an activity-dependent release of neuromodulators. The dynamics control mechanism may be important in the context of various disorders of the brain and may also extend the range of applications of artificial neural networks.

Cybernetics↗
PubMed1993

A method for constructing data-based models of spiking neurons using a dynamic linear-static nonlinear cascade.

This paper describes a general nonlinear dynamical model for neural system identification. It describes an algorithm for fitting a simple form of the model to spike train data, and reports on this algorithm's performance in identifying the structure and parameters of simulated neurons. The central element of the model is a Wiener-Bose dynamic nonlinearity that ensures that the model is able to approximate the behaviour of an arbitrary nonlinear dynamical system. Nonlinearities associated with spike generation and transmission are treated by placing the Wiener-Bose system in cascade with pulse frequency modulators and demodulators, and the static nonlinearity at the output of the Wiener-Bose system is decomposed into a rectifier and a multinomial. This simplifies the model without reducing its generality for neuronal system identification. Model elements can be characterised using standard methods of dynamical systems analysis, and the model has a simple form that can be implemented and simulated efficiently. This model bears a structural resemblance to real neurons; it may be regarded as a connectionist "neuron" that has been generalized in a realistic way to enable it to mimic the behaviour of an arbitrary nonlinear system, or conversely as a general nonlinear model that has been constrained to make it easy to fit to spike train data. Tests with simulated data show that the identification algorithm can accurately estimate the structure and parameters of neuron-like nonlinear dynamical systems using data sets containing only a few hundred spikes.

Animals↗
PubMed1992

Complex dynamics underlying the human electrocardiogram.

Sequences of different human cardiac rhythms terminating in ventricular fibrillation have been studied, both qualitatively and quantitatively, with methods of nonlinear dynamics. The analysis has been applied to ECG epochs belonging to rhythms of increasing electrocardiographic irregularity: from sinus rhythm to prefibrillatory rhythms and then to ventricular fibrillation. The phase portraits of these rhythms have been reconstructed from the ECG recording with the time-delay technique, and their correlation dimensions have been estimated with the algorithm of Grassberger and Procaccia (1983a, b). Different cardiac rhythms exhibit different correlation dimensions that describe the corresponding degrees of complexity. The correlation dimension increases as one proceeds from sinus rhythm to fully developed ventricular fibrillation via intermediate rhythms. The fully developed ventricular fibrillation shows the highest degree of complexity. The dimensional analysis supports the existence of complex dynamics underlying different cardiac rhythms and reveals an increase in dimensional complexity corresponding to an increase in electrocardiographic irregularity. Our results indicate that nonlinear dynamics may be used to assess various dynamic states of the heart and may offer a non-invasive tool to investigate the complex dynamic phenomena occurring during arrhythmia.

Algorithms↗
PubMed1996

Symmetry, broken symmetry, and handedness in bimanual coordination dynamics.

The symmetrical dynamics of 1:1 rhythmic bimanual coordination may be specified by an order parameter equation involving the relative phase between rhythmic components, and an interlimb coupling which determines the relative attractiveness of in-phase and anti-phase patterns. Symmetry breaking of these dynamics can occur via the difference in the natural frequencies, delta omega, of the left and right rhythmic components, or by the intrinsic asymmetrical dynamics of the body. The latter is captured by additional terms that render the symmetrical coupling slightly anisotropic. A major prediction resulting from this step is that although delta omega = 0, as the frequency of coordination is increased, the asymmetrical coupling will increase and the symmetrical coupling will decrease. This results in a greater left-limb bias in left-handers and right-limb bias in right-handers. This "increased handedness" prediction was confirmed in an experiment in which 20 left-handed and 20 right-handed individuals performed 1:1 coordination with hand-held rigid pendulums. Manipulations of left and right pendulum lengths controlled delta omega, and the coupled frequency was determined by a metronome. Also confirmed was the prediction that the small shift in equilibria from in-phase and anti-phase due to the intrinsic asymmetry should be amplified in left-handers when delta omega > 0 and in right-handers when delta omega < 0. Further, the bias in left-handers was more consistent than the bias in right-handers, and a subgroup of right-handers was identified who performed similarly to left-handers. The coordination dynamics of functional asymmetry provides insights into the elementary synergy between the limbs, the dynamical mechanism that modulates it, and the nature of the asymmetry in left-handed and right-handed individuals.

Adult↗
PubMed1980

Relationship between the dynamic range of cochlear nerve fibres and their spontaneous activity.

The dynamic ranges of cochlear nerve fibres in cats were determined automatically and were related to the fibres' rates of spontaneous activity, in both pooled data and data from individual cochlear nerves. The dynamic range represents the range of levels of a tone at the characteristic frequency of the fibre evoking mean discharge rates between spontaneous and saturated activity. In common with the findings of other investigators, the distribution of spontaneous discharge rates was bimodal. The total population could be divided into two sub-populations with spontaneous discharge rates above and below 15 spikes/s, respectively. The mean dynamic range of fibres having spontaneous discharge rates in excess of 15 spikes/s, was 41 dB (+/- 0.65 S.E.); that for fibres with rates below 15 spikes/s was 50 dB (+/- 1.2 S.E.). While the distributions of dynamic ranges of the two populations overlapped, they were significantly different, and dynamic ranges in excess of 60 dB were only found in substantial numbers (23%) in the population having low spontaneous discharge rates. Some of these were not saturated at the highest stimulus levels used.

Animals↗
PubMed1984

Hearing threshold and heart rate in men after repeated exposure to dynamic muscle work, sinusoidal vs stochastic whole body vibration and stable broadband noise.

Changes in the temporary hearing threshold ( TTS2 ) and heart rate (HR) were examined in subjects exposed to stable noise, whole body vibration and dynamic muscular work at a dry-bulb temperature of 30 degrees C. The exposure combinations consisted of three categories of dynamic muscular work with varying loads ( 2W , 4W , 8W ), of two categories of noise and of three categories of vibration. The noise categories were: (1) no noise, and (2) stable, broadband (bandwidth 0.2-16.0 kHz) A-weighted noise with an intensity of 90 dB. The vibration categories were: (1) no vibration, (2) sinusoidal whole body vibration (Z-axis) with a frequency of 5 Hz, and (3) stochastic broadband (bandwidth 2.8-11.2 Hz) whole body vibration. A single test consisted of a control period of 30 min, three consecutive exposure periods of 16 min, each followed by a 4-min post-exposure interval and a recovery period of 15 min. The results of the variance analyses indicated that noise had the most notable effect on the TTS2 values at the hearing frequencies of both 4 and 6 kHz. Of the paired combinations, noise plus vibration and noise plus dynamic muscular work caused the most obvious combined effects. The combined effect of all three factors (noise, vibration and work) on the TTS2 values after three consecutive exposure periods was significant at the 2.5% level at the 4 kHz hearing frequency and at the 5% level at the 6 kHz hearing frequency. The added effect of vibration on enhanced TTS2 values was particularly clear when the vibration was stochastic and when the subjects had a low ( 2W ) working efficiency. Increasing the working efficiency, on the other hand, seemed to retard increases in the hearing threshold. Thus TTS2 values seemed to reflect the changes in HR values. It is as if the low rate of cardiovascular activity during light dynamic muscular work had enabled the manifestation of the cardiovascular effects of noise and vibration; during strenuous dynamic muscular work, however, the high rate of cardiovascular activity aimed in some way at compensating for the effects of noise and vibration on blood circulation.

Adult↗
PubMed1985

Dynamics of sweating in men and women during passive heating.

The dynamics of sweating was investigated at rest in 8 men and 8 women. Electrical skin resistance (ESR), rectal temperature (Tre) and mean skin temperature (Tsk) were measured in subjects exposed to 40 degrees C environmental temperature, 30% relative air humidity, and 1 m X s-1 air flow. Sweat rate was computed from continuous measurement of the whole body weight loss. It was found that increases in Tre, Tsk and mean body temperature (Tb) were higher in women than in men by 0.16, 0.38 and 0.21 degrees C, but only the difference in delta Tb was significant (p less than 0.05). The dynamics of sweating in men and women respectively, was as follows: delay (td) 7.8 and 18.1 min (p less than 0.01), time constant (tau) 7.5 and 8.8 min (N.S.), inertia time (ti) 15.3 and 26.9 min (p less than 0.002), and total body weight loss 153 and 111 g X m-2 X h-1 (p less than 0.001). Dynamic parameters of ESR did not differ significantly between men and women. Inertia times of ESR and sweat rate correlated in men (r = 0.93, p less than 0.001), and in women (r = 0.76, p less than 0.02). In men, delta Tre correlated with inertia time of sweat rate (r = 0.81, p less than 0.01) as well as with the inertia time of ESR (r = 0.83, p less than 0.001). No relation was found between delta Tre and the dynamics of sweating in women. It is concluded that the dynamics of sweating plays a decisive role in limiting delta Tre in men under dry heat exposure. The later onset of sweating in women does not influence the rectal temperature increase significantly. In women, delta Tre is probably limited by a complex interaction of sweating, skin blood flow increase, and metabolic rate decrease.

Adult↗
PubMedDate not supplied

Microbial growth dynamics on the basis of individual budgets.

The popular theories for microbial dynamics by Monod, Pirt and Droop are shown to be special cases of a model for individual budgets, in which growth and maintenance are on the expense of reserve materials. The dynamics of reserve materials is a first order process with a relaxation time proportional to cell length; maintenance is proportional to cell volume, and uptake, which depends hyperbolically on substrate density, is proportional to cell volume as well. Because of the latter, population dynamics depends on the behaviour of the individuals in a simple way, such that the cell volume distribution has no quantitative effect. When uptake is proportional to the surface area of the cell, which is realistic from a physical point of view, the relation between the individual level and the population one becomes more complicated and the cell size and shape distribution affects population dynamics. It is shown how the changing shape of rods modifies uptake and, consequently, growth. The concept of energy conductance, defined as the ratio of the maximum surface area specific uptake and the volume specific energy reserve has been introduced in the analysis of microbial dynamics. The first tentative results indicate that the value for E. coli is close to the mean value for a wide variety of animals. Properties of the model for cell suspension at constant substrate densities are analyzed and tested against a variety of experimental data from the literature on both the individual and the population level.

Animals↗
PubMed1991

Modulation of skin sensitivity by dynamic and isometric exercise in man.

The effect of dynamic cycle ergometer exercise and isometric leg exercise on skin sensitivity was studied in man. Exercise was performed at different loads. Cutaneous sensitivity to innocuous and noxious thermal stimuli was tested using a contact thermostimulator and sensitivity to tactile stimuli was tested using electrical stimuli. During isometric exercise a segmental (the exercising limb), but not a multisegmental, phasic decrease of cutaneous thermal sensitivity to innocuous stimuli was found. At the isometric forces used the effect on tactile and heat pain sensitivity was not significant. During dynamic exercise a multisegmental, load-dependent decrease of sensitivity in all tested sensory modalities was found and this attenuation disappeared gradually after the end of exercise. In contrast to isometric exercise, the decrease of sensitivity produced by dynamic exercise was most evident in tactile sensitivity. The size of the stimulus area (7.9 vs 11.8 cm2) did not have a significant effect on the magnitude of the exercise-induced decrease of cutaneous thermal sensitivity to innocuous stimuli. It was concluded that underlying the modulation of skin sensitivity by dynamic and isometric exercise were mechanisms that were different, at least to a small extent. Isometric exercise produced a segmental modulation of skin sensitivity due to central neuronal mechanisms, independent of exercise-induced stress. Exercise-induced stress could have caused the modulation of skin sensitivity by dynamic exercise.

Adult↗
PubMed1976

Analysis of the dynamic responses of deefferented primary muscle spindle endings to ramp stretch.

A detailed analysis of the complex dynamic response of 8 deefferented primary muscle spindle endings to ramp stretches of the extensor digitorum longus muscle (EDL) was made in anaesthetized cats. The analysis was based on Lennerstand's linear muscle spindle model, in which the dynamic peak, i.e. the peak frequency at the end of the dynamic phase of a ramp stretch, is assumed to consist of three components: a position response, a slow velocity response, and a quick velocity response. The components of the dynamic peaks analysed were fairly well correlated with the static behaviour of the primary muscle spindle endings, the latter, in turn, being regarded as an indicator of the spindles' location in the non-homogeneous extrafusal muscle. The results thus provide a satisfactory explanation of the high correlations between the static and gross dynamic behaviour of deefferented primary muscle spindle endings of the EDL previously reported from our laboratory.

Animals↗
PubMed1982

Response of blood pressure and plasma norepinephrine to propranolol, metoprolol and clonidine during isometric and dynamic exercise in hypertensive patients.

The effects of metropolol (beta 1-selective), propranolol (nonselective) and clonidine (central alpha-stimulant) on plasma norepinephrine, blood pressure and heart rate were assessed at rest, during isometric work and dynamic exercise in 15 patients with moderate hypertension. Metroprolol resulted in a lower diastolic blood pressure during isometric and dynamic exercise that propranolol, which was paralleled by a lower plasma norepinephrine level during dynamic work; both beta-adrenergic blocking compounds resulted in a lower heart rate in all test situations than that obtained with clonidine; clonidine produced similar control of diastolic blood pressure to that obtained with the beta-adrenergic blocking agents, but did not clearly attenuate the systolic blood pressure response to dynamic exercise. Plasma norepinephrine concentrations tended to be lowest following clonidine, especially during dynamic work. The findings support the hypothesis that the central action of clonidine inhibits peripheral release of norepinephrine, but is insufficient to attenuate cardiac stimulation by physical exercise. The fact that propranolol caused higher plasma norepinephrine concentrations than metoprolol during exercise may explain the difference in the blood pressure responses during exercise.

Adult↗
PubMed2000

Diagnosis of enteroceles by dynamic anorectal endosonography.

PURPOSE: Enteroceles are herniations of the lining of the peritoneum and intestinal loops into the pouch of Douglas. They may accompany other pelvic and anorectal disorders or cause outlet obstruction. So far they are only diagnosed by defecography. We investigated the use of dynamic anorectal endosonography to detect this disorder. METHODS: Seventeen female patients with a defecation disorder were investigated by proctoscopy and endoluminal ultrasonography. In 14 patients defecography followed. Endosonography was performed using the curved array 7.5 MHz scanner directed to the ventral rectal wall. Dynamic studies were undertaken during rest and during maximal straining. The minimal distance between the inner verge of the anal canal and the peritoneal cavity was determined. RESULTS: Dynamic endosonography detected enteroceles in six patients in which the pouch of Douglas opened during straining and intestinal loops moved toward the anus. The diagnosis of enteroceles was confirmed in all patients by defecography giving a specificity of 100 percent. No enterocele was detected in the remaining eight patients with defecography, leading to a 100 percent sensitivity for endosonography. Comparing the 6 patients with enteroceles with the 11 patients without enterocele, the peritoneal-anal distances were at rest 3.9 +/- 0.5 and 3.3 +/- 0.5 cm (P < 0.05) and during straining 3.6 +/- 0.5 and 1.3 +/- 0.2 cm (P < 0.001), respectively. The change in peritoneal-anal distance was 2 +/- 0.5 cm in the enterocele group and 0.3 +/- 0.4 cm in the control group (P < 0.001). Two patients with enteroceles had complete rectal prolapse. Four patients with enteroceles underwent surgery. Postsurgical endoluminal endosonography showed closure of the pouch of Douglas. CONCLUSIONS: Enteroceles may be diagnosed by dynamic anorectal endosonography. Compared with defecography dynamic anorectal endosonography is easier to perform, less cumbersome for the patient, and bears no radiation exposure. Therefore, this new diagnostic means may be useful in first-line search for enteroceles, but further studies are needed to prove its sensitivity for screening of this disorder.

Aged↗

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