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At least 1,135 records · Page 63Linked to original sources
PubMed1992

Application of a directed conformational search for generating 3-D coordinates for protein structures from alpha-carbon coordinates.

A directed conformational search algorithm using the program CONGEN (ref. 3), which samples backbone conformers, is described. The search technique uses information from the partially built structures to direct the search process and is tested on the problem of generating a full set of backbone Cartesian coordinates given only alpha-carbon coordinates. The method has been tested on six proteins of known structure, varying in size and classification, and was able to generate the original backbone coordinates with RMSs ranging from 0.30-0.87A for the alpha-carbons and 0.5-0.99A RMSs for the backbone atoms. Cis peptide linkages were also correctly identified. The procedure was also applied to two proteins available with only alpha-carbon coordinates in the Brookhaven Protein Data Bank; thioredoxin (SRX) and triacylglycerol acylhydrolase (TGL). All-atom models are proposed for the backbone of both these proteins. In addition, the technique was applied to randomized coordinates of flavodoxin to assess the effects of irregularities in the data on the final RMS. This study represents the first time a deterministic conformational search was used on such a large scale.

Algorithms↗
PubMed2006

A neural network based method for optical patient set-up registration in breast radiotherapy.

Patient set-up optimization is required in breast-cancer radiotherapy to fill the accuracy gap between personalized treatment planning and uncertainties in the irradiation set-up. Opto-electronic systems allow implementing automatic procedures to minimize the positional mismatches of light-reflecting markers located on the patient surface with respect to a corresponding reference configuration. The same systems are used to detect the position of the irradiated body surface by means of laser spots; patient set-up is then corrected by matching the control points onto a CT based reference model through surface registration algorithms. In this paper, a non-deterministic approach based on Artificial Neural Networks is proposed for the automatic, real-time verification of geometrical set-up of breast irradiation. Unlike iterative surface registration methods, no passive fiducials are used and true real-time performance is obtained. Moreover, the non-deterministic modeling performed by the neural algorithm minimizes sensitivity to intra-fractional and inter-fractional non-rigid motion of the breast. The technique was validated through simulated activities by using reference CT data acquired on four subjects. Results show that the procedure is able to detect and reduce simulated set-up errors and revealed high reliability in patient position correction, even when the surface deformation is included in testing conditions.

Breast Neoplasms↗
PubMed1992

Sexual mixing models: a comparison of analogue deterministic and stochastic models.

Models for sexual partner choice are discussed for the case of highly variable sexual activity in the population. It is demonstrated that the variances in the number of infected persons may be extremely large. For the random mixing model, higher order cumulants are also evaluated. On the basis of these results the applicability of deterministic models and models for expectations only are questioned. A general model is proposed for handling nonrandom, or correlated, mixing. The problem of inconsistency is overcome by considering the couples having sex as the natural unit in the model. In the case of s discrete homogeneous groups it is shown that only (s2) parameters defining the interaction between the groups can be chosen freely. Finally, the effect of correlation in partner choice is demonstrated by a bivariate lognormal model for partner choice.

Female↗
PubMed1999

Consequences of deterministic and random dynamics for the course of affective disorders.

BACKGROUND: Uni- and bipolar affective disorders tend to be recurrent and progressive. Illness patterns can evolve from isolated episodes to more rapid, rhythmic, and "chaotic" mood patterns. Nonlinear deterministic dynamics are currently proposed to explain this progression. However, most natural systems are nonlinear and noisy, and cooperative behavior of possible clinical relevance can result. METHODS: The latter issue has been studied with a mathematical model for progression of disease patterns in affective disorders. RESULTS: Deterministic dynamics can reproduce a progression from stable, to periodic, to chaotic patterns. Noise increases the spectrum of dynamic behaviors, enhances the responsiveness to weak activations, and facilitates the occurrence of aperiodic patterns. CONCLUSIONS: Noise might amplify subclinical vulnerabilities into disease onset and could induce transitions to rapid-changing dysrhythmic mood patterns. We suggest that noise-mediated cooperative behavior, including stochastic resonance, should be considered in appropriate models for affective illness.

Disease Progression↗
PubMed2000

Center of gravity motions and ankle joint stiffness control in upright undisturbed stance modeled through a fractional Brownian motion framework.

The authors modeled the center of gravity vertical projection (CG(v)) and the difference, CP - CG(v), which, combined, constitute the center of pressure (CP) trajectory, as fractional Brownian motion in order to investigate their relative contributions and their spatiotemporal articulation. The results demonstrated that CG(v) and CP - CG(v) motions are both endowed in complementary fashion with strong stochastic and part-deterministic behaviors. In addition, if the temporal coordinates remain similar for all 3 trajectories by definition, the switch between the successive control mechanisms appears for shorter displacements for CP - CG(v) and CG(v) than for CP trajectories. Results deduced from both input (CG(v)) and muscular stiffness (CP - CG(v)) thus provide insight into the way the central nervous system regulates stance control and in particular how CG and CP - CG are controlled.

Adult↗
PubMed2005

Internal noise stochastic resonance for intracellular calcium oscillations in a cell system.

By constructing a mesoscopic stochastic model for intracellular calcium oscillations in a cell system, we have investigated how the internal noise would influence the calcium oscillations of such a system using stochastic simulation methods and chemical Langevin method. It is found that stochastic calcium oscillations appear when the internal noise is considered, while the deterministic model only yields steady state. The performance of such oscillations undergoes a maximum with the variation of the internal noise level, indicating the occurrence of internal noise stochastic resonance. Interestingly, we find that the optimal system size matches well with the real cell size when the control parameter is tuned near the left Hopf bifurcation point, and such a match is robust to the variation of the control parameters.

Biological Clocks↗
PubMed2006

Noise-memory induced excitability and pattern formation in oscillatory neural models.

We report a noise-memory induced phase transition in an array of oscillatory neural systems, which leads to the suppression of synchronous oscillations and restoration of excitable dynamics. This phenomenon is caused by the systematic contributions of temporally correlated parametric noise, i.e., possessing a memory, which stabilizes a deterministically unstable fixed point. Changing the noise correlation time, a reentrant phase transition to noise-induced excitability is observed in a globally coupled array. Since noise-induced excitability implies the restoration of the ability to transmit information, associated spatiotemporal patterns are observed afterwards. Furthermore, an analytic approach to predict the systematic effects of exponentially correlated noise is presented and its results are compared with the simulations.

Action Potentials↗
PubMed1998

A periodogram-based method for the detection of steady-state visually evoked potentials.

The task of objective perimetry is to scan the visual field and find an answer about the function of the visual system. Flicker-burst stimulation--a physiological sensible combination of transient and steady-state stimulation--is used to generate deterministic sinusoidal responses or visually evoked potentials (VEP's) at the visual cortex, which are derived from the electroencephalogram by a suitable electrode array. In this paper we develop a new method for the detection of VEP's. Based on the periodogram of a time-series, we test the data for the presence of hidden periodic components, which correspond to steady-state VEP's. The method is applied successfully to real data.

Electroencephalography↗
PubMed1979

Analysis of "integrate-to-threshold" neural coding schemes.

Methods of analysis for some deterministic and stochastic variants of the integrate-to-threshold neural coding scheme are presented. Adaptation phenomena are modeled by means of feedforward and feedback adaptive threshold control. Simulations of sinusoidal and step responses reproduce satisfactorily the qualitative characteristics of adaptation as compared with physiological data. It is postulated that such adaptive threshold control may be accomplished by the release, or conformation change, of molecules involved in the control of excitable-channel dynamics.

Action Potentials↗
PubMed2001

Evolution of cardiac calcium waves from stochastic calcium sparks.

We present a model that provides a unified framework for studying Ca2+ sparks and Ca2+ waves in cardiac cells. The model is novel in combining 1) use of large currents (approximately 20 pA) through the Ca2+ release units (CRUs) of the sarcoplasmic reticulum (SR); 2) stochastic Ca2+ release (or firing) of CRUs; 3) discrete, asymmetric distribution of CRUs along the longitudinal (separation distance of 2 microm) and transverse (separated by 0.4-0.8 microm) directions of the cell; and 4) anisotropic diffusion of Ca2+ and fluorescent indicator to study the evolution of Ca2+ waves from Ca2+ sparks. The model mimics the important features of Ca2+ sparks and Ca2+ waves in terms of the spontaneous spark rate, the Ca2+ wave velocity, and the pattern of wave propagation. Importantly, these features are reproduced when using experimentally measured values for the CRU Ca2+ sensitivity (approximately 15 microM). Stochastic control of CRU firing is important because it imposes constraints on the Ca2+ sensitivity of the CRU. Even with moderate (approximately 5 microM) Ca2+ sensitivity the very high spontaneous spark rate triggers numerous Ca2+ waves. In contrast, a single Ca2+ wave with arbitrarily large velocity can exist in a deterministic model when the CRU Ca2+ sensitivity is sufficiently high. The combination of low CRU Ca2+ sensitivity (approximately 15 microM), high cytosolic Ca2+ buffering capacity, and the spatial separation of CRUs help control the inherent instability of SR Ca2+ release. This allows Ca2+ waves to form and propagate given a sufficiently large initiation region, but prevents a single spark or a small group of sparks from triggering a wave.

Animals↗
PubMed2006

Deterministic modelling and stochastic simulation of biochemical pathways using MATLAB.

The analysis of complex biochemical networks is conducted in two popular conceptual frameworks for modelling. The deterministic approach requires the solution of ordinary differential equations (ODEs, reaction rate equations) with concentrations as continuous state variables. The stochastic approach involves the simulation of differential-difference equations (chemical master equations, CMEs) with probabilities as variables. This is to generate counts of molecules for chemical species as realisations of random variables drawn from the probability distribution described by the CMEs. Although there are numerous tools available, many of them free, the modelling and simulation environment MATLAB is widely used in the physical and engineering sciences. We describe a collection of MATLAB functions to construct and solve ODEs for deterministic simulation and to implement realisations of CMEs for stochastic simulation using advanced MATLAB coding (Release 14). The program was successfully applied to pathway models from the literature for both cases. The results were compared to implementations using alternative tools for dynamic modelling and simulation of biochemical networks. The aim is to provide a concise set of MATLAB functions that encourage the experimentation with systems biology models. All the script files are available from www.sbi.uni-rostock.de/ publications_matlab-paper.html.

Biochemistry↗
PubMed1993

The case for chaos in childhood epidemics. II. Predicting historical epidemics from mathematical models.

The case for chaos in childhood epidemics rests on two observations. The first is that historical epidemics show various 'fieldmarks' of chaos, such as positive Lyapunov exponents. Second, phase portraits reconstructed from real-world epidemiological time series bear a striking resemblance to chaotic solutions obtained from certain epidemiological models. Both lines of evidence are subject to dispute: the algorithms used to look for the fieldmarks can be fooled by short, noisy time series, and the same fieldmarks can be generated by stochastic models in which there is demonstrably no chaos at all. In the present paper, we compare the predictive abilities of stochastic models with those of mechanistic scenarios that admit to chaotic solutions. The main results are as follows: (i) the mechanistic models outperform their stochastic counterparts; (ii) forecasting efficacy of the deterministic models is maximized by positing parameter values that induce chaotic behaviour; (iii) simple mechanistic models are equal if not superior to more detailed schemes that include age structure; and (iv) prediction accuracy for monthly notifications declines rapidly with time, so that, from a practical standpoint, the results are of little value. By way of contrast, next amplitude maps can successfully forecast successive changes in maximum incidence one or more years into the future.

Child↗
PubMed2003

Stochastic stage-structured modeling of the adaptive immune system.

We have constructed a computer model of the cytotoxic T lymphocyte (CTL) response to antigen and the maintenance of immunological memory. Because immune responses often begin with small numbers of cells and there is great variation among individual immune systems, we have chosen to implement a stochastic model that captures the life cycle of T cells more faithfully than deterministic models. Past models of the immune response have been differential equation based, which do not capture stochastic effects, or agent-based, which are computationally expensive. We use a stochastic stage-structured approach that has many of the advantages of agent-based modeling but is much more efficient. Our model can provide insights into the effect infections have on the CTL repertoire and the response to subsequent infections.

Adaptation, Physiological↗
PubMed1988

Carrier models for the simulation of Hodgkin's disease: a review with some extensions.

Epidemiologists have unearthed a good deal of both anecdotal and statistical evidence to suggest that Hodgkin's disease might be a transmissible entity. This paper critically reviews those findings which have led to the building of a single-region carrier model capable of making deterministic simulations for the temporal incidence of Hodgkin's disease. The results of fitting this model to the monthly incidence of the disease in Greater Manchester between 1962 and 1976 are discussed in relation to the plausibility of the equilibria associated with the more realistic solutions. In the light of this evaluation, the specification of the model is extended to include multi-region settings with more complex infective mechanisms. Finally, the improvements that accrue from adopting a stochastic modelling style are outlined.

Carrier State↗
PubMed2004

Effect of noise on the neutral direction of chaotic attractor.

A chaotic attractor from a deterministic flow must necessarily possess a neutral direction, as characterized by a null Lyapunov exponent. We show that for a wide class of chaotic attractors, particularly those having multiple scrolls in the phase space, the existence of the neutral direction can be extremely fragile in the sense that it is typically destroyed by noise of arbitrarily small amplitude. A universal scaling law quantifying the increase of the Lyapunov exponent with noise is obtained. A way to observe the scaling law in experiments is suggested.

Algorithms↗
PubMed2005

Division accuracy in a stochastic model of Min oscillations in Escherichia coli.

Accurate cell division in Escherichia coli requires the Min proteins MinC, MinD, and MinE as well as the presence of nucleoids. MinD and MinE exhibit spatial oscillations, moving from pole to pole of the bacterium, resulting in an average MinD concentration that is low at the center of the cell and high at the poles. This concentration minimum is thought to signal the site of cell division. Deterministic models of the Min oscillations reproduce many observed features of the system, including the concentration minimum of MinD. However, there are only a few thousand Min proteins in a bacterium, so stochastic effects are likely to play an important role. Here, we show that Monte Carlo simulations with a large number of proteins agree well with the results from a deterministic treatment of the equations. The location of minimum local MinD concentration is too variable to account for cell division accuracy in wild-type, but is consistent with the accuracy of cell division in cells without nucleoids. This finding confirms the need to include additional mechanisms, such as reciprocal interactions with the cell division ring or positioning of the nucleoids, to explain wild-type accuracy.

Adenosine Triphosphatases↗
PubMed2004

Deterministic stochastic resonance in a Rössler oscillator.

We discuss the characteristics of stochastic resonancelike behavior observed in a deterministic system. If a periodically forced Rössler oscillator strays from the phase locking state, it exhibits the intermittent behavior known as phase slips. When the periodic force is modulated by a weak signal, the phase slips synchronize with the weak signal statistically. We numerically demonstrate, in terms of interslip intervals and signal to noise ratio, that the maximum synchronization can be achieved with the optimum intensity of chaotic fluctuations. It is shown that the stochastic resonancelike behavior can be observed regardless of the choice of parameters. The frequency dependence of the signal indicates that there is an optimum frequency for the maximum resonance. The phase slip rate is derived based on the fact that the phase slips are caused by a boundary crisis caused by an unstable-unstable pair bifurcation. The interslip distributions obtained from the derived slip rate and the approximation theory of the time-dependent Poisson process agree with those obtained by numerical simulations. In addition, the maximum enhancement of a weak signal is shown to be achieved by adjusting the chaotic fluctuations even if a signal becomes mixed with noise.

Journal Article↗
PubMed2003

Doubly stochastic coherence via noise-induced symmetry in bistable neural models.

The generation of coherent dynamics due to noise in an activator-inhibitor system describing bistable neural dynamics is investigated. We show that coherence can be induced in deterministically asymmetric regimes via symmetry restoration by multiplicative noise, together with the action of additive noise which induces jumps between the two stable steady states. The phenomenon is thus doubly stochastic, because both noise sources are necessary. This effect can be understood analytically in the frame of a small-noise expansion and is confirmed experimentally in a nonlinear electronic circuit. Finally, we show that spatial coupling enhances this coherent behavior in a form of system-size coherence resonance.

Membrane Potentials↗