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PubMed2000

Carnot's cycle for small systems: irreversibility and cost of operations

In the thermodynamic limit, the existence of a maximal efficiency of energy conversion attainable by a Carnot cycle consisting of quasistatic isothermal and adiabatic processes precludes the existence of a perpetual machine of the second kind, whose cycles yield positive work in an isothermal environment. We employ the recently developed framework of the energetics of stochastic processes (called "stochastic energetics") to reanalyze the Carnot cycle in detail, taking account of fluctuations, without taking the thermodynamic limit. We find that in this nonmacroscopic situation both processes of connection to and disconnection from heat baths and adiabatic processes that cause distortion of the energy distribution are sources of inevitable irreversibility within the cycle. Also, the so-called null-recurrence property of the cumulative efficiency of energy conversion over many cycles and the irreversible property of isolated, purely mechanical processes under external "macroscopic" operations are discussed in relation to the impossibility of a perpetual machine, or Maxwell's demon. This analysis may serve as the basis for the design and analysis of mesoscopic energy converters in the near future.

Journal Article↗

PubMed1978

Mechanism of antigen-induced antibody biosynthesis from antibody precursors, the heavy and light immunoglobulin chains.

The immediate precursors of antibody molecules, the heavy (H) and light (L) peptide chains of the immunoglobulins, combine with each other by means of disulfide bonds formed by dehydrogenation of their cysteine residues. In the absence of an antigen this process yields the heterogeneous mixture of normal immunoglobulins. Antigens or their processed derivatives (Ag) interfere with this stochastic process by noncovalent combination with complementarily fitting H chains. The (Ag.H)(n) complexes thus formed, owing to the loss of rotational and translational freedom, combine preferentially with those L chains whose V(L) regions have some affinity for the determinants of the antigen molecule. Subsequent release of Ag from the (Ag.H.L)(n) complexes yields free antigen and antibody molecules. Each of the released Ag molecules can be used repeatedly for the same reaction cycle and thus can induce the biosynthesis of a large number of antibody molecules. Any macromolecule, natural or synthetic, that has at least a few polar groups and that can penetrate to the nascent H and L chains can thus act as an antigen. Whereas the structure of the H and L chains is genetically determined and transmitted through the germ line, the process induced by the antigen is a phenotypic phenomenon. The antigen acts in this process as a stereospecific cofactor or regulator of the thiol-disulfide transhydrogenation of the combining H and L chains of immunoglobulins.

Antibody Formation↗

PubMed2003

Why are there so few key mutant clones? The influence of stochastic selection and blocking on affinity maturation in the germinal center.

A small number of key somatic mutations lead to high-affinity binding in the anti-hapten immune responses to 2-phenyl-5-oxazolone (phOx) and (4-hydroxy-3-nitrophenyl)acetyl (NP). Affinity maturation models of the germinal center hold that B cells carrying these key mutations are preferentially selected for expansion within the germinal centers. However, additional factors are required to account for some quantitative aspects of affinity maturation in vivo. Radmacher et al. have shown that key mutants are observed in vivo significantly less frequently than expected by these models. To account for this finding, they propose that selection is a stochastic process where key mutants may be overlooked by positive selection or recruited out of the germinal center. While acknowledging that a minimal amount of stochastic selection is probably unavoidable in the germinal center, we instead propose a structural explanation for this key mutant discrepancy. This model is based on the existence of a large number of blocking mutations whose presence can prevent the ability of key mutations to confer high-affinity binding. Using mathematical modeling and computer simulation, we show that in addition to reconciling the key mutant discrepancy, the blocking model accounts for other aspects of experimental data that are not predicted by the stochastic selection model. In particular, the blocking model is consistent with the observation that key mutants generally exhibit a higher number of mutations per sequence in the phOx response, but a lower number in the NP response.

Amino Acid Sequence↗

PubMed1978

Eye movements of African chameleons: spontaneous saccade timing.

Despite asynchrony, saccades of left and right eyes of African chameleons had similar timing statistics. Prominent qualitative aspects of these statistics did not change if one or both eyes were masked. Evidently, an internal stochastic process regulated chameleon saccade generation.

Animals↗

PubMedDate not supplied

Fractal character of the electrocardiogram: distinguishing heart-failure and normal patients.

Statistical analysis of the sequence of heartbeats can provide information about the state of health of the heart. We used a variety of statistical measures to identify the form of the point process that describes the human heartbeat. These measures are based on both interevent intervals and counts, and include the interevent-interval histogram, interval-based periodogram, rescaled range analysis, the event-number histogram, Fano-factor, Allan Factor, and generalized-rate-based periodogram. All of these measures have been applied to data from both normal and heart-failure patients, and various surrogate versions thereof. The results show that almost all of the interevent-interval and the long-term counting statistics differ in statistically significant ways for the two classes of data. Several measures reveal 1/f-type fluctuations (long-duration power-law correlation). The analysis that we have conducted suggests the use of a conveniently calculated, quantitative index, based on the Allan factor, that indicates whether a particular patient does or does not suffer from heart failure. The Allan factor turns out to be particularly useful because it is easily calculated and is jointly responsive to both short-term and long-term characteristics of the heartbeat time series. A phase-space reconstruction based on the generalized heart rate is used to obtain a putative attractor's capacity dimension. Though the dependence of this dimension on the embedding dimension is consistent with that of a low-dimensional dynamical system (with a larger apparent dimension for normal subjects), surrogate-data analysis shows that identical behavior emerges from temporal correlation in a stochastic process. We present simulated results for a purely stochastic integrate-and-fire model, comprising a fractal-Gaussian-noise kernel, in which the sequence of heartbeats is determined by level crossings of fractional Brownian motion. This model characterizes the statistical behavior of the human electrocardiogram remarkably well, properly accounting for the behavior of all of the measures studied, over all time scales.

Electrocardiography↗

PubMed2002

Microscopic analysis of polymerization dynamics with individual actin filaments.

The polymerization-depolymerization dynamics of actin is a key process in a variety of cellular functions. Many spectroscopic studies have been performed in solution, but studies on single actin filaments have just begun. Here, we show that the time course of polymerization of individual filaments consists of a polymerization phase and a subsequent steady-state phase. During the steady-state phase, a treadmilling process of elongation at the barbed end and shortening at the pointed end occurs, in which both components of the process proceed at approximately the same rate. The time correlation of length fluctuation of the filaments in the steady-state phase showed that the polymerization-depolymerization dynamics follow a diffusion (stochastic) process, which cannot be explained by simple association and dissociation of monomers at both ends of the filaments.

Actins↗

PubMed1983

Movements of the luminal contents in two different regions of the caput epididymidis of the rat in vitro.

Transport of the epididymal contents was studied in vitro by filming, for 1-2.5 h, the movements of tiny, stained oil droplets injected through a micropipette into two regions of the lumen of the caput epididymidis: the most proximal part, with the widest outer diameter (region I), and the neighbouring, narrowest portion (region II). The movements of the oil droplets were pendular. Displacement, caused by a contraction of the wall spreading in either direction, was followed by a shorter, usually passive reflux leading to a small net displacement, delta l. The distance of transport during 5 min periods varied between 0.09 and 16.79 mm (median 1.0 mm) in region I and 0.05 and 3.62 mm (median 0.42 mm) in region II. Transport divided into periods when little or no net transport took place (slow transport) and periods when the transport was effective (fast transport). Although the periods of fast transport were infrequent, their significance in transport towards the ductus deferens was high. During 5 min sampling periods of fast transport, the pendular movements were longer in both regions: delta l was longer in region I and the probability of delta l being in the direction of transport was higher than during slow transport in both regions. The mean probability of delta l being in the direction of the ductus deferens was 0.63 in region I and 0.57 in region II. Higher frequency of pendular movements, longer delta l values and higher probability of delta l being towards the ductus deferens in region I than II suggest that the transport speed is higher in region I than II. Transport consisting of short steps occurring with variable probabilities in both directions is a stochastic process.

Animals↗

PubMed1995

[Stochastic models of neuronal activity].

Techniques for modeling of a stochastic activity of neurons are briefly reviewed. Our model is proposed, some experimental results with input Gaussian stochastic processes are discussed, and the concept of e-curves is introduced.

Models, Neurological↗

PubMed2001

Dynamics of moments of FitzHugh-Nagumo neuronal models and stochastic bifurcations.

For the study of the behavior of noisy neuronal models, Rodriguez and Tuckwell have introduced an elegant and systematic method which consists of replacing the system of stochastic differential equations with a system of deterministic equations representing the dynamics of the means, variances, and covariance of the state variables [R. Rodriguez and H.C. Tuckwell, Phys. Rev. E 54, 5585 (1996)]. In this work, we first report a modification of their method in the case of the FitzHugh-Nagumo model which enhances the accuracy of the approximation without including higher order moments. This method is then combined with a self-consistency argument in order to better characterize the behavior of the underlying stochastic processes through the computation of approximate auto- and cross-correlation functions of the state variables. Finally, we argue that the moments' equations can also reveal the existence of stochastic bifurcations, i.e., qualitative changes in the dynamics of stochastic systems.

Action Potentials↗

PubMed2005

Distinguishing random environmental fluctuations from ecological catastrophes for the North Pacific Ocean.

The prospect of rapid dynamic changes in the environment is a pressing concern that has profound management and public policy implications. Worries over sudden climate change and irreversible changes in ecosystems are rooted in the potential that nonlinear systems have for complex and 'pathological' behaviours. Nonlinear behaviours have been shown in model systems and in some natural systems, but their occurrence in large-scale marine environments remains controversial. Here we show that time series observations of key physical variables for the North Pacific Ocean that seem to show these behaviours are not deterministically nonlinear, and are best described as linear stochastic. In contrast, we find that time series for biological variables having similar properties exhibit a low-dimensional nonlinear signature. To our knowledge, this is the first direct test for nonlinearity in large-scale physical and biological data for the marine environment. These results address a continuing debate over the origin of rapid shifts in certain key marine observations as coming from essentially stochastic processes or from dominant nonlinear mechanisms. Our measurements suggest that large-scale marine ecosystems are dynamically nonlinear, and as such have the capacity for dramatic change in response to stochastic fluctuations in basin-scale physical states.

Animals↗

PubMed1999

[Research on stochastic factors of heart rhythm variability in nonlinear dynamic analysis].

In this study, the influence of external noise on heart rhythm variability (HRV) in nonlinear dynamic analysis and the internal stochastic factor of HRV were discussed in connection with their physiological significance. The sampling rate, stationary and non-uniformity time interval were analyzed. An interpolation algorithm for heart period was introduced. The experiment demonstrated that the influence was highly reduced by the mentioned procedure. The internal stochastic factors of HRV were investigated by several nonlinear dynamic methods such as surrogate data, mutual information and nonlinear forecasting. The results suggested the colligation of deterministic chaos and stochastic process should be a favorite to interpret HRV.

Electrocardiography↗

PubMed2005

Linear response to perturbation of nonexponential renewal processes.

We study the linear response of a two-state stochastic process, obeying the renewal condition, by means of a stochastic rate equation equivalent to a master equation with infinite memory. We show that the condition of perennial aging makes the response to coherent perturbation vanish in the long-time limit.

Journal Article↗

PubMed1997

Inversely correlated cycles in speed and turning in an ameba: an oscillatory model of cell locomotion.

Previous biophysical models of ameboid crawling have described cell movement in terms of a persistent random walk. Speed and orientation were treated in the latter model as independent and temporally homogeneous stochastic processes. We show here that, at least in the case of Dictyostelium discoideum, both speed control and reorientation processes involve a deterministic, periodic component. We also show that the processes are synchronized and negatively correlated, as was suggested by earlier findings. That is, increased turning correlates with periods of slow movement. Therefore, previous models are inconsistent with the behavior of cells. Using a heuristic approach, we have developed a mathematical model that describes the statistical properties of the cell's velocity and movement of its centroid. Our observations and the model are consistent with the phenomenological description of ameboid motility as a cyclic process of pseudopod extension and retraction.

Amoeba↗

PubMed2001

A convergence analysis of unconstrained and bound constrained evolutionary pattern search.

We present and analyze a class of evolutionary algorithms for unconstrained and bound constrained optimization on R(n): evolutionary pattern search algorithms (EPSAs). EPSAs adaptively modify the step size of the mutation operator in response to the success of previous optimization steps. The design of EPSAs is inspired by recent analyses of pattern search methods. We show that EPSAs can be cast as stochastic pattern search methods, and we use this observation to prove that EPSAs have a probabilistic, weak stationary point convergence theory. This convergence theory is distinguished by the fact that the analysis does not approximate the stochastic process of EPSAs, and hence it exactly characterizes their convergence properties.

Algorithms↗

PubMed2005

Stochastic evolutionary dynamics on two levels.

We consider a population that is subdivided into groups. Individuals reproduce proportional to their fitness. When a group reaches a certain size it has a probability to split into two groups while another group is eliminated. In this stochastic process, the number of groups is constant, while the total population size fluctuates between well-defined bounds. We calculate the fixation probability of newly introduced mutants under constant selection. We show that the described population structure acts as a suppressor of selection compared to an unstructured population of the same size. The maximum suppression of selection is obtained, when the number of groups equals the number of individuals per group. We also study opposing selection on two or more levels by analysing the evolutionary dynamics of hierarchically embedded Moran processes.

Animals↗

PubMed2004

Coupled amplification and degradation of exogenous RNA injected in amphibian oocytes.

The early development of amphibians takes place in the absence of significant transcription and is controlled at the post-transcriptional level. We have reported that in vitro synthesized transcripts injected into axolotl fertilized eggs or oocytes were not continuously degraded as their abundance apparently fluctuated over time, with detected amounts sometimes higher than initial injected amounts. To further characterize this phenomenon, we have co-injected RNA chain terminators to prevent RNA synthesis. This led to the suppression of fluctuations and to a regular decrease in the amount of transcripts that appeared to be more stable in the presence of inhibitors. These observations indicate a coupling between RNA synthesis and an accelerated degradation. Throughout the time course, cRNA molecules could be detected, and their abundance increased in the early phase of the kinetics, supporting the implication of an RNA-dependent RNA polymerase in an asymmetric amplification process. Finally, when the fate of the injected transcripts was investigated in individual oocytes, we observed an absolute increase in abundance in some but not all oocytes, supporting the existence of a limiting step in the initiation of the RNA amplification stochastic process.

Ambystoma mexicanum↗

PubMed1995

[A model of stochastic activity of the neuron].

Action Potentials↗

PubMed2005

Fractionally integrated process with power-law correlations in variables and magnitudes.

Motivated by the fact that many empirical time series--including changes of heartbeat intervals, physical activity levels, intertrade times in finance, and river flux values--exhibit power-law anticorrelations in the variables and power-law correlations in their magnitudes, we propose a simple stochastic process that can account for both types of correlations. The process depends on only two parameters, where one controls the correlations in the variables and the other controls the correlations in their magnitudes. We apply the process to time series of heartbeat interval changes and air temperature changes and find that the statistical properties of the modeled time series are in agreement with those observed in the data.

Algorithms↗