Biomedical subjects

Charles S Peskin

Publications and source records attributed to Charles S Peskin.

9 recordsLinked to original sources

PubMed2005

A computational fluid dynamics of 'clap and fling' in the smallest insects.

In this paper, we have used the immersed boundary method to solve the two-dimensional Navier-Stokes equations for two immersed wings performing an idealized 'clap and fling' stroke and a 'fling' half-stroke. We calculated lift coefficients as functions of time per wing for a range of Reynolds numbers (Re) between 8 and 128. We also calculated the instantaneous streamlines around each wing throughout the stroke cycle and related the changes in lift to the relative strength and position of the leading and trailing edge vortices. Our results show that lift generation per wing during the 'clap and fling' of two wings when compared to the average lift produced by one wing with the same motion falls into two distinct patterns. For Re=64 and higher, lift is initially enhanced during the rotation of two wings when lift coefficients are compared to the case of one wing. Lift coefficients after fling and during the translational part of the stroke oscillate as the leading and trailing edge vortices are alternately shed. In addition, the lift coefficients are not substantially greater in the two-winged case than in the one-winged case. This differs from three-dimensional insect flight where the leading edge vortices remain attached to the wing throughout each half-stroke. For Re=32 and lower, lift coefficients per wing are also enhanced during wing rotation when compared to the case of one wing rotating with the same motion. Remarkably, lift coefficients following two-winged fling during the translational phase are also enhanced when compared to the one-winged case. Indeed, they begin about 70% higher than the one-winged case during pure translation. When averaged over the entire translational part of the stroke, lift coefficients per wing are 35% higher for the two-winged case during a 4.5 chord translation following fling. In addition, lift enhancement increases with decreasing Re. This result suggests that the Weis-Fogh mechanism of lift generation has greater benefit to insects flying at lower Re. Drag coefficients produced during fling are also substantially higher for the two-winged case than the one-winged case, particularly at lower Re.

Animals↗

PubMed2004

Stochastic simulation of the mammalian circadian clock.

Circadian (nearly 24-h) clocks are remarkably accurate at timing biological events despite the randomness of their biochemical reactions. Here we examine the causes of their immunity to molecular noise in the context of a detailed stochastic mathematical model of the mammalian circadian clock. This stochastic model is a direct generalization of the deterministic mammalian circadian clock model previously developed. A feature of that model is that it completely specifies all molecular reactions, leaving no ambiguity in the formulation of a stochastic version of the model. With parameters based on experimental data concerning clock protein concentrations within a cell, we find accurate circadian rhythms in our model only when promoter interaction occurs on the time scale of seconds. As the model is scaled up by proportionally increasing the numbers of molecules of all species and the reaction rates with the promoter, the observed variability scales as 1/n(0.5), where n is the number of molecules of any species. Our results show that gene duplication increases robustness by providing more promoters with which the transcription factors of the model can interact. Although PER2 mutants were not rhythmic in the deterministic version of this model, they are rhythmic in the stochastic version.

Animals↗

PubMed2004

Model based conjectures on mammalian clock controversies.

We explore some predictions of a previously developed detailed model of molecular timekeeping in mammals (Forger and Peskin, PNAS, 100:14806) in areas where our understanding of clock mechanisms are incomplete. It is conjectured that: (1) the clock's 24-h period depends on mRNA stability. (2) REV-ERBalpha suppresses and/or entrains rhythms in peripheral tissues by regulating CRY1 transcription. (3) CLK:BMAL1 oscillations are suppressed in the suprachiasmatic nuclei to enhance oscillations in other proteins. (4) PER2 is ineffective at causing phase advances because it is not induced by light during the late night. (5) The clock is a limit cycle oscillator that shows characteristics of the evening and morning oscillator model.

Animals↗

PubMed2004

When vortices stick: an aerodynamic transition in tiny insect flight.

We have used computational fluid dynamics to study changes in lift generation and vortex dynamics for Reynolds numbers (Re) between 8 and 128. The immersed boundary method was used to model a two-dimensional wing through one stroke cycle. We calculated lift and drag coefficients as a function of time and related changes in lift to the shedding or attachment of the leading and trailing edge vortices. We find that the fluid dynamics around the wing fall into two distinct patterns. For Re> or =64, leading and trailing edge vortices are alternately shed behind the wing, forming the von Karman vortex street. For Re< or =32, the leading and trailing edge vortices remain attached to the wing during each 'half stroke'. In three-dimensional studies, large lift forces are produced by 'vortical asymmetry' when the leading edge vortex remains attached to the wing for the duration of each half stroke and the trailing edge vortex is shed. Our two-dimensional study suggests that this asymmetry is lost for Re below some critical value (between 32 and 64), resulting in lower lift forces. We suggest that this transition in fluid dynamics is significant for lift generation in tiny insects.

Animals↗

PubMed2003

A detailed predictive model of the mammalian circadian clock.

Experimental data on the circadian (approximately 24-h) clock in mammalian cells are vast, diverse, and detailed. Mathematical models are therefore needed to piece these data together and to study overall clock behavior. Previous models have focused on Neurospora or Drosophila or can be converted to a Drosophila model simply by renaming variables. Those models used Hill-type terms for transcription regulation and Michaelis-Menten type or delay terms for posttranslation regulation. Recent mammalian experimental data call into question some of the assumptions in these approaches. Moreover, gene duplication has led to more proteins in the mammalian system than in lower organisms. Here we develop a detailed distinctly mammalian model by using mass action kinetics. Parameters for our model are found from experimental data by using a coordinate search method. The model accurately predicts the phase of entrainment, amplitude of oscillation, and shape of time profiles of clock mRNAs and proteins and is also robust to parameter changes and mutations.

Animals↗

PubMed2003

A robust numerical algorithm for studying biomolecular transport processes.

We present a numerical algorithm that is well suited for the study of biomolecular transport processes. In the algorithm a continuous Markov process is discretized as a jump process and the jump rates are derived from local solutions of the continuous system. Consequently, the algorithm has two advantages over standard numerical methods: (1) it preserves detailed balance for equilibrium processes, (2) it is able to handle discontinuous potentials. The formulation of the algorithm also allows us to calculate the effective diffusion coefficient or, equivalently, the randomness parameter. We provide several simple examples of how to implement the algorithm. All the MATLAB functions files needed to reproduce the results presented in the article are available from www.amath.unc.edu/Faculty/telston/matlab_functions.

Algorithms↗

PubMed2003

A mathematical study of volume shifts and ionic concentration changes during ischemia and hypoxia.

The response of tissue to ischemia (cessation of blood flow and deprivation of oxygen) includes swelling of the intracellular space, shrinkage of the extracellular space, and an increase in the extracellular potassium concentration. The responses of cardiac and brain tissue to ischemia are qualitatively different in that cardiac tissue shows a rise in extracellular potassium over several minutes from about 5 to 10-12 mM followed by a plateau, while brain tissue shows a similar initial rise followed by a very rapid increase in extracellular potassium to levels of 50-80 mM. During hypoxia the flow of blood (or perfusate) is maintained and, while there is a substantial efflux of potassium from cells, there is little accumulation of potassium in the interstitium. A mathematical model is proposed and studied to try to elucidate the mechanism(s) underlying the increase in extracellular potassium, and the different time courses seen in neural and cardiac tissue. The model involves a Hodgkin-Huxley-type description of transmembrane ion currents, allows for ion concentrations as well as volumes to change for both the intracellular and extracellular space, and includes coupling of damaged tissue to nearby healthy tissue. The model produces a response to ischemia much like that seen in neural tissue, and the mechanism underlying this response in the model is determined. The same mechanism is not present in cardiac ion models, and this may explain the qualitative difference in response shown in cardiac tissue.

Animals↗

PubMed2003

Development and validation of computational models for mammalian circadian oscillators.

Circadian rhythms are endogenous rhythms with a cycle length of approximately 24 h. Rhythmic production of specific proteins within pacemaker structures is the basis for these physiological and behavioral rhythms. Prior work on mathematical modeling of molecular circadian oscillators has focused on the fruit fly, Drosophila melanogaster. Recently, great advances have been made in our understanding of the molecular basis of circadian rhythms in mammals. Mathematical models of the mammalian circadian oscillator are needed to piece together diverse data, predict experimental results, and help us understand the clock as a whole. Our objectives are to develop mathematical models of the mammalian circadian oscillator, generate and test predictions from these models, gather information on the parameters needed for model development, integrate the molecular model with an existing model of the influence of light and rhythmicity on human performance, and make models available in BioSpice so that they can be easily used by the general community. Two new mammalian models have been developed, and experimental data are summarized. These studies have the potential to lead to new strategies for resetting the circadian clock. Manipulations of the circadian clock can be used to optimize performance by promoting alertness and physiological synchronization.

Animals↗

PubMed2002

Numerical analysis of the flux and force generated by a correlation ratchet mechanism.

The correlation ratchet (CR) has been proposed as a possible mechanism for the operation of biomolecular motors. To test whether a CR mechanism is applicable to any particular motor, it is necessary to evaluate the unloaded velocity and the stall force of the CR mechanism. This paper is concerned with efficient numerical procedures for the determination of these quantities. In particular, the numerical results indicate that the stall force of a CR mechanism is quite limited, despite wide variations of the CR parameters.

Biomechanical Phenomena↗