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J P Keener

Publications and source records attributed to J P Keener.

At least 19 recordsLinked to original sources
PubMed2006

How Salmonella Typhimurium measures the length of flagellar filaments.

We present a mathematical model for the growth and length regulation of the filament of the flagellar motor of Salmonella Typhimurium. Under the assumption that the molecular constituents are translocated into the nascent filament by an ATPase and then move by molecular diffusion to the growing end, we find a monotonically decreasing relationship between the speed and the velocity of growth that is inversely proportional to length for a large length. This gives qualitative but not quantitative agreement with data of the velocity of growth. We also propose that the length of filaments is "measured" by the rate of secretion of the sigma(28)-antifactor FlgM, using negative feedback, and present a mathematical model of this regulatory network. The combination of this regulatory network with the length-dependent rate of growth enable the bacterium to detect length shortening and regrow severed flagellar filaments.

Algorithms↗
PubMed2005

A model for length control of flagellar hooks of Salmonella typhimurium.

We present a mathematical model for the growth and length regulation of the hook component of the flagellar motor of Salmonella typhimurium. Under the assumption that the molecular constituents are translocated into the nascent filament by an ATP-ase and then move by molecular diffusion to the growing end, where they polymerize into the growing tube, we find that there is a detectable transition from secretion limited growth to diffusion limited growth. We propose that this transition can be detected by the secretant FliK, allowing FliK to interact with FlhB thereby changing the secretion target of the type III secretion machinery and terminating the growth of the hook.

Bacterial Proteins↗
PubMed2002

Intrinsic H(+) ion mobility in the rabbit ventricular myocyte.

The intrinsic mobility of intracellular H(+) ions was investigated by confocally imaging the longitudinal movement of acid inside rabbit ventricular myocytes loaded with the acetoxymethyl ester (AM) form of carboxy-seminaphthorhodafluor-1 (carboxy-SNARF-1). Acid was diffused into one end of the cell through a patch pipette filled with an isotonic KCl solution of pH 3.0. Intracellular H(+) mobility was low, acid taking 20-30 s to move 40 microm down the cell. Inhibiting sarcolemmal Na(+)-H(+) exchange with 1 mM amiloride had no effect on this time delay. Net H(+)(i) movement was associated with a longitudinal intracellular pH (pH(i)) gradient of up to 0.4 pH units. H(+)(i) movement could be modelled using the equations for diffusion, assuming an apparent diffusion coefficient for H(+) ions (D(H)(app)) of 3.78 x 10(-7) cm(2) s(-1), a value more than 300-fold lower than the H(+) diffusion coefficient in a dilute, unbuffered solution. Measurement of the intracellular concentration of SNARF (approximately 400 microM) and its intracellular diffusion coefficient (0.9 x 10(-7) cm(2) s(-1)) indicated that the fluorophore itself exerted an insignificant effect (between 0.6 and 3.3 %) on the longitudinal movement of H(+) equivalents inside the cell. The longitudinal movement of intracellular H(+) is discussed in terms of a diffusive shuttling of H(+) equivalents on high capacity mobile buffers which comprise about half (approximately 11 mM) of the total intrinsic buffering capacity within the myocyte (the other half being fixed buffer sites on low mobility, intracellular proteins). Intrinsic H(+)(i) mobility is consistent with an average diffusion coefficient for the intracellular mobile buffers (D(mob)) of ~9 x 10(-7) cm(2) s(-1).

Algorithms↗
PubMed2002

Facilitation of intracellular H(+) ion mobility by CO(2)/HCO(3)(-) in rabbit ventricular myocytes is regulated by carbonic anhydrase.

Intracellular H(+) mobility was estimated in the rabbit isolated ventricular myocyte by diffusing HCl into the cell from a patch pipette, while imaging pH(i) confocally using intracellular ratiometric SNARF fluorescence. The delay for acid diffusion between two downstream regions approximately 40 microm apart was reduced from approximately 25 s to approximately 6 s by replacing Hepes buffer in the extracellular superfusate with a 5 % CO(2)/HCO(3)(-) buffer system (at constant pH(o) of 7.40). Thus CO(2)/HCO(3)(-) (carbonic) buffer facilitates apparent H(+)(i) mobility. The delay with carbonic buffer was increased again by adding acetazolamide (ATZ), a membrane permeant carbonic anhydrase (CA) inhibitor. Thus facilitation of apparent H(+)(i) mobility by CO(2)/HCO(3)(-) relies on the activity of intracellular CA. By using a mathematical model of diffusion, the apparent intracellular H(+) equivalent diffusion coefficient (D(H)(app)) in CO(2)/HCO(3)(-)-buffered conditions was estimated to be 21.9 x 10(-7) cm(2) s(-1), 5.8 times faster than in the absence of carbonic buffer. Facilitation of H(+)(i) mobility is discussed in terms of an intracellular carbonic buffer shuttle, catalysed by intracellular CA. Turnover of this shuttle is postulated to be faster than that of the intrinsic buffer shuttle. By regulating the carbonic shuttle, CA regulates effective H(+)(i) mobility which, in turn, regulates the spatiotemporal uniformity of pH(i). This is postulated to be a major function of CA in heart.

Acetazolamide↗
PubMed2001

A mathematical model for quorum sensing in Pseudomonas aeruginosa.

The bacteria Pseudomonas aeruginosa use the size and density of their colonies to regulate the production of a large variety of substances, including toxins. This phenomenon, called quorum sensing, apparently enables colonies to grow to sufficient size undetected by the immune system of the host organism. In this paper, we present a mathematical model of quorum sensing in P. aeruginosa that is based on the known biochemistry of regulation of the autoinducer that is crucial to this signalling mechanism. Using this model we show that quorum sensing works because of a biochemical switch between two stable steady solutions, one with low levels of autoinducer and one with high levels of autoinducer.

Bacterial Proteins↗
PubMed2001

Diffusion induced oscillatory insulin secretion.

Oscillatory secretion of insulin has been observed in many different experimental preparations. Here we examine a mathematical model for in vitro insulin secretion from pancreatic beta cells in a flow-through reactor. The analysis shows that oscillations result because of an important interplay between flow rate of the reactor and insulin diffusion. In particular, if the ratio of flow rate to volume of the reaction bed is too large, oscillations are eliminated, in contradiction to the conclusions of Maki and Keizer (L. W. Maki and Keizer J. Mathematical analysis of a proposed mechanism for oscillatory insulin secretion in perifused HIT-15 cells. Bull. Math. Biol., 57(1995), 569-591). Furthermore, with reasonable numbers for the experimental parameters and the diffusion of insulin, the model equations do not exhibit oscillations.

Bioreactors↗
PubMed2000

Elimination of spiral waves in cardiac tissue by multiple electrical shocks.

We study numerically the elimination of a spiral wave in cardiac tissue by application of multiple shocks of external current. To account for the effect of shocks we apply a recently developed theory for the interaction of the external current with cardiac tissue. We compare two possible feedback algorithms for timing of the shocks: a "local" feedback algorithm 11 (using an external electrode placed directly on the tissue) and a "global" feedback algorithm 22 (using the electrocardiogram). Our main results are: application of the external current causes a parametric resonant drift similar to that reported in previous model computations; the ratio of the threshold of elimination of the spiral wave by multiple shocks to the threshold of conventional single shock defibrillation in our model for cardiac tissue is about 0.5, while earlier, less realistic models predicted the value about 0.2; we show that an important factor for successful defibrillation is the location of the feedback electrode and the best results are achieved if the feedback electrode or the ECG lead is located at the boundary (or edge) of the cardiac tissue; the "local" and the "global" feedback algorithms show similar efficiency.

Algorithms↗
PubMed1999

The biphasic mystery: why a biphasic shock is more effective than a monophasic shock for defibrillation.

We demonstrate that a biphasic shock is more effective than a monophasic shock at eliminating reentrant electrical activity in an ionic model of cardiac ventricular electrical activity. This effectiveness results from early hyperpolarization that enhances the recovery of sodium inactivation, thereby enabling earlier activation of recovering cells. The effect can be seen easily in a model of a single cell and also in a cable model with a ring of excitable cells. Finally, we demonstrate the phenomenon in a two-dimensional model of cardiac tissue.

Electric Countershock↗
PubMed1996

Direct activation and defibrillation of cardiac tissue.

It is shown that inhomogeneity due to gap junctional resistance allows an excitable cable to be directly activated or defibrillated by the application of a large amplitude point stimulus of short duration. Multiple-scale analysis is used to derive a model equation describing the response of the excitable medium to stimuli, and this equation is analyzed to give quantitative estimates of the direct stimulus threshold and the defibrillation threshold. These estimates are shown to be in good agreement with experimental findings.

Electric Countershock↗
PubMed1996

A biophysical model for defibrillation of cardiac tissue.

We propose a new model for electrical activity of cardiac tissue that incorporates the effects of cellular microstructure. As such, this model provides insight into the mechanism of direct stimulation and defibrillation of cardiac tissue after injection of large currents. To illustrate the usefulness of the model, numerical stimulations are used to show the difference between successful and unsuccessful defibrillation of large pieces of tissue.

Animals↗
PubMed1993

Effects of high frequency stimulation on cardiac tissue with an inexcitable obstacle.

We study numerically the effects of high-frequency stimulation in excitable cardiac tissue with an inexcitable obstacle using a Fitz-Hugh Nagumo type model. We show that if the frequency of stimulation is sufficiently high and the size of the inexcitable obstacle is sufficiently large, then a re-entrant pattern can be initiated. We also show that with overdrive stimulation a re-entrant pattern can be removed provided there are no obstacles at which new re-entrant patterns are created.

Animals↗
PubMed1993

Generation of reentry in anisotropic myocardium.

INTRODUCTION: We investigated numerically the effects of the rotation of fiber axis orientation through the myocardial wall on wave propagation. METHODS AND RESULTS: We show that because of this rotation and inherent discrete properties of myocardium, a premature stimulus can create unidirectional conduction block leading to reentry. CONCLUSION: The dynamics of the subsequent reentrant patterns are complicated by the presence of rotational anisotropy, as the center of reentry drifts, and the reentry terminates in finite time when it collides with the domain boundary.

Anisotropy↗
PubMed1991

The effects of discrete gap junction coupling on propagation in myocardium.

A modified cable theory for a bi-domain model of myocardium that incorporates the effect of gap junctions as discrete objects coupling cardiac cells is derived. The theory is shown to be in agreement with a number of experiments that cannot be explained using standard continuous cable theory, and resolves some apparent contradictions on failure of propagation in two-dimensional anisotropic tissue. In addition, some as yet untested predictions of the theory are mentioned.

Action Potentials↗
PubMed1991

An eikonal-curvature equation for action potential propagation in myocardium.

We derive an "eikonal-curvature" equation to describe the propagation of action potential wavefronts in myocardium. This equation is used to study the effects of fiber orientation on propagation in the myocardial wall. There are significant computational advantages to the use of an eikonal-curvature equation over a full ionic model of action potential spread. With this model, it is shown that the experimentally observed misalignment of spreading action potential "ellipses" from fiber orientation in level myocardial surfaces is adequately explained by the rotation of fiber orientation through the myocardial wall. Additionally, it is shown that apparently high propagation velocities on the epicardial and endocardial surfaces are the result of propagation into the midwall region and acceleration along midwall fibers before reemergence at an outer surface at a time preceding what could be accomplished with propagation along the surface alone.

Action Potentials↗
PubMed1988

On the formation of circulating patterns of excitation in anisotropic excitable media.

We present a model of excitable media with the feature that it has a vulnerable phase during which a premature current stimulus will result in the formation of a reentrant self-sustained wave of excitation. The model exploits anisotropic coupling of identical cells, and is therefore useful as a model for the myocardium. We give rigorous verification that there is a vulnerable phase, and demonstrate numerically that permanently rotating waves are formed. Finally, it is shown that the direction of fastest propagation in myocardium is not necessarily the direction of highest safety factor, contrary to commonly accepted opinion.

Action Potentials↗
PubMed1984

The effect of epidemics on genetic evolution.

Mathematical models of a vector-borne infectious disease acting on a host population consisting of three genotypes which differ in susceptibility to, recovery from, and death due to the disease are presented and analyzed. Singular perturbation techniques are used to obtain a single differential equation describing the slow time evolution of gene frequencies.

Biological Evolution↗
PubMed1984

Global bifurcations of a periodically forced nonlinear oscillator.

The effects of periodic pulsatile stimulation on a simple mathematical model of biological oscillations, called the radial isochron clock (RIC), are investigated as a function of stimulus frequency and amplitude. This system can be reduced to a two parameter, one-dimensional circle map. Numerical and topological methods are used to give a very detailed picture of the observed bifurcations over the complete range of parameters. The bifurcations are generic for a class of models which generalize the RIC.

Biological Clocks↗