Biomedical subjects

Lawrence Sirovich

Publications and source records attributed to Lawrence Sirovich.

7 recordsLinked to original sources

PubMed2007

Survival and apoptotic pathways initiated by TNF-alpha: modeling and predictions.

We present a mathematical model which includes TNF-alpha initiated survival and apoptotic cascades, as well as nuclear transcription of IkappaB. These pathways play a crucial role in deciding cell fate in response to inflammation and infection. Our model incorporates known specific protein-protein interactions as identified by experiments. Using these biochemical interactions, we develop a mathematical model of the NF-kappaB-mediated survival and caspase-mediated apoptosis pathways. Using mass action kinetics, we follow the formation of the survival and late complexes as well as the dynamics of DNA fragmentation. The effect of TNF-alpha concentration on DNA fragmentation is modeled and compares well with experiment. Nuclear transcription is also modeled phenomenologically by means of time lagged cytosolic concentrations. This results in transcription related concentrations undergoing under-damped oscillations, in qualitative and quantitative agreement with experiment. Using a tumor cell as a hypothetical model, we explore the interplay between the components of the survival and apoptotic pathways. Results are presented which make predictions on the limits of cellular oscillations in terms of time delay, initial concentration ratios and other features of the model. The model also makes clear predictions on cell viability in terms of DNA damage within the framework of TNF-alpha stimulus duration.

Apoptosis↗

PubMed2006

Dynamics of neural populations: stability and synchrony.

A population formulation of neuronal activity is employed to study an excitatory network of (spiking) neurons receiving external input as well as recurrent feedback. At relatively low levels of feedback, the network exhibits time stationary asynchronous behavior. A stability analysis of this time stationary state leads to an analytical criterion for the critical gain at which time asynchronous behavior becomes unstable. At instability the dynamics can undergo a supercritical Hopf bifurcation and the population passes to a synchronous state. Under different conditions it can pass to synchrony through a subcritical Hopf bifurcation. And at high gain a network can reach a runaway state, in finite time, after which the network no longer supports bounded solutions. The introduction of time delayed feedback leads to a rich range of phenomena. For example, for a given external input, increasing gain produces transition from asynchrony, to synchrony, to asynchrony and finally can lead to divergence. Time delay is also shown to strongly mollify the amplitude of synchronous oscillations. Perhaps, of general importance, is the result that synchronous behavior can exist only for a narrow range of time delays, which range is an order of magnitude smaller than periods of oscillation.

Action Potentials↗

PubMed2004

The organization of orientation and spatial frequency in primary visual cortex.

Many studies have demonstrated that the primary visual cortex contains multiple functional maps of visual properties (e.g., ocular dominance, orientation preference, and spatial-frequency preference), but as yet no consistent picture has emerged as to how these maps are related to one another. Three divergent, prior optical-imaging studies of spatial frequency are reanalyzed and critiqued in this article. Evidence is presented that a nonstimulus-specific response biased the interpretation of results in previous studies. In addition to reexamining four prior cat experiments, we carried out one new experiment. Through the use of different methods and a careful removal of the nonspecific response, we are led in all instances to a unique view of cortical organization for spatial-frequency preference. In particular, we find little apparent evidence for a columnar organization for spatial frequency. The response recorded by each image pixel may be viewed as arising from an admixture of low- and high-spatial-frequency populations. For most pixels, the ratio of these populations is 1:1.

Animals↗

PubMed2003

A pattern analysis of the second Rehnquist U.S. Supreme Court.

The second Rehnquist Court has remained unchanged in composition for 8 yr, resulting in a large temporally stable database. This paper reports on a mathematically objective analysis of this ensemble of rulings aimed at extracting key patterns and latent information. Although the rulings of a nine-justice Court require representation in nine dimensions, smaller spaces describe the Court's actions; e.g., a 2D subspace describes the margins of all decisions, and use of Shannon information shows that the Court acts as if composed of 4.68 ideal justices. Comparison is also made with the 1959-1961 and 1967-1969 Warren Courts. Both Warren Courts have remarkable parallels with the Rehnquist Court. In each instance, we present an optimal mapping of the justices between the Courts, which underscores the similarity in the workings of seemingly dissimilar courts.

Journal Article↗

PubMed2003

Extraction of periodic multivariate signals: mapping of voltage-dependent dye fluorescence in the mouse heart.

In many experimental circumstances, heart dynamics are, to a good approximation, periodic. For this reason, it makes sense to use high-resolution methods in the frequency domain to visualize the spectrum of imaging data of the heart and to estimate the deterministic signal content and extract the periodic signal from background noise in experimental data. In this paper, we describe the first application of a new method that we call cardiac rhythm analysis which uses a combination of principal component analysis and multitaper harmonic analysis to extract periodic, deterministic signals from high-resolution imaging data of cardiac electrical activity, We show that this method significantly increases the signal-to-noise ratio of our recordings, allowing for better visualization of signal dynamics and more accurate quantification of the properties of electrical conduction. We visualize the spectra of three cardiac data sets of mouse hearts exhibiting sinus rhythm, paced rhythm and monomorphic tachycardia. Then, for pedagogical purposes, we investigate the tachycardia more closely, demonstrating the presence of two distinct periodicities in the re-entrant tachycardia. Analysis of the tachycardia shows that cardiac rhythm analysis not only allows for better visualization of electrical activity, but also provides new opportunities to study multiple periodicities in signal dynamics.

Action Potentials↗

PubMed2003

Dynamics of neuronal populations: eigenfunction theory; some solvable cases.

A novel approach to cortical modelling was introduced by Knight and co-workers in 1996. In their presentation cortical dynamics is formulated in terms of interacting populations of neurons, a perspective that is in part motivated by modern cortical imaging. The approach may be regarded as the application of statistical mechanics to neuronal populations, and the simplest exemplar bears a kinship to the Boltzmann equation of kinetic theory. The disarming simplicity of this linear equation hides the complex behaviour it produces. A purpose of this paper is to investigate and reveal its intricacies by treating a series of solvable special cases. In particular we will focus on issues that relate to the spectral analysis of the underlying operators. A fairly thorough treatment is presented for a simple, but still useful example, that has important consequences for more general situations.

Cerebral Cortex↗

PubMed1995

A simple model of chaotic advection and scattering.

In this work, we study a blinking vortex-uniform stream map. This map arises as an idealized, but essential, model of time-dependent convection past concentrated vorticity in a number of fluid systems. The map exhibits a rich variety of phenomena, yet it is simple enough so as to yield to extensive analytical investigation. The map's dynamics is dominated by the chaotic scattering of fluid particles near the vortex core. Studying the paths of fluid particles, it is seen that quantities such as residence time distributions and exit-vs-entry positions scale in self-similar fashions. A bifurcation is identified in which a saddle fixed point is created upstream at infinity. The homoclinic tangle formed by the transversely intersecting stable and unstable manifolds of this saddle is principally responsible for the observed self-similarity. Also, since the model is simple enough, various other properties are quantified analytically in terms of the circulation strength, stream velocity, and blinking period. These properties include: entire hierarchies of fixed points and periodic points, the parameter values at which these points undergo conservative period-doubling bifurcations, the structure of the unstable manifolds of the saddle fixed and periodic points, and the detailed structure of the resonance zones inside the vortex core region. A connection is made between a weakly dissipative version of our map and the Ikeda map from nonlinear optics. Finally, we discuss the essential ingredients that our model contains for studying how chaotic scattering induced by time-dependent flow past vortical structures produces enhanced diffusivities. (c) 1995 American Institute of Physics.

Journal Article↗