Vahid Rezania

Model of ionic currents through microtubule nanopores and the lumen.

It has been suggested that microtubules and other cytoskeletal filaments may act as electrical transmission lines. An electrical circuit model of the microtubule is constructed incorporating features of its cylindrical structure with nanopores in its walls. This model is used to study how ionic conductance along the lumen is affected by flux through the nanopores, both with and without an external potential applied across its two ends. Based on the results of Brownian dynamics simulations, the nanopores were found to have asymmetric inner and outer conductances, manifested as nonlinear IV curves. Our simulations indicate that a combination of this asymmetry and an internal voltage source arising from the motion of the C-terminal tails causes cations to be pumped across the microtubule wall and propagate in both directions down the microtubule through the lumen, returning to the bulk solution through its open ends. This effect is demonstrated to add directly to the longitudinal current through the lumen resulting from an external voltage source applied across the two ends of the microtubule. The predicted persistent currents directed through the microtubule wall and along the lumen could be significant in directing the dissipation of weak, endogenous potential gradients toward one end of the microtubule within the cellular environment.

Continuous model for microtubule dynamics with catastrophe, rescue, and nucleation processes

Microtubules are a major component of the cytoskeleton distinguished by highly dynamic behavior both in vitro and in vivo referred to as dynamic instability. We propose a general mathematical model that accounts for the growth, catastrophe, rescue, and nucleation processes in the polymerization of microtubules from tubulin dimers. Our model is an extension of various mathematical models developed earlier formulated in order to capture and unify the various aspects of tubulin polymerization. While attempting to use a minimal number of adjustable parameters, the proposed model covers a broad range of behaviors and has predictive features discussed in the paper. We have analyzed the range of resultant dynamical behavior of the microtubules by changing each of the parameter values at a time and observing the emergence of various dynamical regimes that agree well with the previously reported experimental data and behavior.

Normal Modes of Rotating Magnetic Stars

We investigate the effect of a magnetic field on the global oscillation modes of a rotating fluid star in the magnetohydrodynamic approximation. We present general equations for the modification of any type of fluid mode due to a general magnetic field that is not aligned with the stars spin axis. In the case of any internal dipole magnetic field, we derive the equations for the frequency corrections to the r-modes. We solve for the frequency correction explicitly for the case when the internal dipole field is force-free, including the uniform density case. In the weak-field limit, the spatial form of the r-mode velocity perturbation is unchanged, but the magnitude of the frequency in the rotating frame increases.

Vorticity affects the stability of neutron stars

The spin rate Omega of neutron stars at a given temperature T is constrained by the interplay between gravitational-radiation instabilities and viscous damping. Navier-Stokes theory has been used to calculate the viscous damping time scales and produce a stability curve for r modes in the (Omega,T) plane. In Navier-Stokes theory, viscosity is independent of vorticity, but kinetic theory predicts a coupling of vorticity to the shear viscosity. We calculate this coupling and show that it can in principle significantly modify the stability diagram at lower temperatures. As a result, colder stars can remain stable at higher spin rates.

A physiologically-based flow network model for hepatic drug elimination I: regular lattice lobule model

We develop a physiologically-based lattice model for the transport and metabolism of drugs in the functional unit of the liver, called the lobule. In contrast to earlier studies, we have emphasized the dominant role of convection in well-vascularized tissue with a given structure. Estimates of convective, diffusive and reaction contributions are given. We have compared drug concentration levels observed exiting the lobule with their predicted detailed distribution inside the lobule, assuming that most often the former is accessible information while the latter is not.

Quasi-periodic oscillations: Resonant shear Alfvén waves in neutron star magnetospheres

We propose a new model for quasi-periodic oscillations (QPOs) based on oscillating magnetohydrodynamic modes in neutron star magnetospheres. We argue that the interaction of the accretion disk with the magnetosphere can excite resonant shear Alfven waves in a region of enhanced density gradients, the region where accretion material flows along the magnetic field lines in the magnetosphere (see Fig. 1). We demonstrate that depending on the distance of this region from the star and the magnetic field strength, the frequency of the field line resonance can range from several Hz (a weaker field, farther from the star), to approximately kHz frequencies (a stronger field, ∼2−10 stellar radii from the star). We show that such oscillations are able to significantly modulate inflow of matter from the high density region toward the stars surface and possibly produce the observed X-ray spectrum. In addition, we show that the observed 2:3 frequency ratio of QPOs is a natural result of our model.

An r-mode in a magnetic rotating spherical layer: application to neutron stars

The combined impact of rotation and magnetic fields on oscillations of stellar fluids is still not well known theoretically. It mixes Alfv´ en and inertial waves. Neutron stars are a place where both effects may be at work. We aim to solve this problem in the context of the r-mode instability in neutron stars, as it appears when these modes are coupled to gravitational radiation. We consider a rotating spherical shell filled with a viscous fluid of infinite electrical conductivity and analyse propagation of model perturbations when a dipolar magnetic field is bathing the fluid layer. We perform an extensive numerical analysis and find that the m = 2 r-mode oscillation is influenced by the magnetic field when the Lehnert number (the ratio ∂

A physiologically-based flow network model for hepatic drug elimination III: 2D/3D DLA lobule models

BackgroundOne of the major issues in current pharmaceutical development is potential hepatotoxicity and drug-induced liver damage. This is due to the unique metabolic processes performed in the liver to prevent accumulation of a wide range of chemicals in the blood. Recently, we developed a physiologically-based lattice model to address the transport and metabolism of drugs in the liver lobule (liver functional unit).MethodIn this paper, we extend our idealized model to consider structural and spatial variability in two and three dimensions. We introduce a hexagonal-based model with one input (portal vein) and six outputs (hepatic veins) to represent a typical liver lobule. To capture even more realistic structures, we implement a novel sequential diffusion-limited aggregation (DLA) method to construct a morphological sinusoid network in the lobule. A 3D model constructed with stacks of multiple 2D sinusoid realizations is explored to study the effects of 3D structural variations. The role of liver zonation on drug metabolism in the lobule is also addressed, based on flow-based predicted steady-state O2 profiles used as a zonation indicator.ResultsWith this model, we analyze predicted drug concentration levels observed exiting the lobule with their detailed distribution inside the lobule, and compare with our earlier idealized models. In 2D, due to randomness of the sinusoidal structure, individual hepatic veins respond differently (i.e. at different times) to injected drug. In 3D, however, the variation of response to the injected drug is observed to be less extreme. Also, the production curves show more diffusive behavior in 3D than in 2D.ConclusionAlthough, the individual producing ports respond differently, the average lobule production summed over all hepatic veins is more diffuse. Thus the net effect of all these variations makes the overall response smoother. We also show that, in 3D, the effect of zonation on drug production characteristics appears quite small. Our new biophysical structural analysis of a physiologically-based 3D lobule can therefore form the basis for a quantitative assessment of liver function and performance both in health and disease

The use of compressive sensing and peak detection in the reconstruction of microtubules length time series in the process of dynamic instability

Microtubules (MTs) are intra-cellular cylindrical protein filaments. They exhibit a unique phenomenon of stochastic growth and shrinkage, called dynamic instability. In this paper, we introduce a theoretical framework for applying Compressive Sensing (CS) to the sampled data of the microtubule length in the process of dynamic instability. To reduce data density and reconstruct the original signal with relatively low sampling rates, we have applied CS to experimental MT lament length time series modeled as a Dichotomous Markov Noise (DMN). The results show that using CS along with the wavelet transform significantly reduces the recovery errors comparing in the absence of wavelet transform, especially in the low and the medium sampling rates. In a sampling rate ranging from 0.2 to 0.5, the Root-Mean-Squared Error (RMSE) decreases by approximately 3 times and between 0.5 and 1, RMSE is small. We also apply a peak detection technique to the wavelet coefficients to detect and closely approximate the growth and shrinkage of MTs for computing the essential dynamic instability parameters, i.e., transition frequencies and specially growth and shrinkage rates. The results show that using compressed sensing along with the peak detection technique and wavelet transform in sampling rates reduces the recovery errors for the parameters.

Building a 3D Virtual Liver: Methods for Simulating Blood Flow and Hepatic Clearance on 3D Structures.

In this paper, we develop a spatio-temporal modeling approach to describe blood and drug flow, as well as drug uptake and elimination, on an approximation of the liver. Extending on previously developed computational approaches, we generate an approximation of a liver, which consists of a portal and hepatic vein vasculature structure, embedded in the surrounding liver tissue. The vasculature is generated via constrained constructive optimization, and then converted to a spatial grid of a selected grid size. Estimates for surrounding upscaled lobule tissue properties are then presented appropriate to the same grid size. Simulation of fluid flow and drug metabolism (hepatic clearance) are completed using discretized forms of the relevant convective-diffusive-reactive partial differential equations for these processes. This results in a single stage, uniformly consistent method to simulate equations for blood and drug flow, as well as drug metabolism, on a 3D structure representative of a liver.