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PubMed2000

Regularization of diffusion-based direction maps for the tracking of brain white matter fascicles.

Magnetic resonance diffusion tensor imaging (DTI) provides information about fiber local directions in brain white matter. This paper addresses inference of the connectivity induced by fascicles made up of numerous fibers from such diffusion data. The usual fascicle tracking idea, which consists of following locally the direction of highest diffusion, is prone to erroneous forks because of problems induced by fiber crossing. In this paper, this difficulty is partly overcomed by the use of a priori knowledge of the low curvature of most of the fascicles. This knowledge is embedded in a model of the bending energy of a spaghetti plate representation of the white matter used to compute a regularized fascicle direction map. A new tracking algorithm is then proposed to highlight putative fascicle trajectories from this direction map. This algorithm takes into account potential fan shaped junctions between fascicles. A study of the tracking behavior according to the influence given to the a priori knowledge is proposed and concrete tracking results obtained with in vivo human brain data are illustrated. These results include putative trajectories of some pyramidal, commissural, and various association fibers.

Algorithms↗

PubMed2000

The measurement of diffusion and perfusion in biological systems using magnetic resonance imaging.

The aim of this review is to describe two recent developments in the use of magnetic resonance imaging (MRI) in the study of biological systems: diffusion and perfusion MRI. Diffusion MRI measures the molecular mobility of water in tissue, while perfusion MRI measures the rate at which blood is delivered to tissue. Therefore, both these techniques measure quantities which have direct physiological relevance. It is shown that diffusion in biological systems is a complex phenomenon, influenced directly by tissue microstructure, and that its measurement can provide a large amount of information about the organization of this structure in normal and diseased tissue. Perfusion reflects the delivery of essential nutrients to tissue, and so is directly related to its status. The concepts behind the techniques are explained, and the theoretical models that are used to convert MRI data to quantitative physical parameters are outlined. Examples of current applications of diffusion and perfusion MRI are given. In particular, the use of the techniques to study the pathophysiology of cerebral ischaemia/stroke is described. It is hoped that the biophysical insights provided by this approach will help to define the mechanisms of cell damage and allow evaluation of therapies aimed at reducing this damage.

Animals↗

PubMed2006

Noise-induced Min phenotypes in E. coli.

The spatiotemporal oscillations of the Escherichia coli proteins MinD and MinE direct cell division to the region between the chromosomes. Several quantitative models of the Min system have been suggested before, but no one of them accounts for the behavior of all documented mutant phenotypes. We analyzed the stochastic reaction-diffusion kinetics of the Min proteins for several E. coli mutants and compared the results to the corresponding deterministic mean-field description. We found that wild-type (wt) and filamentous (ftsZ-) cells are well characterized by the mean-field model, but that a stochastic model is necessary to account for several of the characteristics of the spherical (rodA-) and phospathedylethanolamide-deficient (PE-) phenotypes. For spherical cells, the mean-field model is bistable, and the system can get trapped in a non-oscillatory state. However, when the intrinsic noise is considered, only the experimentally observed oscillatory behavior remains. The stochastic model also reproduces the change in oscillation directions observed in the spherical phenotype and the occasional gliding of the MinD region along the inner membrane. For the PE- mutant, the stochastic model explains the appearance of randomly localized and dense MinD clusters as a nucleation phenomenon, in which the stochastic kinetics at low copy number causes local discharges of the high MinD(ATP) to MinD(ADP) potential. We find that a simple five-reaction model of the Min system can explain all documented Min phenotypes, if stochastic kinetics and three-dimensional diffusion are accounted for. Our results emphasize that local copy number fluctuation may result in phenotypic differences although the total number of molecules of the relevant species is high.

Adenosine Triphosphatases↗

PubMed2006

Nonequilibrium membrane fluctuations driven by active proteins.

We extend a model for nonthermal membrane undulations driven by active (adenosine triphosphate-dependent or light-harvesting) membrane proteins [N. Gov, Phys. Rev. Lett. 93, 268104 (2004)]. The present model accounts for the fact that proteins can diffuse laterally across the membrane surface and that individual proteins are expected to exert forces preferentially in one normal direction over the other (due to their orientation within the bilayer). The addition of these effects alters the scaling of fluctuation amplitudes with system size. Additionally, theoretical arguments and dynamic simulations both suggest that, in certain regimes, the probability distribution of fluctuation amplitudes is expected to be non-Gaussian (in contrast to thermal systems).

Biomechanical Phenomena↗

PubMed2003

Nucleosome repositioning via loop formation.

Active (catalyzed) and passive (intrinsic) nucleosome repositioning is known to be a crucial event during the transcriptional activation of certain eukaryotic genes. Here we consider theoretically the intrinsic mechanism and study in detail the energetics and dynamics of DNA-loop-mediated nucleosome repositioning, as previously proposed by earlier works. The surprising outcome of the present study is the inherent nonlocality of nucleosome motion within this model-being a direct physical consequence of the loop mechanism. On long enough DNA templates the longer jumps dominate over the previously predicted local motion, a fact that contrasts simple diffusive mechanisms considered before. The possible experimental outcome resulting from the considered mechanism is predicted, discussed, and compared to existing experimental findings.

Binding Sites↗

PubMed1997

Stochastic Dispersal Processes in Plant Populations

A dispersal model for airborne pollen based on assumptions about wind directionality, gravity, and a wind threshold at which pollen is taken by the wind is developed, using a three dimensional diffusion approximation. The bivariate probability distribution of pollen receipt by flowers at the same height as the pollen source is derived. Gravity, vertical random movements, and vegetation density turn out to have similar effects on this distribution. Maximum likelihood methods for estimating the combined parameters from data with multiple point or continuous pollen sources, and one or more plant varieties, are developed. Using an example data set from the literature, it is shown that our model gives a better fit than more traditional descriptive dispersal models of the form e-ar b. We also show that estimates of important properties of the dispersal distribution, such as the variances, become considerably smaller using our model than for the more traditional models. Finally, we discuss potential extensions and evolutionary implications of these types of models. Copyright 1997 Academic Press

Journal Article↗

PubMed2004

Asymmetric addition of ceramides but not dihydroceramides promotes transbilayer (flip-flop) lipid motion in membranes.

Transbilayer lipid motion in membranes may be important in certain physiological events, such as ceramide signaling. In this study, the transbilayer redistribution of lipids induced either by ceramide addition or by enzymatic ceramide generation at one side of the membrane has been monitored using pyrene-labeled phospholipid analogs. When added in organic solution to preformed liposomes, egg ceramide induced transbilayer lipid motion in a dose-dependent way. Short-chain (C6 and C2) ceramides were less active than egg ceramide, whereas dihydroceramides or dioleoylglycerol were virtually inactive in promoting flip-flop. The same results (either positive or negative) were obtained when ceramides, dihydroceramides, or diacylglycerols were generated in situ through the action of a sphingomyelinase or of a phospholipase C. The phenomenon was dependent on the bilayer lipid composition, being faster in the presence of lipids that promote inverted phase formation, e.g., phosphatidylethanolamine and cholesterol; and, conversely, slower in the presence of lysophosphatidylcholine, which inhibits inverted phase formation. Transbilayer motion was almost undetectable in bilayers composed of pure phosphatidylcholine or pure sphingomyelin. The use of pyrene-phosphatidylserine allowed detection of flip-flop movement induced by egg ceramide in human red blood cell membranes at a rate comparable to that observed in model membranes. The data suggest that when one membrane leaflet becomes enriched in ceramides, they diffuse toward the other leaflet. This is counterbalanced by lipid movement in the opposite direction, so that net mass transfer between monolayers is avoided. These observations may be relevant to the physiological mechanism of transmembrane signaling via ceramides.

Bacillus cereus↗

PubMed1987

Interferometric technique for investigation of laser thermal retinal damage.

We describe a new technique for investigating laser-tissue interactions based on the use of an interferometric laser exposure pattern. A Michelson interferometer is used to generate a sinusoidal fringe exposure pattern. The periodicity of the fringe pattern may be adjusted from macroscopic dimensions to a scale of microns without the need for an imaging plane. Since fringe pattern periodicity is more adjustable and directly measureable than laser spot size, this technique offers significant advantages for studying the effects of thermal damage and diffusion in the irradiated tissue. In addition, the comparison of tissue response with theoretical models is simplified since the sinusoidal fringe pattern is itself an eigenfunction of the thermal diffusion equation. This technique is demonstrated for argon laser photocoagulation in the rabbit retina. Exposures at durations comparable to the thermal relaxation time produced spatially confined lesions, while those at much longer durations resulted in significant diffusion of the thermal damage beyond the primary targeted regions. The role of thermal diffusion can thus be assessed directly from the ophthalmoscopic and histologic appearances of the lesions. This technique can be employed to study thermal diffusion and other transport phenomena occurring in laser-tissue interactions for a variety of laser sources and tissue targets.

Animals↗

PubMed2006

Combined AFM and two-focus SFCS study of raft-exhibiting model membranes.

Dioleoylphosphatidylcholine/sphingomyelin/cholesterol (DOPC/SM/cholesterol) model membranes exhibit liquid-liquid phase separation and therefore provide a physical model for the putative liquid-ordered domains present in cells. Here we present a combination of atomic force microscopy (AFM) imaging, force measurements, confocal fluorescence imaging and two-focus scanning fluorescence correlation spectroscopy (two-focus SFCS) to obtain structural and dynamical information about this model membrane system. Partition coefficients and diffusion coefficients in the different phases were measured with two-focus SFCS for numerous fluorescent lipid analogues and proteins, while being directly related to the lateral organization of the membrane and its mechanical properties probed by AFM. Moreover we show how the combination of these different approaches is effective in reducing artifacts resulting from the use of a single technique.

Biophysics↗

PubMed1995

Comparison of central core and radially separated models of renal inner medulla.

In this paper we describe the effect of partitioning exchange of ascending thin limb (ATL) and collecting duct (CD) between a central vascular space (CORE) and a radially separated capillary node (NODE) in a mathematical model of the concentrating mechanism of the renal inner medulla. A detailed description of the model has been provided [J. L. Stephenson, J. F. Jen, H. Wang, and R. P. Tewarson. Am. J. Physiol. 268 (Renal Fluid Electrolyte Physiol. 37): F680-F692, 1995]. We define a partition coefficient theta, which denotes the fractional exchange of CD and ATL with the NODE. Thus with theta = 0 we have a central core model, in which the ATL and CD exchange with the CORE only, and with theta = 1 we have a totally radially separated model, in which the ATL and CD exchange with the NODE only. Decreasing the partition coefficient from 1 to 0 effects a continuous transition from a totally radially separated model to a central core model. As this transition progresses with increasing exchange with the CORE, the osmolalities in all structures become nearly the same at the papilla, and the ability to transport salt uphill is lost. This is true even with no radial diffusion. However, radial diffusion and direct exchange with the CORE act synergistically in decreasing osmolality differences at the papilla and the capacity for convective uphill transport. These are lost in a more or less parallel way. There is, however, no significant concomitant change in concentrating ability. These results indicate that models with radial mixing of the interstitial vascular space are probably reasonably good approximations for the inner medulla.

Animals↗

PubMed1998

Use of image-based information in judgments of surface-reflectance properties.

We examined how well we can recover surface-reflectance properties from shading patterns under changes in surface shape. The stimulus we used was a square surface modulated in depth by a low-pass-filtered random field and rendered by the Phong illumination model [Commun. ACM 18, 311 (1975)]. Two different surface images (target and match) were presented side by side, with either the viewing direction or the surface-normal direction rotating around the horizontal axis. The target shape was manipulated by changing the spatial spectrum, and the target reflectance was manipulated by changing the diffuse-reflection coefficient and the specular-reflection exponent (shininess) of the Phong model. The shape parameters of the match stimulus were fixed, but its reflectance parameters were under the control of subjects, who had to make the apparent reflectance of the two surfaces as similar as possible. The results showed that the constant error (difference between simulated and matched values) was large except when the two surfaces had the same shape parameters or when they differed only in scale. The pattern of the constant errors and response variabilities suggests that the judgments of the subjects were based on the similarity of the luminance histogram of the surface image. Our results demonstrate a limitation of surface-reflectance constancy for changes in shape and the importance of image-based information in reflectance judgments. The results are discussed in relation to previous studies that showed effects of spatial layout on surface-reflectance perception.

Color Perception↗

PubMedDate not supplied

Single-file diffusion and neurotransmitter transporters: Hodgkin and Keynes model revisited.

Norepinephrine transporters (NETs) use the Na gradient to remove norepinephrine (NE) from the synaptic cleft of adrenergic neurons following NE release from the presynaptic terminal. By coupling NE to the inwardly directed Na gradient, it is possible to concentrate NE inside cells. This mechanism, which is referred to as co-transport or secondary transport (Läuger, 1991, Electrogenic Ion Pumps, Sinauer Associates) is apparently universal: Na coupled transport applies to serotonin transporters (SERTs), dopamine transporters (DATs), glutamate transporters, and many others, including transporters for osmolites, metabolites and substrates such as sugar. Recently we have shown that NETs and SERTs transport norepinephrine or serotonin as if Na and the transmitter permeated through an ion channel together 'Galli et al., 1998, PNAS 95, 13260-13265; Petersen and DeFelice, 1999, Nature Neurosci. 2, 605-610'. These data are paradoxical because it has been difficult to envisage how NE, for example, would couple to Na if these ions move passively through an open pore. An 'alternating access' model is usually evoked to explain coupling: in such models NE and Na bind to NET, which then undergoes a conformational change to release NE and Na on the inside. The empty transporter then turns outward to complete the cycle. Alternating-access models never afford access to an open channel. Rather, substrates and co-transported ions are occluded in the transporter and carried across the membrane. The coupling mechanism we propose is fundamentally different than the coupling mechanism evoked in the alternating access model. To explain coupling in co-transporters, we use a mechanism first evoked by 'Hodgkin and Keynes (1955) J. Physiol. 128, 61-88' to explain ion interactions in K-selective channels. In the Hodgkin and Keynes model, K ions move single-file through a long narrow pore. Their model accounted for the inward/outward flux ratio if they assumed that two K ions queue within the pore. We evoke a similar model for the co-transport of transmitter and Na. In our case, however, coupling occurs not only between like ions but also between unlike ions (i.e. the transmitter and Na ). We made a replica of the Hodgkin and Keynes mechanical model to test our ideas, and we extended the model with computer simulations using Monte Carlo methods. We also developed an analytic formula for Na coupled co-transport that is analogous to the single-file Ussing equation for channels. The model shows that stochastic diffusion through a long narrow pore can explain coupled transport. The length of the pore amplifies the Na gradient that drives co-transport.

Computer Simulation↗

PubMed1978

Nature of amorphous aluminum hydroxycarbonate.

The titration of sodium carbonate with aluminum nitrate is shown to produce amorphous aluminum hydroxycarbonate. This compound is not stoichiometric, although the maximum carbonate to aluminum ratio appears to be 0.5. The pH conditions for achieving the maximum carbonate content are concentration dependent. A model for the particle surface at the solution interface is proposed. This model accounts for the presence of carbonate directly coordinated to the aluminum and carbonate adsorbed by electrostatic forces. Sodium is present in the diffuse layer and is, therefore, not an integral part of the structure.

Aluminum↗

PubMed1994

The role of arginine 143 in the electrostatics and mechanism of Cu,Zn superoxide dismutase: computational and experimental evaluation by mutational analysis.

Cu,Zn superoxide dismutase protects cells from oxidative damage by removing superoxide radicals in one of the fastest enzyme reactions known. The redox reaction at the active-site Cu ion is rate-limited by diffusion and enhanced by electrostatic guidance. To quantitatively define the electrostatic and mechanistic contributions of sequence-invariant Arg-143 in human Cu,Zn superoxide dismutase, single-site mutants at this position were investigated experimentally and computationally. Rate constants for several Arg-143 mutants were determined at different pH and ionic strength conditions using pulse radiolytic methods and compared to results from Brownian dynamics simulations. At physiological pH, substitution of Arg-143 by Lys caused a 2-fold drop in rate, neutral substitutions (Ile, Ala) reduced the rate about 10-fold, while charge-reversing substitutions (Asp, Glu) caused a 100-fold decrease. Position 143 mutants showed pH dependencies not seen in other mutants. At low pH, the acidic residue mutations exhibited protonation/deprotonation effects. At high pH, all enzymes showed typical decreases in rate except the Lys mutant in which the rate dropped off at an unusually low pH. Increasing ionic strength at acidic pH decreased the rates of the wild-type enzyme and Lys mutant, while the rate of the Glu mutant was unaffected. Increasing ionic strength at higher pH (> 10) increased the rates of the Lys and Glu mutants while the rate of the wild-type enzyme was unaffected. Reaction simulations with Brownian dynamics incorporating electrostatic effects tested computational predictability of ionic strength dependencies of the wild-type enzyme and the Lys, Ile, and Glu mutants. The calculated and experimental ionic strength profiles gave similar slopes in all but the Glu mutant, indicating that the electrostatic attraction of the substrate is accurately modeled. Differences between the calculated and experimental rates for the Glu and Lys mutants reflect the mechanistic contribution of Arg-143. Results from this joint analysis establish that, aside from the Cu ligands, Arg-143 is the single most important residue in Cu,Zn superoxide dismutase both electrostatically and mechanistically, and provide an explanation for the evolutionary selection of arginine at position 143.

Arginine↗

PubMed2002

Deconvolution of compartmental water diffusion coefficients in yeast-cell suspensions using combined T(1) and diffusion measurements.

An NMR method is presented for measuring compartment-specific water diffusion coefficient (D) values. It uses relaxography, employing an extracellular contrast reagent (CR) to distinguish intracellular (IC) and extracellular (EC) (1)H(2)O signals by differences in their respective longitudinal (T(1)) relaxation times. A diffusion-weighted inversion-recovery spin-echo (DW-IRSE) pulse sequence was used to acquire IR data sets with systematically and independently varying inversion time (TI) and diffusion-attenuation gradient amplitude (g) values. Implementation of the DW-IRSE technique was demonstrated and validated using yeast cells suspended in 3 mM Gd-DTPA(2-) with a wet/dry mass ratio of 3.25:1.0. Two-dimensional (2D) NMR data were acquired at 2.0 T and analyzed using numerical inverse Laplace transformation (2D- and sequential 1D-ILT) and sequential exponential fitting to yield T(1) and water D values. All three methods gave substantial agreement. Exponential fitting, deemed the most accurate and time efficient, yielded T(1):D (relative contribution) values of 304 ms:0.023x10(-5) cm(2)/s (47%) and 65 ms:1.24x10(-5) cm(2)/s (53%) for the IC and EC components, respectively. The compartment-specific D values derived from direct biexponential fitting of diffusion-attenuation data were also in good agreement. Extension of the DW-IRSE method to in vivo models should provide valuable insights into compartment-specific water D changes in response to injury or disease. (c) 2002 Elsevier Science (USA).

Contrast Media↗

PubMed2003

Stochastic models for cell motion and taxis.

Certain biological experiments investigating cell motion result in time lapse video microscopy data which may be modeled using stochastic differential equations. These models suggest statistics for quantifying experimental results and testing relevant hypotheses, and carry implications for the qualitative behavior of cells and for underlying biophysical mechanisms. Directional cell motion in response to a stimulus, termed taxis, has previously been modeled at a phenomenological level using the Keller-Segel diffusion equation. The Keller-Segel model cannot distinguish certain modes of taxis, and this motivates the introduction of a richer class of models which is nevertheless still amenable to statistical analysis. A state space model formulation is used to link models proposed for cell velocity to observed data. Sequential Monte Carlo methods enable parameter estimation via maximum likelihood for a range of applicable models. One particular experimental situation, involving the effect of an electric field on cell behavior, is considered in detail. In this case, an Ornstein- Uhlenbeck model for cell velocity is found to compare favorably with a nonlinear diffusion model.

Algorithms↗

PubMed2005

Consequences of mutations in human DNA polymerase gamma.

DNA polymerase gamma is responsible for replication and repair of the mitochondrial genome. Human DNA polymerase gamma is composed of a 140-kDa catalytic subunit and a 55-kDa accessory subunit. Mutations in the gene for the catalytic subunit (POLG) have been shown to be a frequent cause of mitochondrial disorders. To date over 40 disease mutations and 9 nonsynonymous polymorphisms in POLG have been found to be associated with autosomal recessive and dominant progressive external ophthalmoplegia (PEO), Alpers syndrome, sensory ataxia, neuropathy, dysarthria and ophthalmoparesis (SANDO), Parkinsonism, and male infertility. In this paper we review the literature of POLG mutations and discuss their impact on mitochondrial diseases. We also describe a public access web database to annotate POLG mutations for the research community.

Amino Acid Sequence↗

PubMed2003

Stochastic model of autocrine and paracrine signals in cell culture assays.

Autocrine signaling systems are commonly studied under cell culture conditions. In a typical cell culture assay, a layer of liquid medium covers a random two-dimensional dispersion of cells, which secrete ligands. In a growing number of experiments, it is important to characterize the spatial range of autocrine and paracrine cell communication. Currently, the spatial distribution of diffusing signals can be analyzed only indirectly, from their effects on the intracellular signaling or physiological responses of autocrine cells. To directly characterize the spatial range of secreted ligands, we propose a stochastic model for autocrine cell cultures and analyze it using a combination of analytical and computational tools. The two main results derived within the framework of this model are 1), an expression for the fraction of autocrine trajectories, i.e., the probability for a ligand to be trapped by the same cell from which it has been secreted; and 2), an expression for the spatial distribution of trapping points of paracrine trajectories. We test these analytical results by stochastic simulations with efficient Brownian dynamics code and apply our model to analyze the spatial operation of autocrine epidermal growth factor receptor systems.

Algorithms↗