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Biomedical subjects

K Schulten

Publications and source records attributed to K Schulten.

At least 19 recordsLinked to original sources
PubMed1992

Chromophore-protein interactions and the function of the photosynthetic reaction center: a molecular dynamics study.

The coupling between electron transfer and protein structure and dynamics in the photosynthetic reaction center of Rhodopseudomonas viridis is investigated. For this purpose molecular dynamics simulations of the essential portions (a segment of 5797 atoms) of this protein complex have been carried out. Electron transfer in the primary event is modeled by altering the charge distributions of the chromophores according to quantum chemical calculations. The simulations show (i) that fluctuations of the protein matrix, which are coupled electrostatically to electron transfer, play an important role in controlling the electron transfer rates and (ii) that the protein matrix stabilizes the separated electron pair state through rapid (200 fs) and temperature-independent dielectric relaxation. The photosynthetic reaction center resembles a polar liquid in that the internal motions of the whole protein complex, rather than only those of specific side groups, contribute to i and ii. The solvent reorganization energy is about 4.5 kcal/mol. The simulations indicate that rather small structural rearrangements and changes in motional amplitudes accompany the primary electron transfer.

Bacterial Chromatophores↗
PubMed1992

Theory of paramagnetic contrast agents in liposome systems.

We develop a theoretical description of nuclear spin relaxation mediated by MRI contrast agents and transport processes in liposome systems. Such systems compartmentalize the physical space such that paramagnetic contrast agents, which enhance relaxation, are trapped in some subvolume. Due to diffusive transport across compartmental barriers, i.e., across liposome membranes, nuclear spins in the whole volume exhibit fast relaxation. The description developed is based on the diffusion-Bloch equations for the nuclear magnetization with appropriate boundary and continuity conditions. From this set of equations a new inhomogeneous differential equation for the local relaxation times is derived. For simple geometries of compartmentalized spaces the equation can be solved analytically. A simple formula for average relaxation times in liposome systems is presented. The resulting relaxation times agree well with observations.

Contrast Media↗
PubMed1992

Theory of contrast agents in magnetic resonance imaging: coupling of spin relaxation and transport.

The role of diffusive transport on the enhancement of nuclear spin relaxation through NMR contrast agents is described by means of diffusion-Bloch equations. These equations are solved in the mean relaxation time approximation [W. Nadler and K. Schulten, J. Chem. Phys. 82, 151-160 (1985)]. A model presented considers relaxation enhancement in tissue in which contrast agents confined to intravascular spaces affect nuclear spin in the extravascular volume. We show how the mean relaxation time depends on capillary density, on permeability, and on diffusion. A second model describes enhanced phase relaxation of liver tissue in the presence of magnetic particles in Kupffer cells. The relationship between relaxation rate and density of Kupffer cells is investigated. The diagnostic value of enhanced nuclear relaxation in the presence of contrast agents is discussed on the basis of the systematic mathematical results obtained.

Contrast Media↗
PubMed1992

Self-organizing maps: stationary states, metastability and convergence rate.

We investigate the effect of various types of neighborhood function on the convergence rates and the presence or absence of metastable stationary states of Kohonen's self-organizing feature map algorithm in one dimension. We demonstrate that the time necessary to form a topographic representation of the unit interval [0, 1] may vary over several orders of magnitude depending on the range and also the shape of the neighborhood function, by which the weight changes of the neurons in the neighborhood of the winning neuron are scaled. We will prove that for neighborhood functions which are convex on an interval given by the length of the Kohonen chain there exist no metastable states. For all other neighborhood functions, metastable states are present and may trap the algorithm during the learning process. For the widely-used Gaussian function there exists a threshold for the width above which metastable states cannot exist. Due to the presence or absence of metastable states, convergence time is very sensitive to slight changes in the shape of the neighborhood function. Fastest convergence is achieved using neighborhood functions which are "convex" over a large range around the winner neuron and yet have large differences in value at neighboring neurons.

Algorithms↗
PubMed1992

Self-organizing maps: ordering, convergence properties and energy functions.

We investigate the convergence properties of the self-organizing feature map algorithm for a simple, but very instructive case: the formation of a topographic representation of the unit interval [0, 1] by a linear chain of neurons. We extend the proofs of convergence of Kohonen and of Cottrell and Fort to hold in any case where the neighborhood function, which is used to scale the change in the weight values at each neuron, is a monotonically decreasing function of distance from the winner neuron. We prove that the learning dynamics cannot be described by a gradient descent on a single energy function, but may be described using a set of potential functions, one for each neuron, which are independently minimized following a stochastic gradient descent. We derive the correct potential functions for the one- and multi-dimensional case, and show that the energy functions given by Tolat (1990) are an approximation which is no longer valid in the case of highly disordered maps or steep neighborhood functions.

Algorithms↗
PubMed1992

Molecular dynamics simulation on a network of workstations using a machine-independent parallel programming language.

Molecular dynamics simulations investigate local and global motion in molecules. Several parallel computing approaches have been taken to attack the most computationally expensive phase of molecular simulations, the evaluation of long range interactions. This paper reviews these approaches and develops a straightforward but effective algorithm using the machine-independent parallel programming language, Linda. The algorithm was run both on a shared memory parallel computer and on a network of high performance Unix workstations. Performance benchmarks were performed on both systems using two proteins. This algorithm offers a portable cost-effective alternative for molecular dynamics simulations. In view of the increasing numbers of networked workstations, this approach could help make molecular dynamics simulations more easily accessible to the research community.

Algorithms↗
PubMed1991

Molecular dynamics investigation of the interaction between DNA and distamycin.

The complex of the minor groove binding drug distamycin and the B-DNA oligomer d-(CGCAAATTTGCG) was investigated by molecular dynamics simulations. For this purpose, accurate atomic partial charges of distamycin were determined by extended quantum chemical calculations. The complex was simulated without water but with hydrated counterions. The oligomer without the drug was simulated in the same fashion and also with 1713 water molecules and sodium counterions. The simulations revealed that the binding of distamycin in the minor groove induces a stiffening of the DNA helix. The drug also prevents a transition from B-DNA to A-DNA that was found to occur rapidly (30 ps) in the segment without bound distamycin in a water-free environment but not in simulations including water. In other simulations, we investigated the relaxation processes after distamycin was moved from its preferred binding site, either radially or along the minor groove. Binding in the major groove was simulated as well and resulted in a bound configuration with the guanidinium end of distamycin close to two phosphate groups. We suggest that, in an aqueous environment, tight hydration shells covering the DNA backbone prevent such an arrangement and thus lead to distamycin's propensity for minor groove binding.

Base Composition↗
PubMed1991

Molecular dynamics simulation on a network of workstations using a machine-independent parallel programming language.

Molecular dynamics simulations investigate local and global motion in molecules. Several parallel computing approaches have been taken to attack the most computationally expensive phase of molecular simulations, the evaluation of long range interactions. This paper develops a straightforward but effective algorithm for molecular dynamics simulations using the machine-independent parallel programming language, Linda. The algorithm was run both on a shared memory parallel computer and on a network of high performance Unix workstations. Performance benchmarks were performed on both systems using two proteins. This algorithm offers a portable cost-effective alternative for molecular dynamics simulations. In view of the increasing numbers of networked workstations, this approach could help make molecular dynamics simulations more easily accessible to the research community.

Algorithms↗
PubMed1990

Development of feature detectors by self-organization. A network model.

We present a two-layered network of linear neurons that organizes itself as to extract the complete information contained in a set of presented patterns. The weights between layers obey a Hebbian rule. We propose a local anti-Hebbian rule for lateral, hierarchically organized weights within the output layer. This rule forces the activities of the output units to become uncorrelated and the lateral weights to vanish. The weights between layers converge to the eigenvectors of the covariance matrix of input patterns, i.e., the network performs a principal component analysis, yielding all principal components. As a consequence of the proposed learning scheme, the output units become detectors of orthogonal features, similar to ones found in the brain of mammals.

Color Perception↗
PubMed1990

A principle for the formation of the spatial structure of cortical feature maps.

Orientation-selective cells in the striate cortex of higher animals are organized as a hierarchical topographic map of two stimulus features: (i) position in visual space and (ii) orientation. We show that the observed structure of the topographic map can arise from a principle of continuous mapping. For the realization of this principle we use a mathematical model that can be interpreted as an adaptive process changing a set of synaptic weights, or synaptic connection strengths, between two layers of cells. The patterns of orientation preference and selectivity generated by the model are similar to the patterns seen in the visual cortex of macaque monkey and cat and correspond to a neural projection that maps a more than two-dimensional feature space onto a two-dimensional cortical surface under the constraint that shape and position of the receptive fields of the neurons very smoothly over the cortical surface.

Animals↗
PubMed1989

A regularized approach to color constancy.

Color constancy is the ability of color perception independent of the spectrum of the ambient illumination. We present an algorithm that makes use of biologically plausible assumptions concerning the spectra of illumination and surface reflectance in order to solve the undetermined problem of color constancy. We test the proposed algorithm by means of computer simulations and examine its range of performance.

Algorithms↗
PubMed1987

Influence of noise on the function of a "physiological" neural network.

A model neural network with stochastic elements in its millisecond dynamics is investigated. The network consists of neuronal units which are modelled in close analogy to physiological neurons. Dynamical variables of the network are the cellular potentials, axonic currents and synaptic efficacies. The dynamics of the synapses obeys a modified Hebbian rule and, as proposed by v. d. Malsburg (1981, 1985), develop on a time scale of a tenth of a second. In a previous publication (Buhmann and Schulten 1986) we have confirmed that the resulting noiseless auto-associative network is capable of the well-known computational tasks of formal associative networks (Cooper 1973; Kohonen et al. 1984, 1981; Hopfield 1982). In the present paper we demonstrate that random fluctuations of the membrane potential improve the performance of the network. In comparison to a deterministic network a noisy neural network can learn at lower input frequencies and with lower average neural firing rates. The electrical activity of a noisy network is very reminiscent of that observed by physiological recordings. We demonstrate furthermore that associative storage reduces the effective dimension of the phase space in which the electrical activity of the network develops.

Animals↗
PubMed1987

Molecular and stochastic dynamics of proteins.

The rapid fluctuations of protein atoms derived from molecular dynamics simulations can be extrapolated to longer-time motions by effective single-particle stochastic models. This is demonstrated by an analysis of velocity autocorrelation functions for the atoms of lysine side chains in the active site of RNase A. The atomic motions are described by a bounded stochastic model with the friction and noise parameters determined from a molecular dynamics simulation. The low-frequency relaxation behavior is shown to result from collisional damping rather than dephasing. Extrapolation of these results to the quasistochastic motion of the heme group in myoglobin provides an explanation of 57Fe Mössbauer spectroscopic data.

Binding Sites↗
PubMed1986

Noise-induced neural impulses.

The firing pattern of neural pulses often show the following features: the shapes of individual pulses are nearly identical and frequency independent; the firing frequency can vary over a broad range; the time period between pulses shows a stochastic scatter. This behaviour cannot be understood on the basis of a deterministic non-linear dynamic process, e.g. the Bonhoeffer-van der Pol model. We demonstrate in this paper that a noise term added to the Bonhoeffer-van der Pol model can reproduce the firing patterns of neurons very well. For this purpose we have considered the Fokker-Planck equation corresponding to the stochastic Bonhoeffer-van der Pol model. This equation has been solved by a new Monte Carlo algorithm. We demonstrate that the ensuing distribution functions represent only the global characteristics of the underlying force field: lines of zero slope which attract nearby trajectories prove to be the regions of phase space where the distributions concentrate their amplitude. Since there are two such lines the distributions are bimodal representing repeated fluctuations between two lines of zero slope. Even in cases where the deterministic Bonhoeffer-van der Pol model does not show limit cycle behaviour the stochastic system produces a limit cycle. This cycle can be identified with the firing of neural pulses.

Acoustic Stimulation↗
PubMed1986

Associative recognition and storage in a model network of physiological neurons.

We consider a neural network model in which the single neurons are chosen to closely resemble known physiological properties. The neurons are assumed to be linked by synapses which change their strength according to Hebbian rules on a short time scale (100 ms). The dynamics of the network--the time evolution of the cell potentials and the synapses--is investigated by computer simulation. As in more abstract network models (Cooper 1973; Hopfield 1982; Kohonen 1984) it is found that the local dynamics of the cell potentials and the synaptic strengths result in global cooperative properties of the network and enable the network to process an incoming flux of information and to learn and store patterns associatively. A trained net can associate missing details of a pattern, can correct wrong details and can suppress noise in a pattern. The network can further abstract the prototype from a series of patterns with variations. A suitable coupling constant connecting the dynamics of the cell potentials with the synaptic strengths is derived by a mean field approximation. This coupling constant controls the neural sensitivity and thereby avoids both extremes of the network state, the state of permanent inactivity and the state of epileptic hyperactivity.

Animals↗
PubMed1985

A model for the lateral diffusion of "stiff" chains in a lipid bilayer.

We present random walk models for the diffusive motion of lipid probe molecules in a lipid bilayer and calculate the diffusion constants for probes spanning the entire bilayer and for probes extending through one lipid layer only. The "stiffness" of such molecules can explain the observed value of 2/3 for the ratio of these diffusion constants.

Diffusion↗
PubMed1985

A model for the resistance of the proton channel formed by the proteolipid of ATPase.

The conductance observed for single proton channels formed by proteolipids of ATPase (Schindler and Nelson 1982) is rationalized in terms of a hydrogen bonded network model. A simple algebraic expression for the resistance predicted for such a model is presented and the results are compared to the experimental observations. The comparison suggests that the conduction involves a series of bound water molecules and perhaps amino acid side groups.

Electric Conductivity↗