A novel role for MNTB neuron dendrites in regulating action potential amplitude and cell excitability during repetitive firing

Principal cells of the medial nucleus of the trapezoid body (MNTB) are simple round neurons that receive a large excitatory synapse (the calyx of Held) and many small inhibitory synapses on the soma. Strangely, these neurons also possess one or two short tufted dendrites, whose function is unknown. Here we assess the role of these MNTB cell dendrites using patch-clamp recordings, imaging and immunohistochemistry techniques. Using outside-out patches and immunohistochemistry, we demonstrate the presence of dendritic Na(+) channels. Current-clamp recordings show that tetrodotoxin applied onto dendrites impairs action potential (AP) firing. Using Na(+) imaging, we show that the dendrite may serve to maintain AP amplitudes during high-frequency firing, as Na(+) clearance in dendritic compartments is faster than axonal compartments. Prolonged high-frequency firing can diminish Na(+) gradients in the axon while the dendritic gradient remains closer to resting conditions; therefore, the dendrite can provide additional inward current during prolonged firing. Using electron microscopy, we demonstrate that there are small excitatory synaptic boutons on dendrites. Multi-compartment MNTB cell simulations show that, with an active dendrite, dendritic excitatory postsynaptic currents (EPSCs) elicit delayed APs compared with calyceal EPSCs. Together with high- and low-threshold voltage-gated K(+) currents, we suggest that the function of the MNTB dendrite is to improve high-fidelity firing, and our modelling results indicate that an active dendrite could contribute to a `dual` firing mode for MNTB cells (an instantaneous response to calyceal inputs and a delayed response to non-calyceal dendritic excitatory postsynaptic potentials).

Plant-antivenom: Database of anti-venom medicinal plants

Plant-antivenom is a computational Websystem about medicinal plants with anti-venom properties. The system consists of a database of these plants, including scientific publications on this subject and amino acid sequences of active principles from venomous animals. The system relates these data allowing their integration through different search applications. For the development of the system, the first surveys were conducted in scientific literature, allowing the creation of a publication database in a library for reading and user interaction. Then, classes of categories were created, allowing the use of tags and the organization of content. This database on medicinal plants has information such as family, species, isolated compounds, activity, inhibited animal venoms, among others. Provision is made for submission of new information by registered users, by the use of wiki tools. Content submitted is released in accordance to permission rules defined by the system. The database on biological venom protein amino acid sequences was structured from the essential information from National Center for Biotechnology Information (NCBI). Plant-antivenom`s interface is simple, contributing to a fast and functional access to the system and the integration of different data registered on it. Plant-antivenom system is available on the Internet at http://gbi.fmrp.usp.br/plantantivenom.

Modeling the Dynamics of Viral Evolution Considering Competition Within Individual Hosts and at Population Level: The Effects of Treatment

We consider two viral strains competing against each other within individual hosts (at cellular level) and at population level (for infecting hosts) by studying two cases. In the first case, the strains do not mutate into each other. In this case, we found that each individual in the population can be infected by only one strain and that co-existence in the population is possible only when the strain that has the greater basic intracellular reproduction number, R (0c) , has the smaller population number R (0p) . Treatment against the one strain shifts the population equilibrium toward the other strain in a complicated way (see Appendix B). In the second case, we assume that the strain that has the greater intracellular number R (0c) can mutate into the other strain. In this case, individual hosts can be simultaneously infected by both strains (co-existence within the host). Treatment shifts the prevalence of the two strains within the hosts, depending on the mortality induced by the treatment, which is, in turn, dependent upon the doses given to each individual. The relative proportions of the strains at the population level, under treatment, depend both on the relative proportions within the hosts (which is determined by the dosage of treatment) and on the number of individuals treated per unit time, that is, the rate of treatment. Implications for cases of real diseases are briefly discussed.

Implicit Taylor methods for stiff stochastic differential equations

In this paper we discuss implicit Taylor methods for stiff Ito stochastic differential equations. Based on the relationship between Ito stochastic integrals and backward stochastic integrals, we introduce three implicit Taylor methods: the implicit Euler-Taylor method with strong order 0.5, the implicit Milstein-Taylor method with strong order 1.0 and the implicit Taylor method with strong order 1.5. The mean-square stability properties of the implicit Euler-Taylor and Milstein-Taylor methods are much better than those of the corresponding semi-implicit Euler and Milstein methods and these two implicit methods can be used to solve stochastic differential equations which are stiff in both the deterministic and the stochastic components. Numerical results are reported to show the convergence properties and the stability properties of these three implicit Taylor methods. The stability analysis and numerical results show that the implicit Euler-Taylor and Milstein-Taylor methods are very promising methods for stiff stochastic differential equations.

Long-term survivor mixture model with random effects: application to a multi-centre clinical trial of carcinoma

A mixture model incorporating long-term survivors has been adopted in the field of biostatistics where some individuals may never experience the failure event under study. The surviving fractions may be considered as cured. In most applications, the survival times are assumed to be independent. However, when the survival data are obtained from a multi-centre clinical trial, it is conceived that the environ mental conditions and facilities shared within clinic affects the proportion cured as well as the failure risk for the uncured individuals. It necessitates a long-term survivor mixture model with random effects. In this paper, the long-term survivor mixture model is extended for the analysis of multivariate failure time data using the generalized linear mixed model (GLMM) approach. The proposed model is applied to analyse a numerical data set from a multi-centre clinical trial of carcinoma as an illustration. Some simulation experiments are performed to assess the applicability of the model based on the average biases of the estimates formed. Copyright (C) 2001 John Wiley & Sons, Ltd.

A new wavelet-based method for the solution of the population balance equation

A new wavelet-based method for solving population balance equations with simultaneous nucleation, growth and agglomeration is proposed, which uses wavelets to express the functions. The technique is very general, powerful and overcomes the crucial problems of numerical diffusion and stability that often characterize previous techniques in this area. It is also applicable to an arbitrary grid to control resolution and computational efficiency. The proposed technique has been tested for pure agglomeration, simultaneous nucleation and growth, and simultaneous growth and agglomeration. In all cases, the predicted and analytical particle size distributions are in excellent agreement. The presence of moving sharp fronts can be addressed without the prior investigation of the characteristics of the processes. (C) 2001 Published by Elsevier Science Ltd.

Supervisory control of wastewater treatment plants by combining principal component analysis and fuzzy c-means clustering

In this paper a methodology for integrated multivariate monitoring and control of biological wastewater treatment plants during extreme events is presented. To monitor the process, on-line dynamic principal component analysis (PCA) is performed on the process data to extract the principal components that represent the underlying mechanisms of the process. Fuzzy c-means (FCM) clustering is used to classify the operational state. Performing clustering on scores from PCA solves computational problems as well as increases robustness due to noise attenuation. The class-membership information from FCM is used to derive adequate control set points for the local control loops. The methodology is illustrated by a simulation study of a biological wastewater treatment plant, on which disturbances of various types are imposed. The results show that the methodology can be used to determine and co-ordinate control actions in order to shift the control objective and improve the effluent quality.

A comparison of low-storage strategies for spectral analysis in dissipative systems: filter diagonalisation in the Lanczos representation and harmonic inversion of the Chebychev-order-domain autocorrelation function

We compare the performance of two different low-storage filter diagonalisation (LSFD) strategies in the calculation of complex resonance energies of the HO2, radical. The first is carried out within a complex-symmetric Lanczos subspace representation [H. Zhang, S.C. Smith, Phys. Chem. Chem. Phys. 3 (2001) 2281]. The second involves harmonic inversion of a real autocorrelation function obtained via a damped Chebychev recursion [V.A. Mandelshtam, H.S. Taylor, J. Chem. Phys. 107 (1997) 6756]. We find that while the Chebychev approach has the advantage of utilizing real algebra in the time-consuming process of generating the vector recursion, the Lanczos, method (using complex vectors) requires fewer iterations, especially for low-energy part of the spectrum. The overall efficiency in calculating resonances for these two methods is comparable for this challenging system. (C) 2001 Elsevier Science B.V. All rights reserved.

Time-dependent master equation simulation of complex elementary reactions in combustion: Application to the reaction of (CH2)-C-1 with C2H2 from 300-2000 K

Computational simulations of the title reaction are presented, covering a temperature range from 300 to 2000 K. At lower temperatures we find that initial formation of the cyclopropene complex by addition of methylene to acetylene is irreversible, as is the stabilisation process via collisional energy transfer. Product branching between propargyl and the stable isomers is predicted at 300 K as a function of pressure for the first time. At intermediate temperatures (1200 K), complex temporal evolution involving multiple steady states begins to emerge. At high temperatures (2000 K) the timescale for subsequent unimolecular decay of thermalized intermediates begins to impinge on the timescale for reaction of methylene, such that the rate of formation of propargyl product does not admit a simple analysis in terms of a single time-independent rate constant until the methylene supply becomes depleted. Likewise, at the elevated temperatures the thermalized intermediates cannot be regarded as irreversible product channels. Our solution algorithm involves spectral propagation of a symmetrised version of the discretized master equation matrix, and is implemented in a high precision environment which makes hitherto unachievable low-temperature modelling a reality.

Time evolution in the unimolecular master equation at low temperatures: full spectral solution with scalable iterative methods and high precision

A new method is presented to determine an accurate eigendecomposition of difficult low temperature unimolecular master equation problems. Based on a generalisation of the Nesbet method, the new method is capable of achieving complete spectral resolution of the master equation matrix with relative accuracy in the eigenvectors. The method is applied to a test case of the decomposition of ethane at 300 K from a microcanonical initial population with energy transfer modelled by both Ergodic Collision Theory and the exponential-down model. The fact that quadruple precision (16-byte) arithmetic is required irrespective of the eigensolution method used is demonstrated. (C) 2001 Elsevier Science B.V. All rights reserved.

Calculation of product state distributions from resonance decay via Lanczos subspace filter diagonalization: Application to HO2

Resonance phenomena associated with the unimolecular dissociation of HO2 have been investigated quantum-mechanically by the Lanczos homogeneous filter diagonalization (LHFD) method. The calculated resonance energies, rates (widths), and product state distributions are compared to results from an autocorrelation function-based filter diagonalization (ACFFD) method. For calculating resonance wave functions via ACFFD, an analytical expression for the expansion coefficients of the modified Chebyshev polynomials is introduced. Both dissociation rates and product state distributions of O-2 show strong fluctuations, indicating the dissociation of HO2 is essentially irregular. (C) 2001 American Institute of Physics.

Lanczos subspace filter diagonalization: Homogeneous recursive filtering and a low-storage method for the calculation of matrix elements

We develop a new iterative filter diagonalization (FD) scheme based on Lanczos subspaces and demonstrate its application to the calculation of bound-state and resonance eigenvalues. The new scheme combines the Lanczos three-term vector recursion for the generation of a tridiagonal representation of the Hamiltonian with a three-term scalar recursion to generate filtered states within the Lanczos representation. Eigenstates in the energy windows of interest can then be obtained by solving a small generalized eigenvalue problem in the subspace spanned by the filtered states. The scalar filtering recursion is based on the homogeneous eigenvalue equation of the tridiagonal representation of the Hamiltonian, and is simpler and more efficient than our previous quasi-minimum-residual filter diagonalization (QMRFD) scheme (H. G. Yu and S. C. Smith, Chem. Phys. Lett., 1998, 283, 69), which was based on solving for the action of the Green operator via an inhomogeneous equation. A low-storage method for the construction of Hamiltonian and overlap matrix elements in the filtered-basis representation is devised, in which contributions to the matrix elements are computed simultaneously as the recursion proceeds, allowing coefficients of the filtered states to be discarded once their contribution has been evaluated. Application to the HO2 system shows that the new scheme is highly efficient and can generate eigenvalues with the same numerical accuracy as the basic Lanczos algorithm.

Subspace wavepacket evolution with Newton polynomials

Time-dependent wavepacket evolution techniques demand the action of the propagator, exp(-iHt/(h)over-bar), on a suitable initial wavepacket. When a complex absorbing potential is added to the Hamiltonian for combating unwanted reflection effects, polynomial expansions of the propagator are selected on their ability to cope with non-Hermiticity. An efficient subspace implementation of the Newton polynomial expansion scheme that requires fewer dense matrix-vector multiplications than its grid-based counterpart has been devised. Performance improvements are illustrated with some benchmark one and two-dimensional examples. (C) 2001 Elsevier Science B.V. All rights reserved.

Set-valued Markov chains and negative semitrajectories of discretized dynamical systems

Computer simulation of dynamical systems involves a phase space which is the finite set of machine arithmetic. Rounding state values of the continuous system to this grid yields a spatially discrete dynamical system, often with different dynamical behaviour. Discretization of an invertible smooth system gives a system with set-valued negative semitrajectories. As the grid is refined, asymptotic behaviour of the semitrajectories follows probabilistic laws which correspond to a set-valued Markov chain, whose transition probabilities can be explicitly calculated. The results are illustrated for two-dimensional dynamical systems obtained by discretization of fractional linear transformations of the unit disc in the complex plane.