Logistic population growth under random dispersal

Various diffusion processes employed for modelling logistic growth are briefly summarized. A discrete-time, discrete-state space stochastic process for population growth is proposed and analyzed with either Bose-Einstein or Maxwell-Boltzmann statistics for the distribution of offspring in available sites in a restricted region. A diffusion approximation is constructed, which differs from those previously employed. The logistic law is a natural deterministic analog of the diffusion process.     

Coding of odor intensity in a steady-state deterministic model of an olfactory receptor neuron

The coding of odor intensity by an olfactory receptor neuron model was studied under steady-state stimulation. Our model neuron is an elongated cylinder consisting of the following three components: a sensory dendritic region bearing odorant receptors, a passive region consisting of proximal dendrite and cell body, and an axon. First, analytical solutions are given for the three main physiological responses: (1) odorant-dependent conductance change at the sensory dendrite based on the Michaelis-Menten model, (2) generation and spreading of the receptor potential based on a new solution of the cable equation, and (3) firing frequency based on a Lapicque model. Second, the magnitudes of these responses are analyzed as a function of odorant concentration. Their dependence on chemical, electrical, and geometrical parameters is examined. The only evident gain in magnitude results from the activation-to-conductance conversion. An optimal encoder neuron is presented that suggests that increasing the length of the sensory dendrite beyond about 0.3 space constant does not increase the magnitude of the receptor potential. Third, the sensivities of the responses are examined as functions of (1) the concentration at half-maximum response, (2) the lower and upper concentrations actually discriminated, and (3) the width of the dynamic range. The overall gain in sensitivity results entirely from the conductance-to-voltage conversion. The maximum conductance at the sensory dendrite appears to be the main tuning constant of the neuron because it determines the shift toward low concentrations and the increase in dynamic range. The dynamic range of the model cannot exceed 5.7 log units, for a sensitivity increase at low odor concentration is compensated by a sensitivity decrease at high odor concentration.     

Accuracy of neuronal interspike times calculated from a diffusion approximation

The theory of neuronal firing in Stein's model is outlined as well as the corresponding theory for a diffusion approximation which has the same first two infinitesimal moments. The diffusion approximation is derived from the discontinuous model in the limit of large input frequencies and small postsynaptic potential amplitudes. A comparison of the calculated mean interspike intervals is made for various values of the threshold for firing and various input frequencies. The diffusion approximation can underestimate the interspike interval by up to 100% or severely overestimate it, depending on the input frequencies and the threshold. A general relation between the predictions of the two models is deduced.     

A novel and highly conserved collagen (pro(alpha)1(XXVII)) with a unique expression pattern and unusual molecular characteristics establishes a new clade within the vertebrate fibrillar collagen family

The type XXVII collagen gene codes for a novel vertebrate fibrillar collagen that is highly conserved in man, mouse, and fish (Fugu rubripes). The pro(alpha)1(XXVII) chain has a domain structure similar to that of the type B clade chains (alpha1(V), alpha3(V), alpha1(XI), and alpha2(XI)). However, compared with other vertebrate fibrillar collagens (types I, II, III, V, and XI), type XXVII collagen has unusual molecular features such as no minor helical domain, a major helical domain that is short and interrupted, and a short chain selection sequence within the NC1 domain. Pro(alpha)1(XXVII) mRNA is 9 kb and expressed by chondrocytes but also by a variety of epithelial cell layers in developing tissues including stomach, lung, gonad, skin, cochlear, and tooth. By Western blotting, type XXVII antisera recognized multiple bands of 240-110 kDa in tissue extracts and collagenous bands of 150-140 kDa in the conditioned medium of the differentiating chondrogenic ATDC5 cell line. Phylogenetic analyses revealed that type XXVII, together with the closely related type XXIV collagen gene, form a new, third clade (type C) within the vertebrate fibrillar collagen family. Furthermore, the exon structure of the type XXVII collagen gene is similar to, but distinct from, those of the genes coding for the type A or B clade pro(alpha) chains.     

M142.2 (cut-6), a novel Caenorhabditis elegans matrix gene important for dauer body shape

The cuticle of the nematode Caenorhabditis elegans is a collagenous extracellular matrix which forms the exoskeleton and defines the shape of the worm. We have characterized the C. elegans gene M142.2, and we show that this is a developmentally regulated gene important for cuticle structure. Transgenic worms expressing M142.2 promoter fused to green fluorescent protein showed that M142.2 is expressed in late embryos and L2d predauers, in the hypodermal cells which synthesize the cuticle. The same temporal pattern was seen by RT-PCR using RNA purified from specific developmental stages. A recombinant fragment of M142.2 was expressed in Escherichia coli and used to raise an antiserum. Immunohistochemistry using the antiserum localized M142.2 to the periphery of the alae of L1 and dauers, forming two longitudinal ribbons over the hypodermal cells. Loss-of-function of M142.2 by RNAi resulted in a novel phenotype: dumpy dauers which lacked alae. M142.2 therefore plays a major role in the assembly of the alae and the morphology of the dauer cuticle; because of its similarity to the other cut genes of the cuticle, we have named the gene cut-6.     

Random perturbations of spiking activity in a pair of coupled neurons

We examine the effects of stochastic input currents on the firing behaviour of two coupled Type 1 or Type 2 neurons. In Hodgkin–Huxley model neurons with standard parameters, which are Type 2, in the bistable regime, synaptic transmission can initiate oscillatory joint spiking, but white noise can terminate it. In Type 1 cells (models), typified by a quadratic integrate and fire model, synaptic coupling can cause oscillatory behaviour in excitatory cells, but Gaussian white noise can again terminate it. We locally determine an approximate basin of attraction, of the periodic orbit and explain the firing behaviour in terms of the effects of noise on the probability of escape of trajectories from      

A structure prediction for the ligand-binding region of the integrin β subunit: evidence for the presence of a von Willebrand factor A domain

The integrins are a family of cell surface receptors that mediate biologically important adhesive interactions. Integrin-ligand binding has been extensively studied because of the potential for the development of anti-adhesive therapies, but the molecular basis of this interaction is still poorly understood. A conserved region near the N-terminus of the β subunit appears to be of particular importance in ligand binding, but to date this domain has not been expressed in isolation. As a prelude to expression and potential structure determination, we have performed a detailed structure prediction for this region. Primary, secondary and tertiary structure analyses indicate that the region folds into a von Willebrand factor A-domain, thereby potentially placing a previously characterised module at the centre of a key functional region.     

Determination of the inter-spike times of neurons receiving randomly arriving post-synaptik potentials

Stein's model for a neuron receiving randomly arriving post-synaptic potentials is studied from an analytic viewpoint, using some recent results in the theory of first passage times for temporally homogeneous Markov processes. The case when the only input is excitatory can be treated exactly. It is shown that the moments of the firing time are guaranteed to be finite so that the differential-difference equation for the expectation (and higher moments) of the time for the membrane potential to first reach threshold from resting level can be written down. Analytic solutions are obtained in a number of cases with main emphasis on the case when the threshold is twice the epsp magnitude. An invariance principie is formulated wherein at a given mean input frequency and for a given decay parameter, the distribution of firing times depends only on the ratio of threshld to epsp magnitude. For the case where this ratio is two, the variation in the mean discharge rate is obtained as a function of mean input frequency. The results are compared with the experimental data for the Poisson monosynaptic excitation of cat motoneurons by Redmanet al. Agreement between theoretical and experimental values is excellent at input frequencies near 102 sec^-1, and theory underestimates the firing rate below that input frequency. Reasons for the discrepancy are discussed at length including the uncertainties in the neuronal parameters and the dependence of epsp magnitude on mean input frequency. The problem of including an inhibitory input process together with excitation is treated by an approximation procedure when the inhibition is considerably weaker than the excitation. At the input frequency investigated it is shown that when inhibition “half as weak” as the excitation occurs, the mean discharge frequency is approximately halved. In the final section a method of estimating neuronal parameters from the moments of the experimental inter-spike time distribution is outlined.     

The response of a nerve cylinder to spatially distributed white noise inputs

The response of a passive nerve cylinder (or dendritic tree in the equivalent cylinder representation) to random white noise input currents is determined. Results for the mean, variance and covariance of the depolarization are obtained for an arbitrary number of independent spatially distributed inputs. The case of a cylinder with sealed ends is considered in detail. The differences that arise when the input currents are distributed over a small but finite region of space instead of concentrated at a point are investigated. In the case of distributed inputs, the expectation is smoother near the stimulus and the variance becomes finite over the entire cable length including the region of the applied stimulus. Away from the stimulus, there are no appreciable differences between the responses for the two cases. The interaction between an excitatory input and an inhibitory input at various locations is examined and one case of more than two inputs is also analysed to study effects which could not have been discerned from point models for a neuron with random inputs.