The space-clamped Hodgkin-Huxley system with random synaptic input: inhibition of spiking by weak noise and analysis with moment equations

We consider a classical space-clamped Hodgkin-Huxley model neuron stimulated by synaptic excitation and inhibition with conductances represented by Ornstein-Uhlenbeck processes. Using numerical solutions of the stochastic model system obtained by an Euler method, it is found that with excitation only there is a critical value of the steady state excitatory conductance for repetitive spiking without noise and for values of the conductance near the critical value small noise has a powerfully inhibitory effect. For a given level of inhibition there is also a critical value of the steady state excitatory conductance for repetitive firing and it is demonstrated that noise either in the excitatory or inhibitory processes or both can powerfully inhibit spiking. Furthermore, near the critical value, inverse stochastic resonance was observed when noise was present only in the inhibitory input process. The system of 27 coupled deterministic differential equations for the approximate first and second order moments of the 6-dimensional model is derived. The moment differential equations are solved using Runge-Kutta methods and the solutions are compared with the results obtained by simulation for various sets of parameters including some with conductances obtained by experiment on pyramidal cells of rat prefrontal cortex. The mean and variance obtained from simulation are in good agreement when there is spiking induced by strong stimulation and relatively small noise or when the voltage is fluctuating at subthreshold levels. In the occasional spike mode sometimes exhibited by spinal motoneurons and cortical pyramidal cells the assunptions underlying the moment equation approach are not satisfied

The impact on receiving waters of pharmaceutical residues and antibiotic resistant faecal bacteria found in urban waste water effluents

Pharmaceuticals intended for human use are frequently detected in the aquatic environment. This is predominantly from their excretion following ingestion and subsequent discharge in domestic sewage. Wastewater treatment provides an opportunity to control their release to surface waters however, their removal is often incomplete. This thesis addresses this pharmaceutical pathway and the potential impact on the aquatic environment. The progress of bezafibrate, carbamazepine, ciprofloxacin and clarithromycin were monitored through the treatment stages (screened sewage, settled sewage and final effluent) of a large urban wastewater treatment plant (WWTP) and in surface waters up-stream and down-stream of the effluent discharge point. All except clarithromycin were detected in the screened sewage (369 – 2696 ng/L). Reductions in the pharmaceutical concentrations throughout the WWTP (22.5 – 94.3 %) indicate the removal of these compounds is variable. Bezafibrate and carbamazepine were observed at higher concentrations (67.5 - 305.5 ng/L) in surface water down-stream of the effluent discharge point compared to up-stream (31.0 – 116.7 ng/L). The presence of antibiotics in the environment may contribute to the dissemination of antibiotic resistance. The second part of this thesis monitors the prevalence of resistant faecal bacteria through WWTPs and in surface waters. Determination of antibiotic minimum inhibitory concentration (MIC) values for E.coli and E.faecium indicated that the WWTP did not influence the proportions of the resistant bacterial species. Elevated levels of E.coli with acquired ciprofloxacin resistance increased from not detectable in surface waters up-stream to 9.3% down-stream of the WWTP discharge point. The need for standardisation of the interpretation of MIC data is addressed. The potential of ciprofloxacin within surface water to select for ciprofloxacin resistant E.coli were investigated through microcosm studies in the third part of this study. A significant increase (p < 0.05) in the level of resistant E.coli was observed in microcosms exposed to ≥ 5 μg/L ciprofloxacin. At the ciprofloxacin levels typically detected in surface waters receiving treated effluent (<300 ng/L), the levels of resistance amongst E.coli were maintained

Reweighting the New Zealand Household Economic Survey for Tax Microsimuilation Modelling

This paper reports a reweighting exercise for the New Zealand Household Economic Survey, which is the basis of the Treasury's microsimulation model, TaxMod. Comparisons of benefit expenditures in a variety of demographic groups, along with population data, reveal that TaxMod estimates differ substantially from totals based on administrative data, when the weights provided by Statistics New Zealand are used. After describing the method used to compute new weights, the calibration requirements are reported. These relate to the age structure of the population and the number of beneficiaries for Unemployment Benefit, Domestic Purposes Benefit, Invalid's and Sickness Benefits and Family Support and Tax Credits. The revised weights and expenditure estimates are reported and the resulting distribution of income examined. The new weights are found to produce much improved expenditure estimates, without distorting the resulting income distribution. The effects of reweighting are demonstrated using a simple policy simulation.Survey weights; minimum distance; microsimulation

Computational modeling of spike generation in serotonergic neurons of the dorsal raphe nucleu

We consider here a single-compartment model of these neurons which is capable of describing many of the known features of spike generation, particularly the slow rhythmic pacemaking activity often observed in these cells in a variety of species. Included in the model are ten kinds of voltage dependent ion channels as well as calcium-dependent potassium current. Calcium dynamics includes buffering and pumping. In sections 3-9, each component is considered in detail and parameters estimated from voltage clamp data where possible. In the next two sections simplified versions of some components are employed to explore the effects of various parameters on spiking, using a systematic approach, ending up with the following eleven components: a fast sodium current $I_{Na}$, a delayed rectifier potassium current $I_{KDR}$, a transient potassium current $I_A$, a low-threshold calcium current $I_T$, two high threshold calcium currents $I_L$ and $I_N$, small and large conductance potassium currents $I_{SK}$ and $I_{BK}$, a hyperpolarization-activated cation current $I_H$, a leak current $I_{Leak}$ and intracellular calcium ion concentration $Ca_i$. Attention is focused on the properties usually associated with these neurons, particularly long duration of action potential, pacemaker-like spiking and the ramp-like return to threshold after a spike. In some cases the membrane potential trajectories display doublets or have kinks or notches as have been reported in some experimental studies. The computed time courses of $I_A$ and $I_T$ during the interspike interval support the generally held view of a competition between them in influencing the frequency of spiking. Spontaneous spiking could be obtained with small changes in a few parameters from their values with driven spiking.Comment: The abstract has been truncate

A Lower Bound for the First Passage Time Density of the Suprathreshold Ornstein-Uhlenbeck Process

We prove that the first passage time density $\rho(t)$ for an Ornstein-Uhlenbeck process $X(t)$ obeying $dX=-\beta X dt + \sigma dW$ to reach a fixed threshold $\theta$ from a suprathreshold initial condition $x_0>\theta>0$ has a lower bound of the form $\rho(t)>k \exp\left[-p e^{6\beta t}\right]$ for positive constants $k$ and $p$ for times $t$ exceeding some positive value $u$. We obtain explicit expressions for $k, p$ and $u$ in terms of $\beta$, $\sigma$, $x_0$ and $\theta$, and discuss application of the results to the synchronization of periodically forced stochastic leaky integrate-and-fire model neurons.Comment: 15 pages, 1 figur