Transient Response in a Dendritic Neuron Model for Current Injected at One Branch

Mathematical expressions are obtained for the response function corresponding to an instantaneous pulse of current injected to a single dendritic branch in a branched dendritic neuron model. The theoretical model assumes passive membrane properties and the equivalent cylinder constraint on branch diameters. The response function when used in a convolution formula enables one to compute the voltage transient at any specified point in the dendritic tree for an arbitrary current injection at a given input location. A particular numerical example, for a brief current injection at a branch terminal, illustrates the attenuation and delay characteristics of the depolarization peak as it spreads throughout the neuron model. In contrast to the severe attenuation of voltage transients from branch input sites to the soma, the fraction of total input charge actually delivered to the soma and other trees is calculated to be about one-half. This fraction is independent of the input time course. Other numerical examples, which compare a branch terminal input site with a soma input site, demonstrate that, for a given transient current injection, the peak depolarization is not proportional to the input resistance at the injection site and, for a given synaptic conductance transient, the effective synaptic driving potential can be significantly reduced, resulting in less synaptic current flow and charge, for a branch input site. Also, for the synaptic case, the two inputs are compared on the basis of the excitatory post-synaptic potential (EPSP) seen at the soma and the total charge delivered to the soma.     

Paraffin Compression Due to the Rotary Microtome

The extent of compression of microtome sections has been studied for blocks with tissue and also blocks of clear paraffin. Thick sections are commonly compressed 15% or more, while in sections below 5 or 10 μ, compression may exceed 50%. Compensatory thickening of sections occurs. The degree of compression for various paraffin samples and for various conditions of knife edge, temperature, etc., is compared. Microscopical work, particularly where quantitative data or reconstructions are involved, is often seriously unpaired by unrecognized artifacts of sectioning. The present work indicates the magnitude of such artifacts. Compensation for distortions of sections is not easy because tissues, particularly dense tissues, may compress less than the paraffin matrix. Section corrugation is due to this inequality in compression. Absorption of water in section flattening causes some tissue readjustment, but this varies with different tissues and different fixations.