This paper discusses the concepts of fractal geometry in a cellular biological context. It defines the concept of the fractal dimension. D, as a measure of complexity and illustrates the two different general ways of quantitatively measuring D by length-related and mass-related methods. Then, these several Ds are compared and contrasted. A goal of the paper is to find methods other than length-related measures that can distinguish between two objects that have the same D but are structurally different. The mass-related D is shown potentially to be such a measure. The concept of lacunarity, L, is defined and methods of measuring L are illustrated. L is also shown to be a potentially distinguishing measure. Finally, the notion of multifracticality is defined and illustrated to exist in certain individual nerve and glial cells.

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Most quantitative descriptions of neuronal dendrite morphology involve tabulations of measurements and correlations among them. The present work is an attempt to extract from such data a parsimonious set of parameters that are sufficient to describe the quantitative features of individual and pooled dendrites, including their statistical variability. A relatively simple stochastic (Monte Carlo) model was devised to simulate branching dendritic trees. The necessary parameters were then derived directly from measurements of 64 completely reconstructed dendrites belonging to six gastrocnemius alpha-motoneurons, labeled by intracellular injection of HRP. Comparison of actual and simulated dendrites was used to guide the process of parameter extraction. The model included only two processes, one to generate individual branches given their starting diameters and the second to select starting diameters for the daughter branches produced at dichotomous branching points. The stochastic process for branch generation was controlled by probability functions for branching (Pbr) and for terminating (Ptrm), together with a constant rate of branch taper. All model parameters were fixed by motoneuron measurements except for branch taper rate, which was allowed to vary within limits consistent with observed taper rates in order to generate the appropriate total number of branches. The simplest model (model 1), in which Pbr and Ptrm depended only on local branch diameter, produced simulated dendrites that fit many, but not all, characteristics of actual motoneuron dendrites. Two additional properties produced significant improvements in the fit: (1) a small but significant dependence of daughter diameters on the normalized starting diameter of the parent branch, and (2) a dependence of Pbr and Ptrm on distance from the soma as well as on local branch diameter. The process of developing this model revealed unsuspected relations in the original data that suggest the existence of fundamental mechanisms for morphological control. The final model succinctly describes a large amount of data and will enable quantitative comparisons between the dendritic structures of different types of neurons, regardless of their relative sizes.

Single parafoveal cones from human and monkey retinas were examined in a recording microspectrophotometer. Three types of receptors with maximum absorption in the yellow, green, and violet regions of the spectruin were found. Thus the commonly held belief, for which there has previously been no direct and unequivocal evidence, that color vision is mediated by several kinds of receptors (possibly three), each containing photopigments absorbing in diflerent regions of the spectrum, is confirmed.

Activity patterns were recorded from 51 motoneurons in the fifth lumbar ventral root of cats walking on a motorized treadmill at a range of speeds between 0.1 and 1.3 m/s. The muscle of destination of recorded motoneurons was identified by spike-triggered averaging of EMG recordings from each of the anterior thigh muscles. Forty-three motoneurons projected to one of the quadriceps (vastus medialis, vastus lateralis, vastus intermedius, or rectus femoris) or sartorius (anterior or medial) muscles of the anterior thigh. Anterior thigh motoneurons always discharged a single burst of action potentials per step cycle, even in multifunctional muscles (e.g., sartorius anterior) that exhibited more than one burst of EMG activity per step cycle. The instantaneous firing rates of most motoneurons were lowest upon recruitment and increased progressively during a burst, as long as the EMG was still increasing. Firing rates peaked midway through each burst and tended to decline toward the end of the burst. The initial, mean, and peak firing rates of single motoneurons typically increased for faster walking speeds. At any given walking speed, early recruited motoneurons typically reached higher firing rates than late recruited motoneurons. In contrast to decerebrated cats, initial doublets at the beginning of bursts were seen only rarely. In the 4/51 motoneurons that showed initial doublets, both the instantaneous frequency of the doublet and the probability of starting a burst with a doublet decreased for faster walking speeds. The modulations in firing rate of every motoneuron were found to be closely correlated to the smoothed electromyogram of its target muscle. For 32 identified motoneurons, the unit's instantaneous frequencygram was scaled linearly by computer to the rectified smoothed EMG recorded from each of the anterior thigh muscles. The covariance between unitary frequencygram and muscle EMG was computed for each muscle. Typically, the EMG profile of the target muscle accounted for 0.88-0.96 of the variance in unitary firing rate. The EMG profiles of the other anterior thigh muscles, when tested in the same way, usually accounted only for a significantly smaller fraction of the variance. Brief amplitude fluctuations observed in the EMG envelopes were usually also reflected in the individual motoneuron frequencygrams. To further demonstrate the relationship between unitary frequencygrams and EMG, EMG envelopes recorded during walking were used as templates to generate depolarizing currents that were applied intracellularly to lumbar motoneurons in an acute spinal preparation.(ABSTRACT TRUNCATED AT 400 WORDS)

Cat sartorius has two distinct anatomical portions, anterior (SA-a) and medial (SA-m). SA-a acts to extend the knee and also to flex the hip. SA-m acts to flex both the knee and the hip. The objective of this study was to investigate how a "single motoneuron pool" is used to control at least three separate functions mediated by the two anatomical portions of one muscle. Discharge patterns of single motoneurons projecting to the sartorius muscle were recorded using floating microelectrodes implanted in the L5 ventral root of cats. The electromyographic activity generated by the anterior and medial portions of sartorius was recorded with chronically implanted electrodes. The muscle portion innervated by each motoneuron was determined by spike-triggered averaging of the EMGs during walking on a motorized treadmill. During normal locomotion, SA-a exhibited two bursts of EMG activity per step cycle, one during the stance phase and one during the late swing phase. In contrast, every recorded motoneuron projecting to SA-a discharged a single burst of action potentials per step cycle. Some SA-a motoneurons discharged only during the stance phase, whereas other motoneurons discharged only during the late swing phase. In all cases, the instantaneous frequencygram of the motoneuron was well fit by the rectified smoothed EMG envelope generated by SA-a during the appropriate phase of the step cycle. During normal locomotion, SA-m exhibited a single burst of EMG activity per step cycle, during the swing phase. The temporal characteristics of the EMG bursts recorded from SA-m differed from the swing-phase EMG bursts generated by SA-a.(ABSTRACT TRUNCATED AT 250 WORDS)

In order to better understand the organization of the locomotor control system, we examined the temporal patterns of distal hindlimb muscle responses to brief electrical stimulation of cutaneous nerves during walking on a treadmill. Electromyographic recordings were made from twelve muscles; stimuli were applied individually to three nerves at random times throughout the step cycle. A new graphical technique was developed to assist detailed examination of the time course and gating of complex reflex patterns. The short latency reflexes were of two primary types: inhibition of extensors and excitation of flexors; these responses were only evident during locomotor phases in which the respective motoneuron pools were active. Longer-latency response components were gated in a similar but not identical manner, suggesting some independence from the basic locomotory influence on the motoneuronal pool. The phase-dependent gating of reflexes appeared to be consistent with a functional role for reflex responses during locomotion. The reflex responses of muscles with complex anatomical actions were often correspondingly complex.