Interspike Interval Fluctuations in Aplysia Pacemaker Neurons

In recent years, several mathematical models have been put forth to explain the time sequence of spike discharges in single neurons, in terms of synaptic inputs or intrinsic mechanisms. All of these models have been hypothetical, in that intracellular events were assumed, and not measured directly. The purpose of the present work was to study the statistics of the discharge from a preparation where intracellular recording was possible, and relate the observed discharge to measurable cell parameters. Regularly firing “pacemaker neurons” in the visceral ganglion of Aplysia californica were studied, using intracellular stimulating and recording techniques. Measurements were obtained of average curves of membrane potential, threshold for spike initiation, membrane resistance, and fluctuations of potential in the intervals between spontanously occurring spikes. The timing of discharges from these neurons was described quantitatively by interspike-interval histograms, mean and standard deviation of intervals, skewness, and serial correlation coefficients. A mathematical model (contained in a simulation program for the IBM 7094 computer) was constructed, based on discrete fluctuations of membrane potential following each spike and other directly observed intracellular events. It was found that the model could quantitatively account for observed spike trains, including variations in the discharge from one cell to another.     

Membrane Potential Fluctuations Determine the Precision of Spike Timing and Synchronous Activity: A Model Study

It is much debated on what time scale information is encoded by neuronal spike activity. With a phenomenological model that transforms time-dependent membrane potential fluctuations into spike trains, we investigate constraints for the timing of spikes and for synchronous activity of neurons with common input. The model of spike generation has a variable threshold that depends on the time elapsed since the previous action potential and on the preceding membrane potential changes. To ensure that the model operates in a biologically meaningful range, the model was adjusted to fit the responses of a fly visual interneuron to motion stimuli. The dependence of spike timing on the membrane potential dynamics was analyzed. Fast membrane potential fluctuations are needed to trigger spikes with a high temporal precision. Slow fluctuations lead to spike activity with a rate about proportional to the membrane potential. Thus, for a given level of stochastic input, the frequency range of membrane potential fluctuations induced by a stimulus determines whether a neuron can use a rate code or a temporal code. The relationship between the steepness of membrane potential fluctuations and the timing of spikes has also implications for synchronous activity in neurons with common input. Fast membrane potential changes must be shared by the neurons to produce synchronous activity.     

Membrane disruption, fusion and resealing in the course of exocytosis in Paramecium cells

Ca²⁺-ionophore-mediated trichocyst exocytosis was followed by scanning electron microscopy, freeze-cleaving and ultrathin sectioning after surface labelling in vivo with negatively charged hemepeptides. The apical trichocyst membrane and the superposed cell membrane portion (encircled by ˜300 nm large “rings” of membrane-intercalated particles) undergo fragmentation, while both membranes involved fuse with each other within the “rings”. Subsequently cell membrane materials spread centropetally to the region within the “rings” allowing the cell membrane to become resealed and the trichocyst membrane to become detached. Exocytosis does not result in any remarkable integration of trichocyst membrane materials into the cell membrane.     

The role of delayed excitation in the co-ordination of some metathoracic flight motoneurons of a locust

Summary Intracellular recordings have been made from the somata of two metathoracic flight motoneurons, one innervating an elevator muscle of the hindwing, the tergosternal muscle 113 and the other a depressor, the first basalar muscle 127. The locust,Ghortoicetes terminifera was mounted ventral side uppermost with the thorax restrained and opened for access to the thoracic ganglia. Patterns of electrical activity recorded from the thoracic muscles were similar to those shown by a locust during flight when tethered in a more normal posture. In flight the left and right 113 motoneurons each receive a single impulse together at every stroke of the wing, with the 127 muscles active in approximate antiphase. A spike in a 113 motoneuron causes a delayed wave of excitation simultaneously upon itself and its contralateral partner (Fig. 2). The epsp's which form these waves summate and may cause a spike which follows the original one with a delay equal to the wingbeat period. The delayed excitation of the contralateral motoneuron is of larger amplitude than the ipsilateral one so that spikes in either motoneuron must activate separate but symmetrical pathways. A single spike may cause multiple waves in either motoneuron, each separated by intervals equal to the wingbeat period (Fig. 3). In the pathway must be neurons capable of reverberation.A spike in a 113 motoneuron causes a delayed excitation of the ipsilateral 127 motoneuron so that its membrane potential is lowered antiphasically to that of 113 (Fig. 17). A spike in a 127 motoneuron has no effect on the 113 motoneurons. In flight these pathways causing delayed excitation may co-ordinate the motoneurons.The left and right 113 motoneurons receive common synaptic inputs from at least two sources (Fig. 8). These occur as bursts of epsp's at intervals approximately equal to or multiples of the wingbeat period and in the absence of flight. Epsp's of sufficient amplitude cause a spike in the motoneuron which is in the correct phase in the flight pattern relative to any other active motoneurons (Fig. 9). During sustained flight epsp's contribute to the wave of depolarization that the motoneuron undergoes at each wingbeat (Fig. 11). In the absence of the epsp's the motoneuron does not oscillate on its own. At the end of flight bursts of epsp's may continue at the flight frequency long after all activity in the muscles has ceased.Beit Memorial Research Fellow.     

The Cellular Mechanism of Orcadian Rhythms-A View on Evidence, Hypotheses and Problems

A stable period length is a characteristic property of circadian oscillations. The question about whether higher frequency oscillators (0.5-8 hr) contribute to or establish the stable circadian periodicity cannot be answered at present. A sequential coupling of quantal subcycles appears possible on the basis of known “ultradian” oscillations. There is, however, no supporting evidence for such a concept. Phase response curves of the circadian clock derived from various perturbing pulses allow qualitative conclusions concerning the perturbed clock process. Deductions from computer simulations also allow conclusions about the phase of this oscillatory process.

The distinction between processes (a) essential to the clock mechanism, (b) maintaining and controlling the clock (inputs) and (c) depending on the clock (outputs) on the basis of “oscillatory” and “change of φ or τ after perturbation” seems to be useful but not stringent. Protein synthesis may be an essential or input process. Oscillatory changes of this process may be due to periodic translational control or RNA-supply. Circadian changes in protein concentration and/or activity may depend on periodic synthesis, proteolysis, covalent modifications or aggregations. Specific essential proteins have not been identified conclusively. The large overlap between the group of agents and treatments that phase shift the clock and the group that induces stress proteins suggest that the latter may play a role in the controlling (input) or essential domain.

The role of membranes in the clock mechanism is not clear: concepts assuming an essential function are based on circumstantial evidence. The membrane potential as well as Ca²⁺ may be involved in either input or essential function. Ca²⁺ -calmodulin may also be important as concluded from inhibitor experiments. It is tempting to assume that a calmodulin-dependent kinase is part of a periodic protein phosphorylation process, yet it is not clear whether the periodic protein phosphorylation that has been observed is essential or is just another output process.     

A model of the mechanisms of formation of unit activity

Dependence of the temporal structure of the spike discharge of a neuron in a weakly interacting network on the characteristics of excitatory and inhibitory input flows and on cell parameters was analyzed by a mathematical model. The intensity of communication between individual neurons corresponded to the intensity of synaptic communication between real spinal neurons. The temporal course of trace and accommodation processes in the model was similar to that of these processes in real spinal neurons. Connection of inhibitory inputs and an increase in the intensity of their influences were shown to be equivalent to a decrease in the intensity of excitatory input flows. Changes in cell parameters had a significant effect on the spike discharge only in the case of weak input influences (the ratio of the amplitude of the combined ESP evoked by the input spike train to the threshold value of membrane potential at rest was about 1.2:1.0 to 1.4:1.0). An increase in the input flow intensity led to considerable reorganization of the firing pattern: Mean values of interspike intervals and their fluctuations were reduced, histograms of interspike intervals became more symmetrical, and periodic waves appeared on the autocorrelation histograms. It is concluded on the basis of these results and of data in the literature that the main factor determining reorganization of the temporal structure of unit activity in a network of weakly interacting cells is the intensity of the input flow.A. A. Bogomolets Institute of Physiology, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Neirofiziologiya, Vol. 12, No. 2, pp. 199–207, March–April, 1980.     

Neural Coding with Graded Membrane Potential Changes and Spikes

The neural encoding of sensory stimuli is usually investigated for spike responses, although many neurons are known to convey information by graded membrane potential changes. We compare by model simulations how well different dynamical stimuli can be discriminated on the basis of spiking or graded responses. Although a continuously varying membrane potential contains more information than binary spike trains, we find situations where different stimuli can be better discriminated on the basis of spike responses than on the basis of graded responses. Spikes can be superior to graded membrane potential fluctuations if spikes sharpen the temporal structure of neuronal responses by amplifying fast transients of the membrane potential. Such fast membrane potential changes can be induced deterministically by the stimulus or can be due to membrane potential noise that is influenced in its statistical properties by the stimulus. The graded response mode is superior for discrimination between stimuli on a fine time scale.     

Temperature profiles, and the effect of sleep on them, in relation to morningness-eveningness in healthy female subjects

There were 15 healthy female subjects, differing in their position on the “morningness-eveningness” scale, studied for 7 consecutive days, first while living a sedentary lifestyle and sleeping between midnight and 08:00 and then while undergoing a “constant routine.” Rectal temperature was measured at regular intervals throughout this time, and the results were subjected to cosinor analysis both before and after “purification” for the effects of physical activity. Results showed that there was a phase difference in the circadian rhythm of core temperature that was associated with the morningness score, with calculations that “morning types” would be phased earlier than “evening types” by up to about 3h. This difference in phase (which was also statistically significant when the group was divided by a median split into a “morning group” and an “evening group”) could not be attributed to effects of waking activity and existed in spite of the subjects keeping the same sleep-wake schedule. Moreover, it persisted when the subjects' data had been purified and when the data were obtained from the constant routine. That is, there was an endogenous component to this difference in phase of the core temperature. The morning group also showed a greater fall of core temperature during sleep; this was assessed in two ways, the main one being a comparison of constant routine and nychthemeral data sets after correction for any effects of activity. Even though the morning group was sleeping at a later phase of their circadian temperature rhythm than was the evening group, neither group showed a fall of temperature due to sleep that varied with time elapsed since the temperature acrophase. It is concluded that another factor that differs between morning and evening types is responsible for this difference. (Chronobiology International, 18(2), 227-247, 2001)     

Demonstration of membranous patches on isolated chromosomes

High resolution scanning electron microscopy of isolated Chinese hamster ovary metaphase chromosomes revealed “membranous patches” at telomeric and juxtatelomeric regions of the chromosomes. The “membranous patches” remained bound to the chromosomes during centrifugation through dense sucrose, but not after treatment with detergents. These membrane fragments on isolated purified chromosomes may represent a component that binds the chromosome to the inner portion of the nuclear envelope up to late stages of prophase. These chromosome associated membranous patches may represent sites of reformation of the nuclear envelope at telophase.     

Statistical Analysis of Membrane Potential Fluctuations: Relation with Presynaptic Spike Train

In a study of integration at the single neuron level, the relationships between the postsynaptic membrane potential and the presynaptic spike train were analyzed. Fluctuations in membrane potential of neurons in the visceral ganglion of Aplysia were measured and described by histograms. The histogram estimates the probability density function of the membrane potential. Comparisons were made among histograms when there was no synaptic input, and when there was a single input in which variations were made in the PSP (postsynaptic potential) sign, i.e. excitatory or inhibitory, and arrival statistics, e.g. slow or fast, regular, Poisson-like, or patterned. This was examined in cells where the membrane potential was constant and in cells in which there was spontaneous pacemaker activity. The form of the histogram depended on whether the neuron was spontaneously quiescent or a pacemaker, or whether it received presynaptic input and, if it did, on the sign and temporal characteristics of such input. From such histograms the mean firing rate of output spike trains can be predicted; additional information of a temporal nature is required, however, to predict features of the interval structure of the output train. Suggestions are made concerning the way the nervous system might utilize the information summarized in the membrane potential histogram.     

Dynamic relationship between the slow potential and spikes in cockroach ocellar neurons

The relationship between the slow potential and spikes of second-order ocellar neurons of the cockroach, Periplaneta americana, was studied. The stimulus was a sinusoidally modulated light with various mean illuminances. A solitary spike was generated at the depolarizing phase of the modulation response. Analysis of the relationship between the amplitude/frequency of voltage modulation and the rate of spike generation showed that (a) the spike initiation process was bandpass at approximately 0.5-5 Hz, (b) the process contained a dynamic linearity and a static nonlinearity, and (c) the spike threshold at optimal frequencies (0.5-5 Hz) remained unchanged over a mean illuminance range of 3.6 log units, whereas (d) the spike threshold at frequencies of less than 0.5 Hz was lower at a dimmer mean illuminance. The voltage noise in the response was larger and the mean membrane potential level was more positive at a dimmer mean illuminance. Steady or noise current injection during sinusoidal light stimulation showed that (a) the decrease in the spike threshold at a dimmer mean illuminance was due to the increase in the noise variance: the noise had facilitatory effects on the spike initiation; and (b) the change in the mean potential level had little effect on the spike threshold. We conclude that fundamental signal modifications occur during the spike initiation in the cockroach ocellar neuron, a finding that differs from the spike initiation process in other visual systems, including Limulus eye and vertebrate retina, in which it is presumed that little signal modification occurs at the analog-to-digital conversion process.     

Gene flow and genetic drift in a species subject to frequent local extinctions

Two models of the effect of extinction and recolonization on the genetic differentiation of local populations are analyzed. One model is Wright's “island model” in which there is gene flow from a source of fixed gene frequency. The other is an island model with a continuous production of new alleles and gene flow among all the populations. Individual and group selection are not considered. It is shown that the extent of population differentiation and the direction of the effect of the colonization and extinction process depend on the manner in which the propagules that establish new colonies are formed. Two extreme cases are considered. In the “propagule pool” model all the individuals in a single propagule are derived from one population while in the “migrant pool” model, the individuals in a propagule are derived from a random sample of the entire collection of populations.     

Human dehydroepiandrosterone sulfotransferase pharmacogenetics: Quantitative Western analysis and gene sequence polymorphisms

Dehydroepiandrosterone sulfotransferase (DHEA ST) catalyzes the sulfation of DHEA and other hydroxysteroids. DHEA ST enzymatic activity in individual human liver biopsy samples has been shown to vary over a five-fold range, and frequency distribution histograms are bimodal, with approximately 25% of subjects included in a high activity subgroup. We set out to characterize the molecular basis for variation in human liver DHEA ST activity. The first step involved performing quantitative Western analysis of cytosol preparations from 92 human liver samples that had been phenotyped with regard to level of DHEA ST enzymatic activity. There was a highly significant correlation (r_s = 0.635, P < 0.0001) between levels of DHEA ST activity and immunoreactive protein. We next attempted to determine whether the expression of DHEA ST might be controlled, in part, by a genetic polymorphism. DNA was isolated from three “low” and three “high” DHEA ST activity liver samples. Exons and the 5′-flanking region of the DHEA ST gene (STD) were amplified for each of these samples with the polymerase chain reaction (PCR). When compared with “wild type” STD sequence, some of the samples contained a T → C transition at DHEA ST cDNA nucleotide 170, located within exon 2, resulting in a Met 57 → Thr change in amino acid. Other samples contained an A → T transversion at nucleotide 557 within STD exon 4 that resulted in a Glu 186 → Val change. STD exons 2 and 4 were then sequenced for DNA isolated from an additional 87 liver samples that had been phenotyped with regard to level of DHEA ST enzymatic activity. The allele frequency for the exon 2 polymorphism in these samples was 0.027, whereas that for the exon 4 polymorphism was 0.038, but neither polymorphism was systematically related to the level of enzyme activity in these samples. Transient expression in COS-1 cells of cDNA that contained the nucleotide 170 and 557 polymorphisms, either separately or together, resulted in decreased expression of both DHEA ST enzymatic activity and level of immunoreactive protein, but only when the nucleotide 557 variant was present. Identification of common genetic polymorphisms within STD will now make it possible to test the hypothesis that those polymorphisms might alter in vivo expression and/or function of this important human steroid-metabolizing enzyme.     

Statistical Analysis of Motor Unit Firing Patterns in a Human Skeletal Muscle

A statistical analysis of the firing pattern of single motor units in the human brachial biceps muscle is presented. Single motor unit spike trains are recorded and analyzed. The statistical treatment of these spike trains is as stochastic point processes, the theory of which is briefly discussed. Evidence is presented that motor unit spike trains may be modelled by a renewal process with an underlying gaussian probability density. Statistical independence of successive interspike intervals is shown using scatter diagrams; the hypothesis of a gaussian distribution is accepted at the 99th percentile confidence limit, chi-square test, in 90% of the units tested. A functional relationship between the mean and standard deviation is shown and discussed; its implications in obtaining sample size are presented in an appendix.The results of higher order analysis in the form of autocorrelograms and grouped interval histograms are presented. Grouped interval histograms are discussed in the context of motor unit data, and used to confirm the hypothesis that a stable probability density function does not represent a good model of the data at this level of analysis.     

Contribution of response surface design to the development of glycerolysis systems catalyzed by commercial immobilized lipases

Two commercial immobilized lipases (“Lipozyme® IM” and “Novozym® 435”) were tested as biocatalysts for the glycerolysis of olive residue oil in n-hexane aimed at the production of monoglycerides (MG) and diglycerides (DG). A central composite rotatable design (CCRD) was followed to model and optimize glycerolysis as a function of both the amount of biocatalyst (L) and of the molar ratio glycerol/triglycerides (Gly/TG). For both biocatalysts, the production of free fatty acids (FFA) was described by second order models. In terms of MG and DG production, as well as of TG conversion, the best fits were obtained with first-order models. The highest MG productions were in the range 43–45% (w/w, on the basis of total fat) for both biocatalysts tested at a (Gly/TG) ratio of one. In the case of “Novozym 435”, the lowest load used (12%, w/w) gave the best results, in contrast with “Lipozyme IM” with which a concentration of about 26% (w/w) was necessary to obtain the highest production. Under these conditions, the amount of FFA produced was about 2% and 10% (w/w), respectively, for “Novozym 435” and “Lipozyme IM” catalyzed systems. Considering both FFA production and lipase loading, “Novozym 435” was shown to be a better biocatalyst for the glycerolysis of olive residue oil in n-hexane, aimed at the production of MG, than “Lipozyme IM”.     

Investigation of a two-point maximum entropy regularization method for signal enhancement applied to magnetoencephalography data

A two-point maximum entropy method (TPMEM) was investigated for post-acquisition signal recovery in magnetoencephalography (MEG) data, as a potential replacement of a low-pass (LP) filtering technique currently in use. We first applied TPMEM and the LP filter for signal recovery of synthetically noise corrupted MEG “phantom” data sets in which the true underlying signal was known. Results were quantified with the use of visual plots, percent error histograms, and the statistical parameters root mean squared error and Pearson’s correlation coefficient. Synthetically noise corrupted data from a simulated magnetic dipole was used to quantify the improvements gained in using TPMEM over LP filters in reconstructing known dipole parameters such as position, orientation, and magnitude. Finally, we applied TPMEM and LP filters to a sample MEG patient data set. Our results show that TPMEM has improved noise-reduction and signal recovery capabilities than those of the LP filter, and furthermore data processed with TPMEM shows less error in the reconstructed dipole parameters. We propose that TPMEM can be used for MEG signal processing, resulting in improved MEG source characterization.     

Regulation of estrogen receptor protein and messenger ribonucleic acid by estradiol and progesterone in rat uterus

The objective of this study was to examine the mechanisms of estrogen receptor (ER) processing and replenishment in the uterus of ovariectomized rats after estradiol and progesterone treatment. Uterine ER binding activity, ER protein and ER mRNA were measured by receptor binding exchange assay, Western blot and slot blot, respectively. The regulation of ER levels in rat uterus by estradiol and progesterone was very dramatic. Changes in ER protein were faithfully reflected by changes in binding activity. Estradiol caused receptor “processing” within 4 h of administration followed by recovery or “replenishment” of ER levels to the initial level by 20 h. The term “processing” has previously been used to describe the loss of ER binding activity in the early phase of estradiol-action, but it was never clear whether the ligand binding site was inactivated by processing or if the receptor molecule actually disappeared. This study shows that receptor “processing” constitutes disappearance of receptor protein and the later “replenishment” phase represents new ER protein rather than recycling of “processed” receptor. Progesterone-action, on the other hand, influenced only the “replenishment” phase by blocking recovery of ER protein. ER mRNA was suppressed by estradiol at 8 h, after the receptor was “processed” and “replenishment” already initiated. Progesterone, on the other hand, did not alter the steady state level of the message. Other mechanisms, such as regulation of translation rate of existing mRNA and changes in the rate of degradation of ER proteins are more likely involved in acute regulation of ER by these ovarian steroid hormones.     

Motoneuron membrane potentials follow a time inhomogeneous jump diffusion process

Stochastic leaky integrate-and-fire models are popular due to their simplicity and statistical tractability. They have been widely applied to gain understanding of the underlying mechanisms for spike timing in neurons, and have served as building blocks for more elaborate models. Especially the Ornstein–Uhlenbeck process is popular to describe the stochastic fluctuations in the membrane potential of a neuron, but also other models like the square-root model or models with a non-linear drift are sometimes applied. Data that can be described by such models have to be stationary and thus, the simple models can only be applied over short time windows. However, experimental data show varying time constants, state dependent noise, a graded firing threshold and time-inhomogeneous input. In the present study we build a jump diffusion model that incorporates these features, and introduce a firing mechanism with a state dependent intensity. In addition, we suggest statistical methods to estimate all unknown quantities and apply these to analyze turtle motoneuron membrane potentials. Finally, simulated and real data are compared and discussed. We find that a square-root diffusion describes the data much better than an Ornstein–Uhlenbeck process with constant diffusion coefficient. Further, the membrane time constant decreases with increasing depolarization, as expected from the increase in synaptic conductance. The network activity, which the neuron is exposed to, can be reasonably estimated to be a threshold version of the nerve output from the network. Moreover, the spiking characteristics are well described by a Poisson spike train with an intensity depending exponentially on the membrane potential.     

Period responses to Zeitgeber signals stabilize circadian clocks during entrainment

Circadian clocks with characteristic period (τ) can be entrained to light/dark (LD) cycles by means of (i) phase shifts which are due to D/L “dawn” and/or L/D “dusk” transitions, (ii) period changes associated with long-term light exposure, or (iii) by combinations of the above possibilities. Based on stability analysis of a model circadian clock it was predicted that nocturnal burrowing mammals would benefit less from period responses than their diurnal counterparts. The model further predicted that maximal stability of circadian clock is reached when the clock slightly changes both its phase and period in response to light stimuli. Analyses of empirical phase response curve (PRC) and period response curve (τRC) of some diurnal and nocturnal mammals revealed that PRCs of both diurnal and nocturnal mammals have similar waveform while τRCs of nocturnal mammals are of smaller amplitude than those of diurnal mammals. The shape of the τRC also changes with age and with increasing strength of light stimuli. During erratic fluctuations in light intensity under different weather conditions, the stability of phase of entrainment of circadian clocks appears to be achieved by an interplay between phase and period responses and the strength of light stimuli.     

Circadian control of migratory restlessness and the effects of exogenous melatonin in the brambling, Fringilla montifringilla

Circadian pacemakers control both “daytime” activity and nocturnal restlessness of migratory birds, and the daily rhythm of melatonin release from the pineal has been suggested to be involved in the control of migratory activity. To study the phase relations between the two activity components during entrainment and when free running, locomotor activity of bramblings (Fringilla montifringilla) was recorded continuously under a 12:12 “cool light” to “warm light” cycle (CL:WL, ca. 5000 K and ca. 2500 K, respectively) or blue light to red light cycle (BL:RL, maxima at 440 and 650 nm, respectively) at different irradiance ratios. Migratory activity was expressed primarily during the WL or RL phase of the light cycles. Under free-running conditions, the circadian periods τ correlated with the phase relations between day and night (migratory) activity components during preceding entrainment. Bramblings with migratory activity had significantly longer τ at constant light intensity than the same individuals without migratory activity. Birds with migratory activity reentrained faster after a 6h phase shift of the CL:WL cycle than birds without migratory activity. When exogenous melatonin was given in the drinking water (200 μg/mL 1% ethanol or 0.86 mM) to bramblings exposed to 12:12 CL:WL cycles with constant irradiance, the amounts of activity, which were initially higher during the WL phase of the light cycle, were suppressed to similar low levels during both light phases. The systematic changes in the amounts of activity during melatonin treatment were not correlated with consistent changes in entrainment status. The data support the hypothesis that changes in the amplitude and level of the daily melatonin cycle are involved in regulating migratory restlessness, by either allowing or inhibiting nocturnal activity. (Chronobiology International, 17(4), 471-488, 2000)