Summation

About: Summation is a research topic. Over the lifetime, 954 publications have been published within this topic receiving 45593 citations. The topic is also known as: summation & sum of a sequence.

New Types of Experiments Reveal that a Neuron Functions as Multiple Independent Threshold Units.

Abstract: Neurons are the computational elements that compose the brain and their fundamental principles of activity are known for decades. According to the long-lasting computational scheme, each neuron sums the incoming electrical signals via its dendrites and when the membrane potential reaches a certain threshold the neuron typically generates a spike to its axon. Here we present three types of experiments, using neuronal cultures, indicating that each neuron functions as a collection of independent threshold units. The neuron is anisotropically activated following the origin of the arriving signals to the membrane, via its dendritic trees. The first type of experiments demonstrates that a single neuron’s spike waveform typically varies as a function of the stimulation location. The second type reveals that spatial summation is absent for extracellular stimulations from different directions. The third type indicates that spatial summation and subtraction are not achieved when combining intra- and extra- cellular stimulations, as well as for nonlocal time interference, where the precise timings of the stimulations are irrelevant. Results call to re-examine neuronal functionalities beyond the traditional framework, and the advanced computational capabilities and dynamical properties of such complex systems.

Spatial summation of pre-pain and pain in human teeth.

Abstract: The purpose of this work was to investigate the relation between the sensations of pain and ‘pre-pain’ evoked by stimulation of teeth in human subjects. Electrical pulses of progressively increasing amplitude, generated by a computer-controlled stimulator, were applied to 1 or 2 teeth, and the subjects responded by indicating the nature of the resulting sensation. Pre-pain and pain could be readily and rapidly distinguished by all 11 subjects (response latency about 0.4 sec). Both sensations had stable thresholds with relatively small variance (S.D. 10–15% of threshold value) for a given subject. Subjects characterized the stimuli as indifferent or unpleasant, localized, and brief. By using special stimulation strategies (termed ‘optimal trajectories’) for exciting 2 teeth simultaneously, spatial summation for pre-pain was demonstrated in most subjects and for pain in almost all subjects. Spatial summation of pre-pain resulted in pain rather than in more intense pre-pain. These results are consistent with both the dual modality (separate afferent fibers for pre-pain and pain) and the single modality hypotheses (single type of afferent fibers) of tooth pulp sensibility, but favor single modality innervation.

The effects of isoflurane on repeated nociceptive stimuli (central temporal summation)

Abstract: Central temporal summation of afferent nociceptive stimuli is involved in central hyperexcitability. This is assumed to be an important mechanism in the nociceptive system which is probably activated during surgery and trauma. The purpose of the present study was to investigate if isoflurane has a specific effect on central temporal summation in humans. Facilitation of the nociceptive reflex to repeated stimuli can be used to assess central summation in subjects unable to cooperate due to an anaesthetic procedure. The nociceptive reflex to single and repeated (5 pulses delivered at 2 Hz) electrical surface stimuli of the sural nerve were measured in 6 healthy volunteers anaesthetized with isoflurane. A reflex was defined as an EMG signal from the rectus and biceps femoris exceeding 20 microV for more than 10 msec in the 80-200 msec interval after the stimulus. The end-tidal isoflurane concentration was increased in steps of 0.25 vol% from 0.25 to 1.50 vol%. For each concentration the thresholds for the nociceptive reflex were determined as the current intensity that could just elicit a reflex response to single stimulations, and for the repeated stimulations as the current intensity that could just elicit a reflex response to the 4th and/or 5th stimuli in the train of 5 stimuli. The nociceptive reflex to single stimuli was depressed at isoflurane concentrations producing sedation or light anaesthesia (0.25-0.50 vol% end-tidal). In contrast, 2-4-fold higher isoflurane concentrations (1.00-1.50 vol% end-tidal) that normally produce surgical anaesthesia were required to depress the nociceptive reflex to repetitive stimuli. This indicates that central temporal summation in the nociceptive system is a potent mechanism, and that isoflurane has a weak potency for depressing temporal summation in humans. As such isoflurane alone is not adequate for inhibiting surgically evoked hyperexcitability.

Interaction between synaptic excitation and slow afterhyperpolarization current in rat hippocampal pyramidal cells.

Abstract: In many neurones propagation of synaptic signals from dendrites to the site of output at the soma/axon hillock is accompanied by modulation due to the activity of intrinsic postsynaptic ion channels. Thus, excitatory postsynaptic potentials (EPSPs) can be boosted by voltage-gated Na+ and Ca2+ channels (Magee & Johnston, 1995; Lipowsky et al. 1996) and, conversely, voltage-gated K+ currents attenuate EPSP amplitude (Hoffman et al. 1997). Additionally, summation of EPSPs can be regulated by the hyperpolarization-activated cation current, IH (Magee, 1998). However, little is known about the influence of postsynaptic Ca2+-dependent K+ channels on synaptic responses, although these channels are distributed widely in mammalian neurones. The slow AHP current (IsAHP) is a voltage-independent, Ca2+-dependent K+ current which follows short bursts of action potentials and restrains repetitive firing in hippocampal pyramidal neurones. In most studies, this current has been activated by the Ca2+ influx associated with action potentials or large depolarizations. There is, however, evidence to suggest that IsAHP should be apparent during repetitive synaptic activity; the β-adrenergic sensitivity of long-term potentiation (LTP) induction thresholds has been suggested to result from involvement of IsAHP in the postsynaptic response to high-frequency synaptic input (Sah & Bekkers, 1996). This possibility has not been examined carefully, although the presence of such a potential has been mentioned briefly (Doze et al. 1991). During excitatory synaptic input in CA1 pyramidal cells, Ca2+ influx may occur through NMDA receptor channels (Alford et al. 1993; Kovalchuk et al. 2000) or locally activated voltage-gated Ca2+ channels without calcium spiking (Miyakawa et al. 1992; Magee & Johnston, 1995). Therefore, as the first objective of this study, we examined the ability of subthreshold (non-spiking) repetitive excitatory synaptic input to activate Ca2+-dependent K+ current. The results indicate that even without action potentials, synaptic input can generate sufficient Ca2+ influx to elicit Ca2+-dependent K+ current. Thus during normal cellular activity, if IsAHP is active during synaptic input what are the functional consequences of this K+ conductance for synaptic responses detected at the soma? In CA1 pyramidal cells, a substantial IsAHP-like current can be measured in recordings from the soma and/or in proximal apical dendrites (Andreasen & Lambert, 1995; Lancaster & Batchelor, 2000). This location suggests that the sAHP conductance could shape synaptic input propagating to the soma, although this apical dendritic location is under question (Bekkers, 2000). It is clear that intrinsic conductances can modify synaptic responses (see above), but comparable quantification for the sAHP conductance is more difficult because it requires Ca2+ entry which itself might modify synaptic responses (Kyrozis et al. 1996). To overcome this problem, we have used a novel method to elicit steady-state activation and deactivation of IsAHP without measurable elevation of internal Ca2+ (Lancaster & Batchelor, 2000). This has allowed us to quantify the electrical interaction between EPSPs and IsAHP in CA1 neurones. The results indicate that the characteristics of IsAHP are well suited for modulation of temporal summation. Some of this work has been published in abstract form (Lancaster et al. 1999, 2000).