Contribution to the probabilistic theory of neural nets: III. Specific inhibition

The input-output formula is derived for a neuron upon which converge the axones of two other neurons (one excitatory, the other inhibitory) which are themselves subjected to a “Poisson shower” of excitatory stimuli. If the period of latent inhibition, σ, does not exceed one half the refractory period, δ, the input-output curve has no maximum. If, however, σ>δ/2, a maximum exists in the input-output curve. As the outside frequencyx increases without bound, the output frequencyx ₃ approaches an asymptotic value which ranges from 1/δ to 0, depending on the ratio σ/δ. The maximum output (if it exists) is also derived as a function of σ and δ.     

Primary culture and characteristic morphologies of neurons from the cerebral ganglion of the mud crab, <Emphasis Type="Italic">Scylla paramamosain</Emphasis>

Crustacean neurons, obtained from the cerebral ganglion of the mud crab Scylla paramamosain, were successfully cultured in vitro. They maintained typical morphological characteristics and showed better outgrowth in modified Medium 199 (M199) medium than that in Liebowitz’s L-15 medium. Fetal bovine serum (FBS), muscle extracts, and hemolymph of the mud crab S. paramamosain were added as supplements. Only 20% FBS could promote neuron outgrowth, while muscle extracts and hemolymph of S. paramamosain did not improve neuron outgrowth. For cell dissociation, both collagenase type I and trypsin worked well as determined by initial cell viability and following cell outgrowth potential. More than six kinds of cells with different morphological characteristics were identified in the neuron outgrowth. They were “small cells”, “veilers”, “branchers”, “multipolar cells”, “super-large cell”, and “bipolar cells”. Among all of the cells, bipolar cells were identified for the first time in crustacean neurons culture and they could live longer than other cells. The neurons could grow for more than a week before retraction and eventual degradation.     

The pattern of sensory discharge can determine the motor response in young Xenopus tadpoles

Young Xenopus tadpoles were used to test whether the pattern of discharge in specific sensory neurons can determine the motor response of a whole animal. Young Xenopus tadpoles show two main rhythmic behaviours: swimming and struggling. Touch-sensitive skin sensory neurons in the spinal cord of immobilised tadpoles were penetrated singly or in pairs using microelectrodes to allow precise control of their firing patterns. A single impulse in one Rohon-Beard neuron (= light touch) could sometimes trigger “fictive” swimming. Two to six impulses at 30–50 Hz (= a light stroke) reliably triggered fictive swimming. Neither stimulus evoked fictive struggling. Twenty-five or more impulses at 30–50 Hz (= pressure) could evoke a pattern of rhythmic bursts, distinct from swimming and suitable to drive slower, stronger movements. This pattern showed some or all the characteristics of “fictive” struggling. These results demonstrate clearly that sensory neurons can determine the pattern of motor output simply by their pattern of discharge. This provides a simple form of behavioural selection according to stimulus. Accepted: 28 November 1996     

Morphological characterization of single fan-shaped body neurons in <Emphasis Type="Italic">Drosophila melanogaster</Emphasis>

The fan-shaped body is the largest substructure of the central complex in Drosophila melanogaster. Two groups of large-field neurons that innervate the fan-shaped body, viz., F1 and F5 neurons, have recently been found to be involved in visual pattern memory for “contour orientation” and “elevation” in a rut-dependent manner. The F5 neurons have been found to be responsible for the parameter “elevation” in a for-dependent manner. We have shown here that the F1 neuron also affects visual memory for “contour orientation” in a for-dependent way. With the help of Gal4/UAS and FLP-out techniques, we have characterized the morphological features of these two groups of neurons at single neuron resolution. We have observed that F1 or F5 neurons are groups of isomorphic individual neurons. Single F1 neurons have three main arborization regions: one in the first layer of the fan-shaped body, one in the ventral body, and another in the inferior medial protocerebrum. Single F5 neurons have two arborization regions: one in the fifth layer of the fan-shaped body and the other in the superior medial protocerebrum. The polarity of the F1 and F5 neurons has been studied with the Syt-GFP marker. Our results indicate the existence of presynaptic sites of both F1 and F5 neurons located in the fan-shaped body and postsynaptic sites outside of the fan-shaped body. This work was supported by the “973 Program” (2005CB522804 and 2009CB918702), the National Natural Sciences Foundation of China (30621004, 30625022, and 30770682), and the Knowledge Innovation Program of the Chinese Academy of Sciences (KSCX2-YW-R-28).     

Analysis of the exponential decay model of the neuron showing frequency threshold effects

The exponential decay model of a neuron has been analyzed using the “random walk” approach of stochastic processes and an “absorbing barrier” solution is obtained forg ^T (s)—the Laplace transform of the output pulse interval density function. An expression for the mean output frequency is derived from this and a variety of input-output curves plotted which show frequency threshold effects in single neurons. Our results are compared with those of other authors obtained by computer simulation techniques, and the significance of these results discussed with reference to the possible behavior of networks constructed of such neuron units.     

A novel key–lock mechanism for inactivating amino acid neurotransmitters during transit across extracellular space

There are two kinds of neurotransmissions that occur in brain. One is neuron to neuron at synapses, and the other is neuron to glia via extracellular fluid (ECF), both of which are important for maintenance of proper neuronal functioning. For neuron to neuron communications, several potent amino acid neurotransmitters are used within the confines of synaptic space. However, their presence at elevated concentrations in extra-synaptic space could be detrimental to well organized neuronal functioning. The significance of the synthesis and release of N-acetylaspartylglutamate (NAAG) by neurons has long been a puzzle since glutamate (Glu) itself is the “key” that can interact with all Glu receptors on membranes of all cells. Nonetheless, neurons synthesize this acetylated dipeptide, which cannot be catabolized by neurons, and release it to ECF where its specific physiological target is the Glu metabotropic receptor 3 on the surface of astrocytes. Since Glu is excitotoxic at elevated concentrations, it is proposed that formation and release of NAAG by neurons allows large quantities of Glu to be transported in ECF without the risk of injurious excitotoxic effects. The metabolic mechanism used by neurons is a key–lock system to detoxify Glu during its intercellular transit. This is accomplished by first synthesizing N-acetylaspartate (NAA), and then joining this molecule via a peptide bond to Glu. In this paper, a hypothesis is presented that neurons synthesize a variety of relatively nontoxic peptides and peptide derivatives, including NAA, NAAG, homocarnosine (γ-aminobutyrylhistidine) and carnosine (β-alanylhistidine) from potent excitatory and inhibitory amino acids for the purpose of releasing them to ECF to function as cell-specific neuron-to-glia neurotransmitters.     

Low voltage-activated Ca2+ conductances in thalamic neurons

Low voltage-activated (LVA) Ca²⁺ conductances were characterized in the neurons of the associative laterodorsal (LD) thalamic nucleus in rat brain slices and in enzymatically isolated thalamic units using electrophysiological techniques. Voltage dependence, kinetics of inactivation, pharmacology, and selectivity of the LVA current in the thalamic neurons from animals older than 14 postnatal days were consistent with the existence of two, “fast” and “slow,” subtypes of LVA Ca²⁺ channels. “Slow” LVA current in enzymatically isolated thalamic neurons was much less prominent, compared with that in slice neurons, suggesting that respective channels are predominatly located on the distal dendrites. “Fast” Ca²⁺ channels were sensitive to nifedipine (K _d−2.6 μM) and La³⁺ (K _d−1.0 mM), whereas “slow” Ca²⁺ channels were sensitive to Ni²⁺ (25 μM). Selectivity of the “fast” Ca²⁺ channels was similar to that found for the LVA Ca²⁺ channels in other preparations (I _Ca:I _Sr:I _Ba−1.0: 1.23: 0.94), while selectivity of the “slow” Ca²⁺ channels more resembled selectivity of the HVA Ca²⁺ channels (I _Ca:I _Sr:I _Ba−1.0: 2.5: 3.4).     

Parasitism and symbiosis in an N-person non-constant-sum continuous game

A non-constant-sum continuous game analyzed in a previous paper by one of the authors (A. Rapoport,Bull. Math. Biophysics,18, 15–30, 1956) is extended from two toN players with special emphasis onN=3. It is shown that the concept of stability becomes in this case one of “pairwise stability,” and depends on the so-called distribution matrix of rewards. The distribution matrix and the collusion structure jointly determine the end states of the game. Conditions which lead to the emergence of one, two, or no “parasites” are derived. An apparatus is described which provides a physical analogue of the game, making possible the isolation of behavioral variables under the prescribed conditions of the game.     

GABAA- and AMPA-like receptors modulate the activity of an identified neuron within the central pattern generator of the pond snail Lymnaea stagnalis

To examine the neurochemistry underlying the firing of the RPeD1 neuron in the respiratory central pattern generator of the pond snail, Lymnaea stagnalis, we examined electrophysiologically and pharmacologically either “active” or “silent” preparations by intracellular recording and pharmacology. GABA inhibited electrical firing by hyperpolarizing RPeD1, while picrotoxin, an antagonist of GABA_A receptors, excited silent cells and reversed GABA-induced inhibition. Action potential activity was terminated by 1 mM glutamate (Glu) while silent cells were depolarized by the GluR agonists, AMPA, and NMDA. Kainate exerted a complex triphasic effect on membrane potential. However, only bath application of AMPA desensitized the firing. These data indicate that GABA inhibits RPeD1 via activation of GABA_A receptors, while Glu stimulates the neuron by activating AMPA-sensitive GluRs.     

The smallest value of the axon density for which ‘ignition’ can occur in a random net

As shown by A. Rapoport (1952), when a very brief stimulation or “instantaneous input” is applied to a random net, the subsequent events are determined by the parameters of the net as follows: If the axon densitya is sufficiently large and the fraction γ of the neurons initially stimulated exceeds a certain value γ₁ (theover-all threshold of the net for instantaneous stimulation), excitation will spread through the net until a steady state is reached in which a fraction γ₂ ⩾ γ₁ of the neurons is firing (“ignition phenomenon”). If γ < γ₁ the activity in the net dies out. However, if the axon density is too small, the activity will ultimately die out, no matter how large the fraction of initially stimulated neurons. Thus there exists a limiting valueA of the axon density below which the net cannot “ignite”. ThisA is a function ofh, theindividual threshold of the neurons constituting the net (we assume hereh≥2, since forh=1 the situation is essentially different). Geometrically γ₁ and γ₂ are determined as the two intersection points of a straight line with a sigmoid curve. Whena<A the two curves do not intersect and fora=A they are tangent. In this paper the “tangency case” is investigated and the general features of the functionA(h) are determined. It is shown thatA increases monotonically withh (as one would expect). For all values ofh>1 we haveA(h)>h, but the fractionA(h)/h and the derivativedA(h)/dh approach unity ash increases. An analytical expression of the functionA(h) valid for very large values ofh is derived.     

Molecular analysis and mapping of two genes encoding maize glutathione S-transferases (GST I and GST II)

Maize glutathione S-transferase (GST) isozymes are encoded by a gene family comprising at least five genes, three of which (Gst I, II andIII) have recently been isolated and sequenced. The enzymes are active as homo or heterodimers and exhibit intraspecific polymorphism including a “null” variant for the two major isoforms expressed in roots. Northern blot analyses performed on total root RNA from “null” and “plus” genotypes, usingGst I- andGst II-specific probes, indicated that theGst I gene controls the expression of the two major GST isoforms expressed in roots.Gst I andGst II were mapped by RFLP analysis using an F₂ population of 149 individuals previously characterized.Gst I was localized on the long arm of chromosome 8, while two putativeGst II loci were mapped to chromosomes 8 (70 cM fromGst I) and 10, respectively.     

Contribution to the probabilistic theory of neural nets: I. Randomization of refractory periods and of stimulus intervals

Aggregates of neurons are considered in which the frequency of occurrence of neurons with a specified value of the refractory period follows certain probability distributions. Input-output functions are derived for such aggregates. In particular, if input and output intensities are defined in terms of stimulus frequencies and firing frequencies per neuron respectively, it is shown that a rectangular distribution of refractory periods leads to a logarithmic input-output curve. If input and output are defined in terms of the total number of stimuli and firings in the aggregate, it is shown how the “mobilization” picture leads to the logarithmic input-output curve. By randomizing the intervals between stimuli received by a single neuron and by introducing an inhibitory neuron a very simple “filter net” can be constructed whose output will be sensitive to a particular range of the input, and this range can be made arbitrarily small.     

Preliminary study of taxonomy ofAzotobacter andAzomonas by using rocket line immunoelectrophoresis

Rocket line immunoelectrophoresis was used to study the taxonomy ofAzotobacter andAzomonas assessed by reaction with antiserum to the AVO₂ strain ofAzotobacter. Forty-five cultures, comprising seventeen species in five genera, showed that antigen “β”, like high-titer somatic agglutination, was restricted to all 11 strains ofAzotobacter vinelandii and to one strain which has been namedAzotobacter macrocytogenes (10EM). A thermoresistant antigen (“γ”) was found to be shared by all strains and species ofAzotobacter andAzomonas investigated.     

pH-Induced Molten Globule State of <Emphasis Type="Italic">Rhizopus niveus</Emphasis> Lipase is More Resistant Against Thermal and Chemical Denaturation Than Its Native State

Here, we have characterized four pH-dependent states: alkaline state, “B” (pH 9.0), native state, “N” (pH 7.4), acid-induced state, “A” (pH 2.2) and molten globule state, “MG” (pH 1.8) of Rhizopus niveus lipase (RNL) by CD, tryptophanyl fluorescence, ANS binding, DLS, and enzyme activity assay. This “MG” state lacks catalytic activity and tertiary structure but it has native-like significant secondary structure. The “R _h” of all the four states of RNL obtained from DLS study suggests that the molecular compactness of the protein increases as the pH of solution decreases. Kinetic analysis of RNL shows that it has maximum catalytic efficiency at state “B” which is 15-fold higher than state “N.” The CD and tryptophanyl fluorescence studies of RNL on GuHCl and temperature-induced unfolding reveal that the “MG” state is more stable than the other states. The DSC endotherms of RNL obtained at pH 9.0, 7.4, and 2.2 were with two transitions, while at pH 1.8 it showed only a single transition.     

Some remarks on the Kedem-Katchalsky equations for non-electrolytes

The Kedem-Katchalsky equation for the flow of a non-electrolyte through a homogeneous membrane is shown to be a first order expansion of an exact integral of the Spiegler-Bearman-Kirkwood frictional equations under the assumption that the partial frictional coefficients, ζ _ij , are concentration independent. The equations are solved in terms of volume flow; there are no water-to-volume flow correction terms for the permeability, ω, or the reflection coefficient, σ. The precision of the expansion depends upon the magnitude of the water flow. The frictional coefficientsf _sm andf _sw are given as functions of the experimentally determined parameters ω and σ; the frictions, are shown to be independent ofL _p .     

Synchronized changes to relative neuron populations in postnatal human neocortical development

Mammalian prenatal neocortical development is dominated by the synchronized formation of the laminae and migration of neurons. Postnatal development likewise contains “sensitive periods” during which functions such as ocular dominance emerge. Here we introduce a novel neuroinformatics approach to identify and study these periods of active development. Although many aspects of the approach can be used in other studies, some specific techniques were chosen because of a legacy dataset of human histological data (Conel in The postnatal development of the human cerebral cortex, vol 1–8. Harvard University Press, Cambridge, 1939–1967). Our method calculates normalized change vectors from the raw histological data, and then employs k-means cluster analysis of the change vectors to explore the population dynamics of neurons from 37 neocortical areas across eight postnatal developmental stages from birth to 72 months in 54 subjects. We show that the cortical “address” (Brodmann area/sub-area and layer) provides the necessary resolution to segregate neuron population changes into seven correlated “k-clusters” in k-means cluster analysis. The members in each k-cluster share a single change interval where the relative share of the cortex by the members undergoes its maximum change. The maximum change occurs in a different change interval for each k-cluster. Each k-cluster has at least one totally connected maximal “clique” which appears to correspond to cortical function.     

Pilocarpine-induced epileptiform activity of isolatedCA1 hippocampal neurons

Cellular mechanisms of pilocarpine-induced epileptiform activity in isolatedCA1 andCA3 hippocampal neurons were studied using a current-clamp technique. Isolated unipolar neurons dominate after enzymatic treatment of theCA1 tissue, whereas large multipolar neurons are mainly located in theCA3 area. Measurements of the membrane potential in these two groups of neurons showed that most of them are “silent” cells. Only a small group of neurons from theCA3 area displayed spontaneous electrical activity. Pilocarpine, a well known epileptogenic compound, induced rhythmic waveform changes in the membrane potential in some “silent” unipolar neurons from theCA1 area, whereas in another more numerous group of neurons it induced only steady depolarization of the membrane. Application of tetrodotoxin, the selective blocker of Na⁺ channels, blocked generation of action potentials induced inCA1 neurons by pilocarpine, but exerted no effect on waveform shifts of the membrane potential. It is suggested that the mechanism underlying epileptogenic action of pilocarpine on the brain activity in rats is based on the induction of waveform changes in the membrane potential in unipolar neurons of theCA1 hippocampal area.     

Mycobacterium leprae — The outer lipoidal surface

There is now a considerable body of evidence to suggest that the phthiocerol-containing lipids, including the phenolic glycolipids, comprise the so-called “peribacillary substance”, “spherical droplets”, “foamy structures” and “capsular materials” ofMycobacterium leprae. Thus, the phthiocerol-containing lipid capsule may be directly responsible for the intracellular survival ofMycobacterium leprae.     

Organismic sets: II. Some general considerations

The theory of organismic sets, developed in previous papers (Bull. Math. Biophysics,29, 139–152; 389–393; 643–647) is further generalized. To conform better with some biological and sociological facts the basic definitions are made more general. The conclusion is reached that every organismic setS _o is in general the union of three disjoined subsetsS _o1 ,S _o2 andS _o3 . Of these the subsetS _o1 , called the “core” is equivalent to an organismic set defined in previous publications. Its functioning is essential for the functioning ofS _o . The subsetsS _o2 andS _o3 , taken alone, are not organismic sets. The first of them is responsible for such biological or sociological functions which are not necessary for the “immediate” survival ofS _o but which are important for adaptation to changing environment and are therefore essential for a “long range survival.” The second one,S _o3 , is responsible for biological or social functions which are irrelevant for the survival ofS _o . Biological and sociological examples ofS _o2 andS _o3 are given. In addition to the fundamental theorem established in the first of the above mentioned papers, three new conclusions are derived. One is that in organismic sets of order higher than zero not all elements are specialized. The second is that every organismic set of order higher than zero is mortal. The third is that with increasing specialization the intensities of some activities in some elements ofS _o are reduced. Again the biological and sociological examples are given. At the end some very general speculations are made on the possible relation between biology and physics and on the possibility of “relationalizing” physics.     

Branching dendrites with resonant membrane: a “sum-over-trips” approach

Dendrites form the major components of neurons. They are complex branching structures that receive and process thousands of synaptic inputs from other neurons. It is well known that dendritic morphology plays an important role in the function of dendrites. Another important contribution to the response characteristics of a single neuron comes from the intrinsic resonant properties of dendritic membrane. In this paper we combine the effects of dendritic branching and resonant membrane dynamics by generalising the “sum-over-trips” approach (Abbott et al. in Biol Cybernetics 66, 49–60 1991). To illustrate how this formalism can shed light on the role of architecture and resonances in determining neuronal output we consider dual recording and reconstruction data from a rat CA1 hippocampal pyramidal cell. Specifically we explore the way in which an I _h current contributes to a voltage overshoot at the soma.