A theory of steady-state activity in nerve-fiber networks II: The simple circuit

It is found that for a simple circuit of neurons, if this contains an odd number of inhibitory fibers, or none at all, or if the product of the activity parameters is less than unity, then the stimulus pattern always determines uniquely the steady-state activity. For circuits not of one of these types, it is possible to classify exclusively and exhaustively all possible activity patterns into three types, here called “odd”, “even”, and “mixed”. For any pattern of odd type and any pattern of even type there always exists a stimulus pattern consistent with both, but in no other way can such an association of activity patterns be made.     

A theory of steady-state activity in nerve-fiber networks: I. Definitions and preliminary lemmas

As an essay towards the determination of the effect of structural relations among nerve fibers upon the character of their activity, preliminary consideration is given to the steady-state activity of some simple neural structures. It is assumed as a first approximation that while acted upon by a constant stimulus, each fiber reaches a steady-state activity whose intensity is a linear function of the applied stimulus. It is shown by way of example that for a simple two-fiber circuit of inhibitory neurons knowledge of the stimuli applied to the separate fibers does not necessarily suffice to determine uniquely the activity that will result. On the other hand, there are deduced certain restrictions on the possible types of activity that may be consistent with a given pattern of applied stimulation.     

A theory of steady-state activity in nerve-fiber networks: IV.N circuits with a common synapse

Conditions under which either of two distinct activity patterns may arise from the same stimulus pattern are deduced for the case of a net-work which consists ofN simple circuits all jointed at a common synapse. If the product of the activity parameters of all the fibers in any circuit is called the activity parameter of the circuit, or, more briefly, the circuit parameter, then the condition for the existence of such mutually consistent activity patterns is that there be a sum of circuit paramaters which is not less than unity.     

The emergence of long-lasting transients of activity in simple neural networks

The question was investigated whether longlasting transients of activity, observed to occur in the intact cerebral cortex (EEG slow () waves and K complexes) as well as in isolated tissues cultured in vitro, can also emerge in a model network of excitatory and inhibitory cells. We show that such transients can indeed occur even if the cells do not have built-in slow kinetics. For certain parameter settings, the network is in a bistable state in which periods of increased activity (long-lasting transients) alternate with minimal activity. Transients are triggered by spontaneously firing cells (noise), which, rather than via a build-up of recurrent synaptic inhibition, also initiate their termination. During a transient, the network continually makes transitions from one equilibrium to another as a result of spontaneous firing until it is switched back to the quiescent state, i.e., after a variable period of time of noise-induced transitions the transient is terminated. If the network is small, activity can terminate even without inhibition. In large networks, inhibition keeps the network sensitive to spontaneously firing cells by holding it in the neighbourhood of a critical point between active and quiescent state.     

The sucked-flow analyser: A simple apparatus for automatic determination of steady-state enzyme kinetics

The sucked-flow analyser is a modified stopped-flow apparatus for automatic measurements of initial rates of enzyme reactions at varying concentrations of substrate or inhibitor. The flow through the system is driven by a water suction pump and regulated by magnetic valves. Sample and reagent solution are aspired through tubes whose resistances to laminar flow determine a precise ratio of mixing in the observation cell. A minicomputer controls all operations, collects the data and calculates the results. Measurements on teh β-galactosidase and the cytochome P-450 reactions are presented.     

Circular dichroism of polynucleotides: A simple theory

A particularly simple theory of circular dichroism is described and applied to the polynucleotides. It works surprisingly well and predicts the conservative spectrum of DNA and the more intense nonconservative spectrum of RNA. The anomalously low intensity of the CD of the nucleic acids is shown to be a natural consequence of the cancellation of the rotational strengths of the many CD bands. The theory's many successes and predictions as well as its weaknesses are discussed.     

The theory of macromolecular networks

Network theory has evolved from the simplest rubber materials and is just entering the biological area. The existing theories are studied and the modifications required for biological applications are reviewed. The issues involved are: the balance between entropy and internal energy, the rigidity and flexibility of molecules, the stability of the networks, the origin of the intermolecular forces and the entanglement problems of swelling and precipitation.     

A simple theory of algal deposition

SUMMARY. A model describing the deposition of algae in a turbulent environment is outlined, it being assumed that all algae falling on the bed are trapped there forever. Its main features are that, above a certain threshold of turbulence the rate of deposition is independent of the turbulent intensity, and the rate of algal loss by sedimentation, in such conditions, is described by a first order kinetic equation. The hydraulic conditions under which algae settle at their intrinsic, still-water rate and those for which the model is applicable, are examined. Some ecological implications of the model are discussed.     

The linear theory of neuron networks: The dynamic problem

The development of a general theory of neuron-networks is here extended to cases of non-steady state activity. Conditions for stability and neutrality of an equilibrium point are set up, and the possible functions representing the variation of excitation over time are enumerated. The inverse network problem is considered—which is, given a preassigned pattern of activity over time, to construct when possible a neuron-network having this pattern. Finally, a canonical form for neuron networks is derived, in the sense of a network of a certain special topological structure which is equivalent in activity characteristics to any given network.     

The linear theory of neuron networks: The static problem

The construction of a theory of activity in neuron networks of arbitrary topological structure is commenced under the linear excitation hypothesis: we consider conditions for possible steady-state equilibria, deferring a dynamical treatment to the sequel.     

A theory of membrane permeability: III. The effect of hydrostatic pressure

Using expressions derived in previous papers, the author investigates the behavior of a cell immersed in an infinite medium, under the influence of diffusion of a single solute and flow of water. The effect of hydrostatic pressure on the system is taken into account. It is found that, depending on the values of certain parameters, the cell can collapse, burst, reach a stationary stable state, or execute undamped oscillations; a cell must burst or collapse unless its volume is an increasing function of internal pressure, and it can execute stable oscillations only if its membrane acts as a “potential well” to the molecules of the solute.     

A theory for species co-occurrence in interaction networks

The study of species co-occurrences has been central in community ecology since the foundation of the discipline. Co-occurrence data are, nevertheless, a neglected source of information to model species distributions and biogeographers are still debating about the impact of biotic interactions on species distributions across geographical scales. We argue that a theory of species co-occurrence in ecological networks is needed to better inform interpretation of co-occurrence data, to formulate hypotheses for different community assembly mechanisms, and to extend the analysis of species distributions currently focused on the relationship between occurrences and abiotic factors. The main objective of this paper is to provide the first building blocks of a general theory for species co-occurrences. We formalize the problem with definitions of the different probabilities that are studied in the context of co-occurrence analyses. We analyze three species interactions modules and conduct multi-species simulations in order to document five principles influencing the associations between species within an ecological network: (i) direct interactions impact pairwise co-occurrence, (ii) indirect interactions impact pairwise co-occurrence, (iii) pairwise co-occurrence rarely are symmetric, (iv) the strength of an association decreases with the length of the shortest path between two species, and (v) the strength of an association decreases with the number of interactions a species is experiencing. Our analyses reveal the difficulty of the interpretation of species interactions from co-occurrence data. We discuss whether the inference of the structure of interaction networks is feasible from co-occurrence data. We also argue that species distributions models could benefit from incorporating conditional probabilities of interactions within the models as an attempt to take into account the contribution of biotic interactions to shaping individual distributions of species.     

The general fluid circuit theory of active chloride absorption

The original fluid circuit theory used to explain active intestinal absorption of chloride is modified to include diffusion and secretion of chloride and osmosis. The general differential equation developed is integrated in a particular case. The definition, “effective concentration of chloride in the fluid passing into the intestinal lumen,” leads to simplified general expressions.     

Cation Transport in Escherichia coli : III. Potassium fluxes in the steady-state

The present study is concerned with the measurement of the unidirectional K flux in E. coli. Methods are described by means of which a fairly dense suspension of cells may be maintained in a well defined steady-state with respect to the intracellular K concentration and the pH of the medium. The kinetics of K⁴² exchange under these conditions are consistent with the presence of a single intracellular K compartment with a unidirectional K flux of 1 pmol/(cm² sec.). This rate is independent of the extracellular K concentration over the range studied. The simultaneous rate of H secretion averages 16 pmols/(cm² sec.) indicating that in the steady-state the efflux of metabolically produced H is not linked mole for mole to K movement.     

A simple method for the simulation of steady-state diffusion through membranes: pressure-tuned,boundary-driven molecular dynamics

We present a novel molecular dynamics-based simulation technique for investigating gas transport through membranes. In our simulations, the main control parameters are the partial pressure for the components on the input side of the membrane and the total pressure on the output side. The essential point of our scheme is that this pressure control should be realised by adjusting the particle numbers in the input and output side control cells indirectly. Although this perturbation is applied sufficiently far from the membrane, the bulk-phase properties are well controlled in a simulation cell of common size. Numerical results are given for silicalite-1 membrane with permeating CH₄, CO₂, H₂ and N₂ gases as well as with binary mixtures of CO₂ with the other three components. To describe interactions between particles, we used the simple shifted and cut Lennard–Jones potential with parameters available in the literature. It is expected that the proposed technique can be applied to several other types of membranes and transported fluids in order to support the development of a deeper understanding of separation processes.