The statistical relationship between connectivity and neural activity in fractionally connected feed-forward networks.

It is desirable to have a statistical description of neuronal connectivity in developing tractable theories on the development of biological neural networks and in designing artificial neural networks. In this paper, we bring out a relationship between the statistics of the input environment, the degree of network connectivity, and the average postsynaptic activity. These relationships are derived using simple neurons whose inputs are only feed-forward, excitatory and whose activity is a linear function of its inputs. In particular, we show that only the empirical mean of the pairwise input correlations, rather than the full matrix of all such correlations, is needed to produce an accurate estimate of the number of inputs necessary to attain a prespecified average postsynaptic activity level. Predictions from this work also include distributional aspects of connectivity and activity as shown by a combination of analysis and simulations.

The influence of limited presynaptic growth and synapse removal on adaptive synaptogenesis.

This report continues our research into the effectiveness of adaptive synaptogenesis in constructing feed-forward networks which perform good transformations on their inputs. Good transformations are characterized by the maintenance of input information and the removal of statistical dependence. Adaptive synaptogenesis stochastically builds and sculpts a synaptic connectivity in initially unconnected networks using two mechanisms. The first, synaptogenesis, creates new, excitatory, feed-forward connections. The second, associative modification, adjusts the strength of existing synapses. Our previous implementations of synaptogenesis only incorporated a postsynaptic regulatory process, receptivity to new innervation (Adelsberger-Mangan and Levy 1993a, b). In the present study, a presynaptic regulatory process, presynaptic avidity, which regulates the tendency of a presynaptic neuron to participate in a new synaptic connection as a function of its total synaptic weight, is incorporated into the synaptogenesis process. In addition, we investigate a third mechanism, selective synapse removal. This process removes synapses between neurons whose firing is poorly correlated. Networks that are constructed with the presynaptic regulatory process maintain more information and remove more statistical dependence than networks constructed with postsynaptic receptivity and associative modification alone. Selective synapse removal also improves network performance, but only when implemented in conjunction with the presynaptic regulatory process.

Adaptive synaptogenesis constructs networks that maintain information and reduce statistical dependence.

This report demonstrates the effectiveness of two processes in constructing simple feedforward networks which perform good transformations on their inputs. Good transformations are characterized by the minimization of two information measures: the information loss incurred with the transformation and the statistical dependency of the output. The two processes build appropriate synaptic connections in initially unconnected networks. The first process, synaptogenesis, creates new synaptic connections; the second process, associative synaptic modification, adjusts the connection strength of existing synapses. Synaptogenesis produces additional innervation for each output neuron until each output neuron achieves a firing rate of approximately 0.50. Associative modification of existing synaptic connections lends robustness to network construction by adjusting suboptimal choices of initial synaptic weights. Networks constructed using synaptogenesis and synaptic modification successfully preserve the information content of a variety of inputs. By recording a high-dimensional input into an output of much smaller dimension, these networks drastically reduce the statistical dependence of neuronal representations. Networks constructed with synaptogenesis and associative modification perform good transformations over a wide range of neuron firing thresholds.

Information maintenance and statistical dependence reduction in simple neural networks.

This study compares the ability of excitatory, feed-forward neural networks to construct good transformations on their inputs. The quality of such a transformation is judged by the minimization of two information measures: the information loss of the transformation and the statistical dependency of the output. The networks that are compared differ from each other in the parametric properties of their neurons and in their connectivity. The particular network parameters studied are output firing threshold, synaptic connectivity, and associative modification of connection weights. The network parameters that most directly affect firing levels are threshold and connectivity. Networks incorporating neurons with dynamic threshold adjustment produce better transformations. When firing threshold is optimized, sparser synaptic connectivity produces a better transformation than denser connectivity. Associative modification of synaptic weights confers only a slight advantage in the construction of optimal transformations. Additionally, our research shows that some environments are better suited than others for recording. Specifically, input environments high in statistical dependence, i.e. those environments most in need of recoding, are more likely to undergo successful transformations.

Elimination and restoration of voltage dependence in the mitochondrial channel, VDAC, by graded modification with succinic anhydride.

The major permeability pathways of the outer mitochondrial membrane are the voltage-gated channels called VDAC. It is known that the conductance of these channels decreases as the transmembrane voltage is increased in the positive or negative direction. These channels are known to display a preference for anions over cations of similar size and valence. It was proposed (Doring & Colombini, 1985b) that a set of positive charges lining the channel may be responsible for both voltage dependence and selectivity. A prediction of this proposal is that progressive replacement of the positive charges with negative charges should at first diminish, and then restore, voltage dependence. At the same time, the channel's preference for anions over cations should diminish then reverse. Succinic anhydride was used to perform these experiments as it replaces positively charged amino groups with negatively charged carboxyl groups. When channels, which had been inserted into phospholipid membranes, were treated with moderate amounts of the anhydride, they lost their voltage dependence and preference for anions. With further succinylation, voltage dependence was regenerated while the channels became cation selective. The voltage needed to close one-half of the channels increased in those treatments in which voltage dependence was diminished. As voltage dependence was restored, the voltage needed to close half of the channels decreased. The energy difference between the open and closed state in the absence of an applied field changed little with succinylation, indicating that the procedure did not cause large changes in VDAC's structure but specifically altered those charges responsible for voltage gating and selectivity.