Localization of function via lesion analysis

This article presents a general approach for employing lesion analysis to address the fundamental challenge of localizing functions in a neural system. We describe functional contribution analysis (FCA), which assigns contribution values to the elements of the network such that the ability to predict the network's performance in response to multilesions is maximized. The approach is thoroughly examined on neurocontroller networks of evolved autonomous agents. The FCA portrays a stable set of neuronal contributions and accurate multilesion predictions that are significantly better than those obtained based on the classical single lesion approach. It is also used for a detailed synaptic analysis of the neurocontroller connectivity network, delineating its main functional backbone. The FCA provides a quantitative way of measuring how the network functions are localized and distributed among its elements. Our results question the adequacy of the classical single lesion analysis traditionally used in neuroscience and show that using lesioning experiments to decipher even simple neuronal systems requires a more rigorous multilesion analysis.     

Controlled analysis of neurocontrollers with informational lesioning

How does one aim to understand neural information processing? One of the difficult first challenges is to identify the roles of the network's elements. To this end a functional contribution analysis (FCA) method has been developed and applied for studying the neurocontrollers of evolutionary autonomous agents (EAAs). The FCA processes data composed of multiple lesion experiments and the corresponding performance levels that the agent obtains under these lesions. It calculates the contribution values (CVs) of the network's elements such that the ability to predict the agent's performance under new, unseen lesions is maximized. Previous analysis has found a strong dependence of the CVs and the prediction error on the specific type of lesioning method used, i.e. on the way in which the activity of lesioned neurons is disrupted. We present a new, informational lesioning method (ILM), which views a lesion as a noisy channel and applies a controlled lesion to the network by varying the lesioning level from large to arbitrarily small magnitudes. Studying the ILM within the FCA framework, our main results are threefold: first, that lower lesioning levels permit more accurate FCA predictions; second, that the usage of minute ILM lesioning levels can uncover the long-term effects of elements on the network's functioning; and third, that as the lesioning level decreases, the CVs tend to approach limit values, reflecting the importance of these elements in the intact, normal-functioning neurocontroller.     

Fair attribution of functional contribution in artificial and biological networks

This letter presents the multi-perturbation Shapley value analysis (MSA), an axiomatic, scalable, and rigorous method for deducing causal function localization from multiple perturbations data. The MSA, based on fundamental concepts from game theory, accurately quantifies the contributions of network elements and their interactions, overcoming several shortcomings of previous function localization approaches. Its successful operation is demonstrated in both the analysis of a neurophysiological model and of reversible deactivation data. The MSA has a wide range of potential applications, including the analysis of reversible deactivation experiments, neuronal laser ablations, and transcranial magnetic stimulation "virtual lesions," as well as in providing insight into the inner workings of computational models of neurophysiological systems.     

Neuronal regulation: A mechanism for synaptic pruning during brain maturation

Human and animal studies show that mammalian brains undergo massive synaptic pruning during childhood, losing about half of the synapses by puberty. We have previously shown that maintaining the network performance while synapses are deleted requires that synapses be properly modified and pruned, with the weaker synapses removed. We now show that neuronal regulation, a mechanism recently observed to maintain the average neuronal input field of a postsynaptic neuron, results in a weight-dependent synaptic modification. Under the correct range of the degradation dimension and synaptic upper bound, neuronal regulation removes the weaker synapses and judiciously modifies the remaining synapses. By deriving optimal synaptic modification functions in an excitatory-inhibitory network, we prove that neuronal regulation implements near-optimal synaptic modification and maintains the performance of a network undergoing massive synaptic pruning. These findings support the possibility that neural regulation complements the action of Hebbian synaptic changes in the self-organization of the developing brain.     

Statistical analysis of the quantal basis of secretory granule formation

ABSTRACT The size distribution of vesicles exocytosed from secretory cells displays quantal nature, vesicle volume is periodic multi‐modal, suggesting that these heterogeneous vesicles are aggregate sums of a variable number of homogeneous basic granules. Whether heterogeneity is a lumping‐together artifact of the measurement or an inherent intra‐cell feature of the vesicles is an unresolved question. Recent empirical evidence will be provided for the quantal nature of intra‐cell vesicle volume, supporting the controversial paradigm of homotypic fusion: basic cytoplasmic granules fuse with each other to create heterogeneously sized vesicles. An EM‐algorithm‐based method is presented for the conversion of multi‐modal to quantal data that provides as by‐product estimates of means and variances of basic granule packaging. Microsc. Res. Tech. 77:1–10, 2014. © 2013 Wiley Periodicals, Inc.     

A single-iteration threshold Hamming network

We analyze in detail the performance of a Hamming network classifying inputs that are distorted versions of one of its m stored memory patterns, each being a binary vector of length n. It is shown that the activation function of the memory neurons in the original Hamming network may be replaced by a simple threshold function. By judiciously determining the threshold value, the "winner-take-all" subnet of the Hamming network (known to be the essential factor determining the time complexity of the network's computation) may be altogether discarded. For m growing exponentially in n, the resulting threshold Hamming network correctly classifies the input pattern in a single iteration, with probability approaching 1.     

Function suggests nano-structure: towards a unified theory for secretion rate,a statistical mechanics approach

The inventory of secretory granules along the plasma membrane can be viewed as maintained in two restricted compartments. The release-ready pool represents docked granules available for an initial stage of fast, immediate secretion, followed by a second stage of granule set-aside secretion pool, with significantly slower rate. Transmission electron microscopy ultra-structural investigations correlated with electrophysiological techniques and mathematical modelling have allowed the categorization of these secretory vesicle compartments, in which vesicles can be in various states of secretory competence. Using the above-mentioned approaches, the kinetics of single vesicle exocytosis can be worked out. The ultra-fast kinetics, explored in this study, represents the immediately available release-ready pool, in which granules bound to the plasma membrane are exocytosed upon Ca²⁺ influx at the SNARE rosette at the base of porosomes. Formalizing Dodge and Rahamimoff findings on the effect of calcium concentration and incorporating the effect of SNARE transient rosette size, we postulate that secretion rate (rate), the number (X) of intracellular calcium ions available for fusion, calcium capacity (0 ≤ M ≤ 5) and the fusion nano-machine size (as measured by the SNARE rosette size K) satisfy the parsimonious M–K relation rate ≈ C × [Ca²⁺]^min(X,M)e^−K/2.     

Linearization of local probabilistic sensitivity via sample re-weighting

Local probabilistic sensitivity of input variable X with respect to output variable Z is proportional to the derivative of the conditional expectation E(X|z). This paper reports on experience in computing this conditional expectation. Linearized estimates are found to give acceptable performance, but are not generally applicable. A new method of linearization based on re-weighting a Monte Carlo sample is introduced. Results are comparable to the linearized estimates, but this method is more widely applicable. Results generally improve by conditioning on a small window around z.     

Function suggests nano-structure: electrophysiology supports that granule membranes play dice

Cellular communication depends on membrane fusion mechanisms. SNARE proteins play a fundamental role in all intracellular fusion reactions associated with the life cycle of secretory vesicles, such as vesicle–vesicle and vesicle plasma membrane fusion at the porosome base in the cell plasma membrane. We present growth and elimination (G&E), a birth and death model for the investigation of granule growth, its evoked and spontaneous secretion and their information content. Using a statistical mechanics approach in which SNARE components are viewed as interacting particles, the G&E model provides a simple ‘nano-machine’ of SNARE self-aggregation behind granule growth and secretion. Results from experimental work, mathematical calculations and statistical modelling suggest that for vesicle growth a minimal aggregation of three SNAREs is required, while for the evoked secretion one SNARE is enough. Furthermore, the required number of SNARE aggregates (which varies between cell types and is nearly proportional to the square root of the mean granule diameter) affects and is statistically identifiable from the size distributions of spontaneous and evoked secreted granules. The new statistical mechanics approach to granule fusion is bound to have a significant changing effect on the investigation of the pathophysiology of secretory mechanisms and methodologies for the investigation of secretion.     

A new approach to censored lifetime variables

A new statistical test with applications to censored lifetime data has been found. This test makes no assumptions about the dependence structure underlying the censoring. Here we describe the background to the test and give an algorithm to implement it. A number of numerical examples are given to illustrate how the algorithm may be applied.