Predictions for and lack of maximal information transmission in the neuromuscular junction

The gist: The theoretical and experimental distributions for neurotransmitter concentrations at the Drosophila neuromuscular junction show very little agreement, indicating that the Drosophila NMJ does not shape its distribution of synaptic vesicle release probabilities in order to maximize information transmission from nervous system to muscle.

Information Theory Framework

Information theory provides a framework for examining how effectively biological systems encode and transmit signals, where mutual information I[X; Y] quantifies the amount of information retained through a process. This is calculated as the reduction in uncertainty about the input upon knowing the output, defined by I[X; Y] = H[X] − H[XY]. The channel capacity C has an operational definition as the amount of information that can be passed through the information channel. The paper notes that rate-distortion theory or traditional infomax applies when the organism controls the input distribution ρ(x) rather than the information channel itself.

Neuromuscular Junction as an Input-Output System

The neuromuscular junction converts a chemical signal into an electrical response that ultimately results in muscle contraction, where the input is neurotransmitter concentration and the output is current flow. The transformation can be understood as defining an input-output system where the input is the neurotransmitter concentration sensed by receptors in the synaptic cleft, and the output is current that flows. Variability across release sites is part of biology, meaning synaptic output is formed not just by average release, but also by how probability is distributed across individual sites.

Optimal Input Distributions

The optimal input distribution ρ∗(x) that maximizes mutual information I[X; Y] is sought, which for a channel with approximately conditionally Gaussian noise yields the optimal input distribution as ρ∗(x) = 1/Z ∫dȳ¯(x) dx σyx. For cholinergic systems, assuming a large number of receptors N, the binomial distribution becomes approximately Gaussian, allowing the use of the small-noise approximation with mean current J¯ = J0N popen,nAChR and variance σ2J = J20N popen,nAChR(1 − popen,nAChR). This leads to the optimal distribution over neurotransmitter concentrations being determined by the physiological dose-response relationship popen(c).

Glutamatergic System Complexity

The glutamatergic information channel is more complicated because there are two types of iGluRs, type A and type B, which have slightly different dissociation constants Kd, effective Hill coefficients nH, and currents jA/B. The total current J is the sum of currents through both receptor types: J = jANopen,A + jBNopen,B. In the limit of a large number of receptors, this current J can be approximated as Gaussian with mean and variance depending on the fractions α and the biophysical constants. This leads to a more complicated optimal distribution over glutamate concentration ρ∗(c).

Channel Capacity and Comparison

The channel capacity C is calculated using the small-noise approximation, yielding C = log2 Z √2πe. For both cholinergic and glutamatergic systems, the channel capacity is found to be roughly 8 bits when the total number of receptors is around 10,000. This capacity is not so sensitive to details of the biophysical channel. Comparing this to other systems, such as Drosophila gene expression patterning which has a channel capacity of about 1.5 bits, suggests that the Drosophila NMJ does not maximize information transmission.

Conclusion on Maximization

The comparison between empirical histograms and the histograms expected from theoretical considerations if information transmission was maximized at the Drosophila NMJ shows a failure of the order-of-magnitude calculation to match the empirical measurements by such a degree that it must be the case that information transmission is not maximized at the Drosophila NMJ. The dissociation constants for the Drosophila NMJ iGluRs differ so greatly from what they would need to be for a match that no amount of uncertainty in quantities like the number of neurotransmitters per vesicle are going to change that the empirical histogram has most of its weight in low concentrations while the informationmaximizing distribution has its weight in relatively high concentrations.

Alterations if Equilibrium Membrane Potential Changes

If membrane voltage changes, the dose-response relationship popen(c) would change according to a statistical mechanical model. However, the optimal input distributions do not change by much when membrane potential fluctuates. This suggests that the approximation to ignore voltage coupling is likely alright for an order-of-magnitude calculation.

Comparison to Empirical Distribution

The empirical probability distribution of synaptic vesicle release probability translates to a rough estimate of empirical histogram for concentrations of neurotransmitters that does not match order-of-magnitude theoretical predictions based on maximal information transmission. The conversion from release probability to estimated neurotransmitter concentration also adds uncertainty. The estimate of about 8 bits depends on the fitted response curve, the assumed receptor population size, and the binomial noise model. It is therefore an order-of-magnitude estimate under the assumptions of the model, not a directly measured biological value. The dissociation constants for the Drosophila NMJ iGluRs differ so greatly from what they would need to be for a match that no amount of uncertainty in quantities like the number of neurotransmitters per vesicle are going to change that the empirical histogram has most of its weight in low concentrations while the informationmaximizing distribution has its weight in relatively high concentrations.

Summary

The paper investigates how effectively biological systems preserve information about their inputs by analyzing neurotransmitter concentration transformation at the neuromuscular junction. It uses information theory, specifically mutual information, to test whether the Drosophila NMJ maximizes information transmission from nervous system to muscle. The analysis derives theoretical optimal input distributions based on dose-response relationships and compares them to experimental data from a Drosophila NMJ. The results indicate that the Drosophila NMJ does not maximize information transmission, suggesting that receptor activation can be studied in terms of information flow structure rather than just maximization.

Acknowledgments

We wish to acknowledge Gautam Agarwal for useful comments and encouragement. The paper references numerous works spanning information theory, neural spike trains, and biochemical signaling networks.

References

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[2] C. Waltermann and E. Klipp, Information theory based approaches to cellular signaling, Biochimica et Biophysica Acta (BBA)-General Subjects 1810, 924 (2011).

[3] H. B. Barlow et al., Possible principles underlying the transformation of sensory messages, Sensory communication 1, 217 (1961).

[4] S. P. Strong, R. Koberle, R. R. D. R. Van Steveninck, and W.

1. Optimal Input Distribution Prediction for Neurotransmitter Concentration: The system can predict that the optimal distribution over neurotransmitter concentrations is somewhat sensitive to details of the dose-response relationship, allowing for targeted experiments examining empirical input distributions in regimes like saturation where small amounts of experimental error could have large consequences.

2. Channel Capacity Estimation Based on Receptor Dynamics: The AI can estimate channel capacity using the formula C = log2 Z + log2 sqrt(2pi e), where Z is derived from the dose-response relationship, suggesting that for a total number of receptors around 10,000, NMJs across different types yield channel capacities roughly equal to 8 bits.

3. Discrimination Between Receptor Types: The system can differentiate between cholinergic and glutamatergic systems by calculating their respective optimal input distributions; the paper notes that "the dissociation constants for the Drosophila NMJ iGluRs differ so greatly from what they would need to be for a match that no amount of uncertainty in quantities like the number of neurotransmitters per vesicle are going to change."

4. Assessing Maximization Potential: The AI can compare empirical probability distributions against theoretical predictions derived from maximal information transmission; the result shows a failure of the order-of-magnitude calculation to match the empirical measurements, leading to a conclusion that information transmission is not maximized at the Drosophila NMJ.

A key question in theoretical biology is how effectively biological systems preserve information about their inputs while operating under physical and functional constraints. We examine that question at the neuromuscular junction (NMJ) by studying how neurotransmitter concentration is transformed into current at both cholinergic and glutamatergic NMJs. An information maximization analysis was used to derive a theoretical distribution over neurotransmitter concentrations based on biological understandings of dose-response relationships. These theoretical distributions were compared to an experimentally derived distribution obtained from a Drosophila NMJ. The theoretical and experimental distributions showed very little agreement, indicating that the Drosophila NMJ may not shape its distribution of synaptic vesicle release probabilities in order to maximize information transmission from nervous system to muscle. Predictions for cholinergic systems are provided.