Separating wiring-specific from statistical control of dynamics in complete connectomes - clarifying which connectome-based claims rest on wiring alone
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Separating wiring-specific from statistical control of dynamics in complete connectomes - clarifying which connectome-based claims rest on wiring alone
Separating Wiring-Specific from Statistical Control of Dynamics in a Complete Connectome
Summary
This methodology addresses a fundamental question in connectomics: How far does a wiring diagram alone fix a circuit's activity versus finer physiological details it doesn't record? The approach uses complete synaptic wiring diagrams as fixed, rate-based dynamical operators without fitted single-neuron parameters, comparing them against a hierarchy of randomized networks preserving coarser wiring statistics.
Key Findings
Separation Principle
Statistical Control (Regime)
Networks preserving only coarse wiring statistics reproduce overall dynamical regime
How strongly and how richly the network responds is mostly statistical
Network strength/richness of response = statistical property
Wiring-Specific Control (Geometry)
Precise connection patterns set WHERE activity travels
Wiring determines WHICH circuits shape dynamics
Sparse input confinement to specific pathways (e.g., compact olfactory pathway)
Randomized networks flood pathways that wiring keeps sparse
Mushroom Body Dominance
The insect learning center (mushroom body) takes an outsized role in leading adjoint-side modes
Adjoint modes = directions weighting which neurons shape recurrent dynamics
Wiring-specific geometry emphasizes learning center computational role
Coarse Statistics → Regime
Coarse statistics set the dynamical regime
Precise connection patterns set the geometry
This separation clarifies which connectome-based claims rest on wiring alone
Methodology Details
Rate-Based Dynamical Operator
Fixed Parameters
Complete connectome runs as fixed rate-based operator
NO single-neuron parameter fitting
Model behavior reflects wiring + connection strengths only
NOT tuned single-neuron physiology
Dynamical Regime Analysis
Fixed to one dynamical regime
Compare against hierarchy of randomized networks
Each preserves coarser wiring description
Randomization Hierarchy
Level 0: Complete precise wiring
Level 1: Preserve coarse statistics only
Level 2: Preserve regional connection patterns
Level 3: Preserve connectivity distributions
Metrics
KL divergence on eigenvalue spectra
Frobenius norm on operator matrices
Wasserstein distance on dynamical trajectories
Activity confinement measures
Implementation Guidelines
Step 1: Obtain Complete Connectome
# Example: Drosophila larval connectome# Requires: Electron microscopy reconstruction data# Input: Complete synaptic wiring diagram with:# - All neuron positions# - All synaptic connections# - Connection strengths (synaptic counts)
Step 2: Build Rate-Based Operator
# Rate-based dynamical modelimport numpy as np
classConnectomeOperator:
def__init__(self, wiring_matrix, connection_strengths):
self.W = wiring_matrix # NxN connectivity matrixself.S = connection_strengths # Synaptic countsself.N = len(wiring_matrix) # Number of neuronsdefcompute_operator(self):
# Construct dynamical operator A# A = W * S (weighted by connection strengths)self.A = self.W * self.S
returnself.A
