Fig 1.
Flexible connectivity under constraints.
(a) Mushroom body circuitry (cartoon based on [38]). (b) Synaptic weights occupy a K-dimensional space. K is the number of synaptic partners. The solution spaces for computational tasks are subspaces of the synaptic weight space, with dimension up to K. Constraints also define subspaces with dimension up to K. A tight constraint defines a small subspace with low potential overlap with computational solution spaces. (c) A loose constraint defines a large subspace, with greater potential overlap with computational solution spaces. (d) Cartoon of a postsynaptic resource constraint: a neuron with M = 3 units of postsynaptic weight (e.g., receptors) to distribute amongst two synaptic partners. (e) Cartoon of a presynaptic resource constraint a neuron with M = 4) units of synaptic weight (e.g., vesicles) to distribute amongst two partners. (f) Number of possible connectivity configurations for different values of K and M (given by the binomial coefficient).
Fig 2.
Constraints on total synaptic weights.
(a-c) An upper bound on the total synaptic weight. (d-f) A fixed total synaptic weight. (a) For two inputs with a total synaptic weight of at most , the synaptic weights must live in the area under a line segment from
to
(a regular 1-simplex). (b) For three inputs, the synaptic weights must live in the volume under a regular two-simplex. (c) Volume of the K − 1 simplex as a function of the number of presynaptic partners, K, for different maximal net weights
. (d) For two inputs with a total synaptic weight fixed at
, the synaptic weight configurations must be on the line segment from
to
. (e) The solution space for the fixed net weight constraint with three inputs is an equilateral planar triangle (a regular 2-simplex). (f) Surface area of the regular K − 1 simplex as a function of the number of presynaptic partners, K, for different net synaptic weights
.
Fig 3.
Kenyon cell degree distributions in larval D. melanogaster.
(a) Distribution of number of postsynaptic partners for larval KCs. Shaded histograms: empirical distribution. Solid lines: the marginal simplex area distribution at the maximum likelihood value of α, after integrating out the number of synapses against its empirical distribution. Dotted lines: the maximum likelihood binomial distribution. (b) Lower bound for the log evidence ratio (log odds) for the fixed net weight and binomial wiring models. Positive numbers favor the fixed weight model. Evidences computed by a Laplace approximation of the marginalization over the parameters. (c) Lower bound for the log odds for the fixed net weight and bounded net weight models; positive numbers favor the fixed weight model. (d) Log likelihood of the fixed net weight model (
) as a function of the scaling between synapse counts and net synaptic weights, α. (e-h) Same as (a-d) but for inputs to larval KCs.
Fig 4.
Mushroom body output neuron degree distributions in larval D. melanogaster.
(a) Number of inputs to MBONs. Shaded histograms: empirical distribution. Black curve: the marginal simplex area distribution at the maximum likelihood value of α, after integrating out the number of synapses against its empirical distribution. Blue curve: the maximum likelihood binomial distribution. (b) Lower bound for the log evidence ratio (log odds) for the fixed net weight and binomial wiring models. Positive numbers favor the fixed weight model. Evidences computed by a Laplace approximation of the marginalization over the parameters. (c) Likelihood vs model parameter for the fixed net weight (black) and binomial (blue) models).
Fig 5.
Kenyon cell degree distributions in adult D. melanogaster.
(a) Distribution of number of postsynaptic partners for adult KCs. Shaded histograms: empirical distribution. Solid lines: the marginal simplex area distribution at the maximum likelihood value of α, after integrating out the number of synapses against its empirical distribution. Dotted lines: the maximum likelihood binomial distribution. (b) Lower bound for the log evidence ratio (log odds) for the fixed net weight and binomial wiring models. Positive numbers favor the fixed weight model. Evidences computed by a Laplace approximation of the marginalization over the parameters. (c) Lower bound for the log odds for the fixed net weight and bounded net weight models; positive numbers favor the fixed weight model. (d) Log likelihood of the fixed net weight model as a function of the scaling between synapse counts and net synaptic weights. (e-h) Same as (a-d) but for inputs to adult KCs.
Fig 6.
Relation between number of synaptic partners and synapse counts in D. melanogaster Kenyon cells.
(a) Inputs to Kenyon cells (KCs) of the first instar larva. (b) Outputs of the first instar KCs. (c) Inputs to adult KCs in the α lobe. (d) Outputs of adult KCs in the α lobe.
Table 1.
Correlation of number of synapses and number partners in larval Kenyon cells.
Table 2.
Correlation of number of synapses and number partners in adult alpha lobe Kenyon cells.
Fig 7.
Synaptic weight configurations.
a) Two example configurations of K = 4 synaptic weights with . b) Two examples of K = 5 synaptic weights with sum bounded by
.