Convergent collapse, divergent route: neuromodulatory control of the direction and gain of synaptic consolidation

Neuromodulators are classically described as setting the rate of synaptic learning. Here we develop a framework in which a single eligibility-trace mechanism is controlled along two dissociable channels: neuromodulators set the direction of plastic change — norepinephrine (NE) and serotonin (5-HT), through opposite transformations of the eligibility trace — and the gain of its consolidation — dopamine (DA). On one consolidation equation, dw/dt = η·e(t)·DA(t)·σ(w), the trace term e(t) carries direction while DA(t) carries consolidation gain, yielding two dissociable loci of failure that converge on a single pathological endpoint: saturation of the consolidated synaptic weight w, collapse of the effective learning rate κ, and loss of plastic reversibility. Because both channels drive the same collapse by different routes, the disorders they produce converge at their endpoint yet stay distinct on the way to it. Direction failures instantiate as opposite regimes: sustained NE excess biases the trace toward potentiation and locks in threat circuits (anxiety); a sustained 5-HT deficit withdraws the depressing trace and leaves compulsive circuits unable to be depotentiated (obsessive-compulsive disorder, OCD). A gain failure is proposed as the aberrant-salience-to-stabilization route to psychosis, in which mis-scaled dopaminergic consolidation fixes traces selected on noise. We specify a candidate molecular substrate — NMDA-dependent calcium opens the trace, parvalbumin-interneuron gating converts it — and introduce a formal cholinergic reset parameter γ_ACh that suppresses prior precision independently of synaptic weight, converting the pathological fixed-point attractor into a competitive equilibrium and defining the conditions under which the collapse is escapable. Numerical simulations illustrate the direction- and gain-channel collapse routes and the cholinergic escape. The framework yields falsifiable predictions that distinguish the regimes in reversal-learning, EEG and neuroimaging, including a neuroimaging dissociation underlying SSRI-induced motivational blunting. It reframes a class of chronic disorders as convergent endpoints of neuromodulatory control that remain distinct along the route by which they are reached — a joint convergence and divergence that no single-axis control of the learning rate can generate — and casts the reversibility of that control as a cholinergic variable.