Modulating STDP Balance Impacts the Dendritic Mosaic

The ability for cortical neurons to adapt their input/output characteristics and information processing capabilities ultimately relies on the interplay between synaptic plasticity, synapse location, and the nonlinear properties of the dendrite. Collectively, they shape both the strengths and spatial arrangements of convergent afferent inputs to neuronal dendrites. Recent experimental and theoretical studies support a clustered plasticity model, a view that synaptic plasticity promotes the formation of clusters or hotspots of synapses sharing similar properties. We have previously shown that spike timing-dependent plasticity (STDP) can lead to synaptic efficacies being arranged into spatially segregated clusters. This effectively partitions the dendritic tree into a tessellated imprint which we have called a dendritic mosaic. Here, using a biophysically detailed neuron model of a reconstructed layer 2/3 pyramidal cell and STDP learning, we investigated the impact of altered STDP balance on forming such a spatial organization. We show that cluster formation and extend depend on several factors, including the balance between potentiation and depression, the afferents' mean firing rate and crucially on the dendritic morphology. We find that STDP balance has an important role to play for this emergent mode of spatial organization since any imbalances lead to severe degradation- and in some case even destruction- of the mosaic. Our model suggests that, over a broad range of of STDP parameters, synaptic plasticity shapes the spatial arrangement of synapses, favoring the formation of clustered efficacy engrams.


SUPPLEMENTARY DATA: LAYER 2/3 PYRAMIDAL CELL MODEL DETAILS
We present the set of ionic currents used in our layer 2/3 pyramidal cell model. The descriptions of the ionic currents used in the simulations were the same or similar to those used in previous modeling studies (Iannella et al., 2010;Iannella and Tanaka, 2006;Iannella et al., 2004;Mainen et al., 1995;Rhodes and Gray, 1994;Rhodes and Llinás, 2001;Traub et al., 2003) and are given below. Note that the values of maximal conductances for each respective ion channel are listed below.
The values of maximal conductances for each respective ion channel are listed in Table 1. at the end of this document.

Leak current I leak
Sodium current I Na Transient potassium A-current I K(A) Potassium H-current I K(H) Calcium gated potassium current I K(Ca) Muscarinic potassium current I M Medium afterhyperpolarization current I mAHP where E leak = −80 mV, E Na = 50 mV, E Kdr = E K(A) = E K(Ca) = E mAHP = E sAHP = −90 mV, and E K(H) = −35 mV, F = 96485 C mol −1 is Faraday's constant, R = 8.1345 J o K −1 mol −1 is the gas constant, and T denotes absolute temperature in o K (degrees kelvin). Intracellular calcium dynamics Calcium accumulation, extrusion, diffusion and buffering was simulated according to the following simple model which accounts for these processes by a simple exponential decay, where [Ca] ∞ = 20µM is the equilibrium concentration of intracellular calcium, [Ca] i denotes the concentration of intracellular free calcium, τ Ca = 20 msec is the diffusion rate constant, d is the depth of a shell just beneath the membrane, I Ca(HVA) and I Ca(T) respectively denotes the calcium current through L-type and T-type calcium channels, and I Ca(NMDA) = 0.1I NMDA is a fractional calcium current through postsynaptic NMDA receptors where 10% of the NMDA-mediated current is carried by calcium (Garaschuk et al., 1996;Burnashev et al., 1995).
The synaptic currents that are generated due to the incoming spike activity transmitted by impinging afferent fibers onto various locations across the dendrite result in depolaration and neuronal firing. The description of the four different synaptic currents generated by their respective underlying receptor types: AMPA, GABA A , GABA B , and NMDA, were modeled as follows, AMPA conductance and current: Note that only the synaptic efficacies or weights of AMPA currents generated at dendritic location j are denoted by w j (t) and altered via STDP. All other weights (maximal conductances) associated with the other synaptic currents (NMDA, GABA A , and GABA B ) are fixed.
GABA A conductance and current: is the Heaviside step function, w j denotes the efficacy of the AMPA conductance in synapse j, and F is a normalization factor such that an event with g = 1 generates a peak conductance of 1 µS. The maximal AMPA g AMPA and GABA A g GABA A conductance were 5 and 2 nS, respectively. Onset and decay time constants were τ AMPA o = 0.2 msec and τ AMPA d = 1.5 msec for AMPA and τ GABA A o = 1.2 msec and τ GABA A d = 9 msec GABA A conductances, respectively. Excitatory AMPA weights were initialized to w j (t) = 0.5, but later changed by STDP.

NMDA conductance and current:
The postsynaptic NMDA conductance was modeled using a simple two state kinetic scheme represented by the following two state diagram where α and β represent forward and backward voltage independent reaction rates. Defining ζ as the fraction of receptors in the open state of synapse j, then the above two state reaction is described by the following first order kinetic equation: where α = 10 (msec) −1 and β = 0.0125 (msec) −1 denotes the forward binding and backward unbinding rates, respectively. The concentration [T] denotes a pulse of neurotransmitter of duration 1.1 msec in the synaptic cleft. The NMDA conductance is given by, Frontiers while the NMDA current is, where the reversal potential is E NMDA rev = 0, and B(V ) represents magnesium block described by the following voltage dependent process, where the extracellular magnesium concentration was set to a value of [ GABA B conductance and current: Post synaptic GABA B receptor responses are activated by an intracellular second messenger system, mediated by fast G-protein binding to K + channels, whose state diagram is represented by the following kinetic scheme The activated and desensitized forms of the receptor G and D respectively arise after neurotransmitter T binds to the receptor R o . Concurrently, the active form of the G-protein G is produced after the inactive form G o has been catalyzed by R, and consequently binds to open K + channels, with n = 4 binding sites.
The above kinetic scheme can be simplified, by assuming Michaelis-Menton kinetics, fast binding to K + channels, quasi stationarity of the intermediate enzymatic reactions, no receptor desensitization, and an excess of inactive G-proteins G o , to the following system, is the maximal conductance of GABA B receptors, g GABA B j (t) denotes the GABA B conductance, K d is the dissociation constant of G-protein binding to K + channels, and E GABA B rev = −95 mV is the reversal potential.