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docs/src/tutorials/neural_assembly.jl

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+# #Tutorial on building a neural assembly from bottom-up
+
+
+# ### Single spiking neuron from Hodgkin-Huxley model
+
+# Hodgkin-Huxley (HH) formalism to describe membrane potential of a single neuron
+
+ #md ```math
+ #md   \begin{align}
+ #md   C_m\frac{dV}{dt} &= -g_L(V-V_L) - {g}_{Na}m^3h(V-V_{Na}) -{g}_Kn^4(V-V_K) + I_{in} - I_{syn} \\
+ #md   \frac{dm}{dt} &= \alpha_{m}(V)(1-m) + \beta_{m}(V)m \\ 
+ #md   \frac{dh}{dt} &= \alpha_{h}(V)(1-h) + \beta_{h}(V)h \\
+ #md   \frac{dn}{dt} &= \alpha_{n}(V)(1-n) + \beta_{n}(V)n 
+ #md   \end{align}
+ #md ```
+
+# A single HH neuron can be simulated as follows
+
+#md ```@example neural_assembly
+using Neuroblox
+using MetaGraphs
+using DifferentialEquations
+using Random
+using Plots
+using Statistics
+
+# define a single excitatory neuron 'blox' with steady input current I_in = 0.5 microA/cm2
+nn1 = HHNeuronExciBlox(name=Symbol("nrn1"), I_bg=0.5)
+
+# add the single neuron 'blox' as a single node in a graph
+g = MetaDiGraph()
+add_blox!.(Ref(g), [nn1])
+# md ```
+
+
+#md ```@example neural_assembly
+# create an ODESystem from the graph
+@named sys = system_from_graph(g)
+sys = structural_simplify(sys)
+length(unknowns(sys))
+# md```
+
+# To solve the system, we first create an Ordinary Differential Equation Problem and then solve it over the tspan of (0,1e) using a Vern7() solver.  The solution is saved every 0.1ms. The unit of time in Neuroblox is 1ms.
+
+#md ```@example neural_assembly
+prob = ODEProblem(sys, [], (0.0, 1000), [])
+sol = solve(prob, Vern7(), saveat=0.1)
+plot(sol.t,sol[1,:],xlims=(0,1000),xlabel="time (ms)",ylabel="mV")
+# ```
+
+
+# ### Connecting three neurons through synapses to make a small local circuit
+
+# define three neurons, two excitatory and one inhibitory
+nn1 = HHNeuronExciBlox(name=Symbol("nrn1"), I_bg=0.5)
+nn2 = HHNeuronInhibBlox(name=Symbol("nrn2"), I_bg=0.7)
+nn3 = HHNeuronExciBlox(name=Symbol("nrn3"), I_bg=0.8)
+assembly = [nn1,nn2,nn3] 
+
+# add the three neurons as nodes in a graph
+g = MetaDiGraph()
+add_blox!.(Ref(g), [assembly])
+
+# connect the nodes with the edges (synapses in this case), with the synaptic weights specified as arguments
+add_edge!(g, 1, 2, :weight, 1) #connection from node 1 to node 2 (nn1 to nn2)
+add_edge!(g, 2, 3, :weight, 1) #connection from node 2 to node 3 (nn2 to nn3)
+
+# create an ODESystem from the graph and then solve it using an ODE solver
+@named sys = system_from_graph(g)
+sys = structural_simplify(sys)
+prob = ODEProblem(sys, [], (0.0, 1000), [])
+sol = solve(prob, Vern7(), saveat=0.1)
+
+# plotting membrane voltage activity of all neurons
+ss=convert(Array,sol) 
+st=unknowns(sys)    #collecting all the state variables from the whole ODEsystem
+vlist=Int64[] 
+for ii = 1:length(st)     
+    if contains(string(st[ii]), "V(t)")   #extracting only voltage variables
+            push!(vlist,ii)
+    end
+end
+
+# creating a matrix where every row represents the voltage time series of a single neuron.
+V = ss[vlist,:]
+
+# creating a matrix where every row represents the voltage time series of a single neuron, with an added constant. 
+# This makes all the time timeseries stacked up in the plot.
+
+V_stack=zeros(length(vlist),length(sol.t))  
+for ii = 1:length(vlist)
+    V_stack[ii,:] .= V[ii,:] .+ 200*(ii-1)   
+end
+plot(sol.t,V_stack[:,:]',color= "blue",label=false)
+
+
+
+