3D olfactory bulb: operators (Migliore et al, 2015)

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Accession:168591
"... Using a 3D model of mitral and granule cell interactions supported by experimental findings, combined with a matrix-based representation of glomerular operations, we identify the mechanisms for forming one or more glomerular units in response to a given odor, how and to what extent the glomerular units interfere or interact with each other during learning, their computational role within the olfactory bulb microcircuit, and how their actions can be formalized into a theoretical framework in which the olfactory bulb can be considered to contain "odor operators" unique to each individual. ..."
Reference:
1 . Migliore M, Cavarretta F, Marasco A, Tulumello E, Hines ML, Shepherd GM (2015) Synaptic clusters function as odor operators in the olfactory bulb. Proc Natl Acad Sci U S A 112:8499-504 [PubMed]
Model Information (Click on a link to find other models with that property)
Model Type: Realistic Network;
Brain Region(s)/Organism:
Cell Type(s): Olfactory bulb main mitral GLU cell; Olfactory bulb main interneuron granule MC GABA cell;
Channel(s): I Na,t; I A; I K;
Gap Junctions:
Receptor(s): AMPA; NMDA; Gaba;
Gene(s):
Transmitter(s): Gaba; Glutamate;
Simulation Environment: NEURON; Python;
Model Concept(s): Activity Patterns; Dendritic Action Potentials; Active Dendrites; Synaptic Plasticity; Action Potentials; Synaptic Integration; Unsupervised Learning; Sensory processing; Olfaction;
Implementer(s): Migliore, Michele [Michele.Migliore at Yale.edu]; Cavarretta, Francesco [francescocavarretta at hotmail.it];
Search NeuronDB for information about:  Olfactory bulb main mitral GLU cell; Olfactory bulb main interneuron granule MC GABA cell; AMPA; NMDA; Gaba; I Na,t; I A; I K; Gaba; Glutamate;
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figure1eBulb3D
readme.html
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# packages of various functions.
from copy import copy
from math import *

def distance(p, q):
    x = p[0] - q[0]
    y = p[1] - q[1]
    z = p[2] - q[2]
    return sqrt(x ** 2 + y ** 2 + z ** 2)

class Spherical:
    @staticmethod
    def to(p, center=[0,0,0]):
        rho = distance(p, center)
        
        p = copy(p); p[0] -= center[0]; p[1] -= center[1]; p[2] -= center[2]
        
        phi = atan2(p[1], p[0])
        try:
            theta = acos(p[2] / rho)
        except ZeroDivisionError:
            theta = acos(p[2] / 1e-8)
            
        return rho, phi, theta

    @staticmethod
    def xyz(rho, phi, theta, center=[0,0,0]):
        x = rho * cos(phi) * sin(theta) + center[0]
        y = rho * sin(phi) * sin(theta) + center[1]
        z = rho * cos(theta) + center[2]
        return [ x, y, z ]

def centroid(pts):
    x = 0.
    y = 0.
    z = 0.
    for p in pts:
        x += p[0]
        y += p[1]
        z += p[2]
    x /= len(pts)
    y /= len(pts)
    z /= len(pts)
    return [ x, y, z ]

# for elliptical coords
class Ellipsoid:
    
    def __init__(self, pos, axis):
        self.__pos = copy(pos)
        halfAxis = copy(axis)
        for i in range(3): halfAxis[i] /= 2.
        self.__inverse = halfAxis[0] < halfAxis[1]
        self.__halfAxis = halfAxis
        
        # eccentricity
        a = 0; b = 1;
        if halfAxis[a] < halfAxis[b]: b = 0; a = 1
        
        self.__eccen = sqrt(halfAxis[a] ** 2 - halfAxis[b] ** 2) / halfAxis[a]
        
    def intersect(self, p, u):
        A = 0.
        B = 0.
        C = -1
        v = []

        for i in range(3):
            A += (u[i]/self.__halfAxis[i])** 2
            B += 2*u[i]*(p[i]-self.__pos[i]) / (self.__halfAxis[i]**2)
            C += ((p[i]-self.__pos[i])/self.__halfAxis[i])**2

        delta = B ** 2 - 4 * A * C
        t0 = (-B+sqrt(delta)) / (2*A)
        t1 = (-B-sqrt(delta)) / (2*A)
        if abs(t0) < abs(t1):
            t = t0
        else:
            t = t1

        q = []
        for i in range(3):
            q.append(p[i] + t * u[i])
        return q
    
    def project(self, pos):
        return self.intersect(pos, versor(pos, self.__pos))


    def R(self, phi): return self.__halfAxis[0] / sqrt(1 - (self.__eccen * sin(phi)) ** 2)

    # from elliptical to cartesian
    def toXYZ(self, h, lamb, phi):
        N = self.R(phi)
        XYProj = (N + h) * cos(phi)
        p = [ XYProj * cos(lamb),
              XYProj * sin(lamb),
              ((1 - self.__eccen ** 2) * N + h) * sin(phi) ]
        if self.__inverse: aux = p[0]; p[0] = p[1]; p[1] = aux
        for i in range(3): p[i] += self.__pos[i]
        return p

    # from cartesian to elliptical
    def toElliptical(self, pt):
        x = pt[0] - self.__pos[0]
        y = pt[1] - self.__pos[1]
        z = pt[2] - self.__pos[2]
        
        if self.__inverse: aux = y; y = x; x = aux
            
        lamb = atan2(y, x)

        p = sqrt(x ** 2 + y ** 2)
        try:
            phi = atan(z / ((1 - self.__eccen ** 2) * p))
        except ZeroDivisionError:
            phi = atan(z / 1e-8)

        MAXIT = int(1e+4)
        for i in range(MAXIT):
            phi1 = phi
            N = self.R(phi)
            h = p / cos(phi) - N
            try:
                phi = atan(z /  ((1 - self.__eccen ** 2 * N / (N + h)) * p))
            except ZeroDivisionError:
                phi = atan(z / 1e-8)
            if abs(phi - phi1) < 1e-8: break
        return h, lamb, phi

    def getZ(self, pt):            
        x = pt[0]; y = pt[1]
        try:
            return self.__pos[2] + self.__halfAxis[2] * sqrt(1 - ((x - self.__pos[0]) / self.__halfAxis[0]) ** 2 - ((y - self.__pos[1]) / self.__halfAxis[1]) ** 2)
        except ValueError:
            return None

    def normalRadius(self, pt):
        r = 0.
        for i in range(3): r += ((pt[i] - self.__pos[i]) / self.__halfAxis[i]) ** 2
        return r

# laplace rng
def rLaplace(r, mu, b):
    p = r.uniform(0, 1)
    if p > .5: return -log((1 - p) * 2) * b + mu
    return log(p * 2) * b + mu

# return versor between two points
def versor(p, q):
        d = distance(p, q)
        v = [ 0 ] * 3
        for i in range(3): v[i] = (p[i] - q[i]) / d
        return v

# return points on line
def getP(t, v, q):
            p = [ 0 ] * 3
            for i in range(3): p[i] = t * v[i] + q[i]
            return p
        
# stretch a section
def stretchSection(sec, p):
    dx = (sec[-1][0] - p[0]) / (len(sec) - 1)
    dy = (sec[-1][1] - p[1]) / (len(sec) - 1)
    dz = (sec[-1][2] - p[2]) / (len(sec) - 1)
    for k in range(1, len(sec)):
        sec[k][0] -= k * dx
        sec[k][1] -= k * dy
        sec[k][2] -= k * dz

class Matrix:
    @staticmethod
    def RZ(phi):
        return [[cos(phi),-sin(phi),0], [sin(phi),cos(phi),0], [0,0,1]]
    
    @staticmethod
    def RY(theta):
        return [[cos(theta),0,sin(theta)],[0,1,0],[-sin(theta),0,cos(theta)]]
    
    @staticmethod
    def prod(m, v):
        ret_v = [0]*len(v)
        for i in range(len(m)):
            for j in range(len(m[i])):
                ret_v[i] += v[j] * m[i][j]
        return ret_v
    
def convert_direction(phi, theta, phibase, thetabase, inv=False):
    u = Spherical.xyz(1, phi, theta)
    if inv:
        m1 = Matrix.RZ(-phibase)
        m2 = Matrix.RY(-thetabase)
    else:
        m2 = Matrix.RZ(phibase)
        m1 = Matrix.RY(thetabase)
    return Spherical.to(Matrix.prod(m2, Matrix.prod(m1, u)))[1:]
        
        
        


    
    

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