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illustrates how intracellular transport works in MOOSE. We have a +an elongated soma in which molecules start out at the left and are transported +to the right. Note that they spread out as they go along, +This is because the transport is implemented as drift-diffusion, in which a +fraction of the molecules move to the next location each timestep. The +equation is + + ``flux = motorConst * conc / spacing`` + +for a uniform cylinder. MOOSE applies suitable scaling terms if the neuronal +geometry is non-uniform. + +:: + + import moose + import numpy as np + import pylab + import rdesigneur as rd + + moose.Neutral( '/library' ) + moose.Neutral( '/library/transp' ) + moose.CubeMesh( '/library/transp/dend' ) + A = moose.Pool( '/library/transp/dend/A' ) + A.diffConst = 0 + A.motorConst = 1e-6 # Metres/sec + + rdes = rd.rdesigneur( + turnOffElec = True, + #This subdivides the length of the soma into 0.5 micron voxels + diffusionLength = 0.5e-6, + cellProto = [['somaProto', 'soma', 2e-6, 50e-6]], + chemProto = [['transp', 'transp']], + chemDistrib = [['transp', 'soma', 'install', '1' ]], + plotList = [ + ['soma', '1', 'dend/A', 'conc', 'Concentration of A'], + ['soma', '1', 'dend/A', 'conc', 'Concentration of A', 'wave'], + ], + moogList = [['soma', '1', 'dend/A', 'conc', 'A Conc', 0, 20 ]] + ) + rdes.buildModel() + moose.element( '/model/chem/dend/A[0]' ).concInit = 0.1 + moose.reinit() + rdes.displayMoogli( 1, 80, rotation = 0, azim = -np.pi/2, elev = 0.0 ) + +In this example we explicitly create the single-molecule reaction system, +and assign a motorConst of 1 micron/sec to the molecule A. We start off with +all the molecules in a single voxel on the left of the cylinder, and then +watch the molecules move. +Once the molecules reach the end of the cylindrical soma, they have nowhere +further to go so they pile up. + +.. figure:: ../../../../images/ex7.3_1.png + :alt: Transport frame 1. +.. figure:: ../../../../images/ex7.3_2.png + :alt: Transport frame 2. +.. figure:: ../../../../images/ex7.3_3.png + :alt: Transport frame 3. +.. figure:: ../../../../images/ex7.3_4.png + :alt: Transport frame 4. +.. figure:: ../../../../images/ex7.3_5.png + :alt: Transport frame 5. +.. figure:: ../../../../images/ex7.3_6.png + :alt: Transport frame 6. + + Frames at increasing intervals from the transport simulation showing + spreading and piling up of the molecule at the right end of the cylinder. + +Suggestions: + + - Play with different motor rates. + - The motor constant sign detemines the direction of transport. See + what happens if you get it going in the opposite direction. + - Consider how you could avoid the buildup in the last voxel. + - Consider how to achieve a nice exponential falloff over a + much longer range than possible with diffusion. + +Travelling oscillator +~~~~~~~~~~~~~~~~~~~~~ + +*ex7.4_travelling_osc.py* + +Here we put a chemical oscillator into a cylinder, and activate motor transport +in one of the molecules. The oscillatory zone slowly moves to the right, with +an amplification in the last compartment due to end-effects. + +:: + + import moose + import numpy as np + import pylab + import rdesigneur as rd + rdes = rd.rdesigneur( + turnOffElec = True, + diffusionLength = 2e-6, + chemProto = [['makeChemOscillator()', 'osc']], + chemDistrib = [['osc', 'soma', 'install', '1' ]], + plotList = [ + ['soma', '1', 'dend/a', 'conc', 'Concentration of a'], + ['soma', '1', 'dend/b', 'conc', 'Concentration of b'], + ['soma', '1', 'dend/a', 'conc', 'Concentration of a', 'wave'], + ], + moogList = [['soma', '1', 'dend/a', 'conc', 'a Conc', 0, 360 ]] + ) + a = moose.element( '/library/osc/kinetics/a' ) + b = moose.element( '/library/osc/kinetics/b' ) + s = moose.element( '/library/osc/kinetics/s' ) + a.diffConst = 0 + b.diffConst = 0 + a.motorConst = 1e-6 + + rdes.buildModel() + moose.reinit() + + rdes.displayMoogli( 1, 400, rotation = 0, azim = -np.pi/2, elev = 0.0 ) + +.. figure:: ../../../../images/ex7.4_travelling_osc.png + :alt: Travelling Oscillator + + Snapshot of travelling oscillator waveform at t = 198. + +Suggestions: + + - What happens if all molecules undergo transport? + - What happens if b is transported opposite to a? + - What happens if there is also diffusion? + +Bidirectional transport +~~~~~~~~~~~~~~~~~~~~~~~ + +*ex7.5_bidirectional_transport.py* + +This is almost identical to ex7.4, except that we implement bidirectional +transport. Molecule a goes from left to right, and b and s go from +right to left. Here we see that the system builds up with large oscillations +in the middle as the molecules converge, then the peaks collapse when +the molecules go away. + +:: + + import moose + import numpy as np + import pylab + import rdesigneur as rd + rdes = rd.rdesigneur( + turnOffElec = True, + diffusionLength = 2e-6, + numWaveFrames = 50, + chemProto = [['makeChemOscillator()', 'osc']], + chemDistrib = [['osc', 'soma', 'install', '1' ]], + plotList = [ + ['soma', '1', 'dend/a', 'conc', 'Concentration of a', 'wave', 0, 1800], + ['soma', '1', 'dend/b', 'conc', 'Concentration of b', 'wave', 0, 500], + ['soma', '1', 'dend/s', 'conc', 'Concentration of s', 'wave', 0, 1200], + ], + moogList = [['soma', '1', 'dend/a', 'conc', 'a Conc', 0, 600 ]] + ) + a = moose.element( '/library/osc/kinetics/a' ) + b = moose.element( '/library/osc/kinetics/b' ) + s = moose.element( '/library/osc/kinetics/s' ) + a.diffConst = 0 + b.diffConst = 0 + a.motorConst = 2e-6 + b.motorConst = -2e-6 + s.motorConst = -2e-6 + + rdes.buildModel() + moose.reinit() + + rdes.displayMoogli( 1, 250, rotation = 0, azim = -np.pi/2, elev = 0.0 ) + +.. figure:: ../../../../images/ex7.5_a.png + :alt: Travelling Oscillator molecule a + +.. figure:: ../../../../images/ex7.5_b.png + :alt: Travelling Oscillator molecule b + +.. figure:: ../../../../images/ex7.5_s.png + :alt: Travelling Oscillator molecule + +Above we see *a*, *b*, *s* at a point where the transport has collected the +molecules toward the middle of the cylinder, so the oscillations are large. +Below we see molecule *a* later, when it has gone past the *b* and *s* pools +and so the reaction system is depleted and does not oscillate. + +.. figure:: ../../../../images/ex7.5_a_later.png + :alt: Travelling Oscillator molecule a later. + + + Multiscale models: single compartment ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ -- GitLab