Distributed cerebellar plasticity implements adaptable gain control (Garrido et al., 2013)

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Accession:150067
We tested the role of plasticity distributed over multiple synaptic sites (Hansel et al., 2001; Gao et al., 2012) by generating an analog cerebellar model embedded into a control loop connected to a robotic simulator. The robot used a three-joint arm and performed repetitive fast manipulations with different masses along an 8-shape trajectory. In accordance with biological evidence, the cerebellum model was endowed with both LTD and LTP at the PF-PC, MF-DCN and PC-DCN synapses. This resulted in a network scheme whose effectiveness was extended considerably compared to one including just PF-PC synaptic plasticity. Indeed, the system including distributed plasticity reliably self-adapted to manipulate different masses and to learn the arm-object dynamics over a time course that included fast learning and consolidation, along the lines of what has been observed in behavioral tests. In particular, PF-PC plasticity operated as a time correlator between the actual input state and the system error, while MF-DCN and PC-DCN plasticity played a key role in generating the gain controller. This model suggests that distributed synaptic plasticity allows generation of the complex learning properties of the cerebellum.
Reference:
1 . Garrido JA, Luque NR, D'Angelo E, Ros E (2013) Distributed cerebellar plasticity implements adaptable gain control in a manipulation task: a closed-loop robotic simulation Front. Neural Circuits 7:159:1-20 [PubMed]
Model Information (Click on a link to find other models with that property)
Model Type: Realistic Network;
Brain Region(s)/Organism: Cerebellum;
Cell Type(s): Cerebellum deep nucleus neuron;
Channel(s):
Gap Junctions:
Receptor(s):
Gene(s):
Transmitter(s):
Simulation Environment: C or C++ program; MATLAB; Simulink;
Model Concept(s): Long-term Synaptic Plasticity;
Implementer(s): Garrido, Jesus A [jesus.garrido at unipv.it]; Luque, Niceto R. [nluque at ugr.es];
%RBFGBELLS S function that convert a monodimensial entry (joint position in
%degree) into a multidemsional output. This output feeds to a mossy block
%
%       function [sys,x0,str,ts] =
%      RBFgauss(t,x,u,flag,PasoGrado,numRBFs,sigma)
%
%Function parameters:
% 
%-PasoGrado. Degree step.the joint spatial state  (from 0 to 180 degree)is
%            divided in step, This parameter fixs the minimun step.
%
%-numRBFs. Indicate how many RBFs this block is going to use
%
%-sigma. Parameter that defines a gauss distribution.
%
%The symmetric Gaussian function depends on two parameters: 
%  
%   GAUSSMF(X, [SIGMA, C]) = EXP(-(X - C).^2/(2*SIGMA^2));
%
% SIGMA GIVEN BY THE USER AND C GIVEN DYNAMICALLY
%
% See also: RAD2DEG, RBFGAUSS, RBFBELL, RBFTRIM, RBFTRAP, GAUSSMF.

%   2007 Niceto Luque Sola
%

function [sys,x0,str,ts] = fRBFgauss1optimal(t,x,u,flag,PasoGrado,numRBFs,sigma,limitinf,limitsup,numfig,ver)

persistent RBF1s

%SFUNTMPL General M-file S-function template
%   With M-file S-functions, you can define you own ordinary differential
%   equations (ODEs), discrete system equations, and/or just about
%   any type of algorithm to be used within a Simulink block diagram.
%
%   The general form of an M-File S-function syntax is:
%       [SYS,X0,STR,TS] = SFUNC(T,X,U,FLAG,P1,...,Pn)
%
%   What is returned by SFUNC at a given point in time, T, depends on the
%   value of the FLAG, the current state vector, X, and the current
%   input vector, U.
%
%   FLAG   RESULT             DESCRIPTION
%   -----  ------             --------------------------------------------
%   0      [SIZES,X0,STR,TS]  Initialization, return system sizes in SYS,
%                             initial state in X0, state ordering strings
%                             in STR, and sample times in TS.
%   1      DX                 Return continuous state derivatives in SYS.
%   2      DS                 Update discrete states SYS = X(n+1)
%   3      Y                  Return outputs in SYS.
%   4      TNEXT              Return next time hit for variable step sample
%                             time in SYS.
%   5                         Reserved for future (root finding).
%   9      []                 Termination, perform any cleanup SYS=[].
%
%
%   The state vectors, X and X0 consists of continuous states followed
%   by discrete states.
%
%   Optional parameters, P1,...,Pn can be provided to the S-function and
%   used during any FLAG operation.
%
%   When SFUNC is called with FLAG = 0, the following information
%   should be returned:
%
%      SYS(1) = Number of continuous states.
%      SYS(2) = Number of discrete states.
%      SYS(3) = Number of outputs.
%      SYS(4) = Number of inputs.
%               Any of the first four elements in SYS can be specified
%               as -1 indicating that they are dynamically sized. The
%               actual length for all other flags will be equal to the
%               length of the input, U.
%      SYS(5) = Reserved for root finding. Must be zero.
%      SYS(6) = Direct feedthrough flag (1=yes, 0=no). The s-function
%               has direct feedthrough if U is used during the FLAG=3
%               call. Setting this to 0 is akin to making a promise that
%               U will not be used during FLAG=3. If you break the promise
%               then unpredictable results will occur.
%      SYS(7) = Number of sample times. This is the number of rows in TS.
%
%
%      X0     = Initial state conditions or [] if no states.
%
%      STR    = State ordering strings which is generally specified as [].
%
%      TS     = An m-by-2 matrix containing the sample time
%               (period, offset) information. Where m = number of sample
%               times. The ordering of the sample times must be:
%
%               TS = [0      0,      : Continuous sample time.
%                     0      1,      : Continuous, but fixed in minor step
%                                      sample time.
%                     PERIOD OFFSET, : Discrete sample time where
%                                      PERIOD > 0 & OFFSET < PERIOD.
%                     -2     0];     : Variable step discrete sample time
%                                      where FLAG=4 is used to get time of
%                                      next hit.
%
%               There can be more than one sample time providing
%               they are ordered such that they are monotonically
%               increasing. Only the needed sample times should be
%               specified in TS. When specifying than one
%               sample time, you must check for sample hits explicitly by
%               seeing if
%                  abs(round((T-OFFSET)/PERIOD) - (T-OFFSET)/PERIOD)
%               is within a specified tolerance, generally 1e-8. This
%               tolerance is dependent upon your model's sampling times
%               and simulation time.
%
%               You can also specify that the sample time of the S-function
%               is inherited from the driving block. For functions which
%               change during minor steps, this is done by
%               specifying SYS(7) = 1 and TS = [-1 0]. For functions which
%               are held during minor steps, this is done by specifying
%               SYS(7) = 1 and TS = [-1 1].

%   Copyright 1990-2002 The MathWorks, Inc.
%   $Revision: 1.18 $

%
% The following outlines the general structure of an S-function.
%

switch flag,

  %%%%%%%%%%%%%%%%%%
  % Initialization %
  %%%%%%%%%%%%%%%%%%
  case 0,
      
    [sys,x0,str,ts,RBF1s]=mdlInitializeSizes(PasoGrado,numRBFs,limitinf,limitsup,sigma,RBF1s);

  %%%%%%%%%%%%%%%
  % Derivatives %
  %%%%%%%%%%%%%%%
  case 1,
    sys=mdlDerivatives(t,x,u);

  %%%%%%%%%%
  % Update %
  %%%%%%%%%%
  case 2,
    sys=mdlUpdate(t,x,u);

  %%%%%%%%%%%
  % Outputs %
  %%%%%%%%%%%
  case 3,
    
      [sys]=mdlOutputs(t,x,u,PasoGrado,numRBFs,limitinf,limitsup,numfig,ver,RBF1s);
  %%%%%%%%%%%%%%%%%%%%%%%
  % GetTimeOfNextVarHit %
  %%%%%%%%%%%%%%%%%%%%%%%
  case 4,
    sys=mdlGetTimeOfNextVarHit(t,x,u);

  %%%%%%%%%%%%%
  % Terminate %
  %%%%%%%%%%%%%
  case 9,
    sys=mdlTerminate(t,x,u);

  %%%%%%%%%%%%%%%%%%%%
  % Unexpected flags %
  %%%%%%%%%%%%%%%%%%%%
  otherwise
    error(['Unhandled flag = ',num2str(flag)]);

end

% end sfuntmpl

%
%=============================================================================
% mdlInitializeSizes
% Return the sizes, initial conditions, and sample times for the S-function.
%=============================================================================
%
function [sys,x0,str,ts,RBF1s]=mdlInitializeSizes(PasoGrado,numRBFs,limitinf,limitsup,sigma,RBF1s)

%
% call simsizes for a sizes structure, fill it in and convert it to a
% sizes array.
%
% Note that in this example, the values are hard coded.  This is not a
% recommended practice as the characteristics of the block are typically
% defined by the S-function parameters.
%
sizes = simsizes;
sizes.NumContStates  = 0;
sizes.NumDiscStates  = 0;
sizes.NumOutputs     = numRBFs;
sizes.NumInputs      = -1;
sizes.DirFeedthrough = 1;
sizes.NumSampleTimes = 1;   % at least one sample time is needed

sys = simsizes(sizes);
valores=limitinf:PasoGrado:limitsup;
%center displacement
    %a=-0.2*numRBFs/length(valores);
    %b=0.2*numRBFs/length(valores);
    %for i=1:numRBFs,
        %error(i) = a + (b-a) * rand(1);


     % error(i)=1+40*randn(1);
    %end
A=fRBF(valores,numRBFs,sigma,zeros(1,numRBFs));%c code
%A=fRBF(valores,numRBFs,sigma,error);%c code
RBF1s=A';
%
% initialize the initial conditions
%
x0  = [];

%
% str is always an empty matrix
%
str = [];

%
% initialize the array of sample times
%
ts  = [-1 0];

% end mdlInitializeSizes

%
%=============================================================================
% mdlDerivatives
% Return the derivatives for the continuous states.
%=============================================================================
%
function sys=mdlDerivatives(t,x,u)

sys = [];

% end mdlDerivatives

%
%=============================================================================
% mdlUpdate
% Handle discrete state updates, sample time hits, and major time step
% requirements.
%=============================================================================
%
function sys=mdlUpdate(t,x,u)

sys = [];

% end mdlUpdate

%
%=============================================================================
% mdlOutputs
% Return the block outputs.
%=============================================================================
%
function [sys]=mdlOutputs(t,x,u,PasoGrado,numRBFs,limitinf,limitsup,numfig,ver,RBF1s)
%Fast RBFs implemented in C
%valores=limitinf:PasoGrado:limitsup;
entrada= u(1);
Ibase=0.1;  %Ibase for french codification 0.1*2.17;0.1 in regular codification;
len=length(RBF1s(1,:))-1;

indice=((entrada-limitinf)/(limitsup-limitinf))*len + 1;
sys=RBF1s(:,round(indice))+Ibase;

if ver==1
    x=limitinf:PasoGrado:limitsup;
    subplot(7,2,numfig)
    plot(x,RBF1s(1:numRBFs,:),'b')
    title('Posición Articular')
    hold on
    plot(entrada,RBF1s(:,round(indice))+Ibase,'rx')
    hold off
end
% end mdlOutputs

%
%=============================================================================
% mdlGetTimeOfNextVarHit
% Return the time of the next hit for this block.  Note that the result is
% absolute time.  Note that this function is only used when you specify a
% variable discrete-time sample time [-2 0] in the sample time array in
% mdlInitializeSizes.
%=============================================================================
%
function sys=mdlGetTimeOfNextVarHit(t,x,u)

sampleTime = 1; %  Example, set the next hit to be one second later.
sys = t + sampleTime;

% end mdlGetTimeOfNextVarHit

%
%=============================================================================
% mdlTerminate
% Perform any end of simulation tasks.
%=============================================================================
%
function sys=mdlTerminate(t,x,u)

sys = [];

% end mdlTerminate

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