NumHH - Revision history

Carver: /* Creating Models From The Key and Template Files */

2009-02-24T19:31:08Z

‎Creating Models From The Key and Template Files

Carver: /* Creating Models From The Key and Template Files */

2009-02-24T19:25:38Z

‎Creating Models From The Key and Template Files

Carver: /* Numerical Solution of Differential Equations */

2009-02-24T19:14:25Z

‎Numerical Solution of Differential Equations

Carver: /* Numerical Solution of Differential Equations */

2009-02-24T19:14:06Z

‎Numerical Solution of Differential Equations

Carver: /* Time Step Function */

2009-02-24T19:10:52Z

‎Time Step Function

Carver: /* Step Function */

2009-02-24T17:22:02Z

‎Step Function

Carver: /* Homework */

2009-02-24T17:18:06Z

‎Homework

Carver: /* Changing the Key File */

2009-02-24T17:04:34Z

‎Changing the Key File

Carver: /* Creating Models From The Key and Template Files */

2009-02-24T16:57:58Z

‎Creating Models From The Key and Template Files

Carver: /* Changing the Key File */

2009-02-24T16:55:26Z

‎Changing the Key File

@@ Line 113: / Line 113: @@
   CreateData(HH)
-This creates and plots data (input and measurements as a function of time).  You can plot other things (like the state variable, stateM) with the commands
+This creates and plots data (input and measurements as a function of time). It saves the data in the file HH.mat, (the filename is the "prefix" in the key file). If you load the saved file, you can plot other things (like the state variable, stateM, with the commands:
   load HH
@@ Line 122: / Line 122: @@
   out
-For a list of things you can plot.
+For a list of things you can plot).
 The final step of the process is the likelihood calculation.  For this you need two functions, plus [http://www.mathworks.com/matlabcentral/fileexchange/15235 Freeware code] that it uses.

@@ Line 76: / Line 76: @@
 == Creating Models From The Key and Template Files ==
-Download the following (or the zip file in note below):
+Download the following (or the [[Media:ClassCode.zip|zip file]], see note below):
 * [[Media:HH_step_template.m|HH_step_template.m]]: This is the function that steps from one time to the next.

@@ Line 58: / Line 58: @@
 Here k is the rate constant, 1/k is the time constant, 1/k is <math> \frac{C}{g_L} = RC </math> in the notation above.  A leaky cell is what is called an RC circuit -- a resistor and capacitor together in a circuit.  The time constant of an RC circuit is RC.  The bigger k, the higher the rate of convergence, and the smaller the time constant 1/k.  The time constant is the time it takes the solution to decay to 1/e of its value.
-Solution of differential equations happens at discrete times: <big> <math> y_k </math> </big>, separated by small time intervals <big> <math> \Delta t </math> <big>.
+Solution of differential equations happens at discrete times: <big> <math> y_k </math> </big>, separated by small time intervals <big> <math> \Delta t </math> </big>.
 The simplest way of solving this equation is with Euler's method:

@@ Line 58: / Line 58: @@
 Here k is the rate constant, 1/k is the time constant, 1/k is <math> \frac{C}{g_L} = RC </math> in the notation above.  A leaky cell is what is called an RC circuit -- a resistor and capacitor together in a circuit.  The time constant of an RC circuit is RC.  The bigger k, the higher the rate of convergence, and the smaller the time constant 1/k.  The time constant is the time it takes the solution to decay to 1/e of its value.
-Solution of differential equations happens at discrete times: <big> <math> y_k </math> </big>, separated by small time intervals dt.
+Solution of differential equations happens at discrete times: <big> <math> y_k </math> </big>, separated by small time intervals <big> <math> \Delta t </math> <big>.
 The simplest way of solving this equation is with Euler's method:

@@ Line 30: / Line 30: @@
 This function returns the nextState (state at current time plus oneDT) as a function of current state (stateV,stateM,stateN,stateH) input (injectedCurrent) noise (PNoise) and parameters (param).
-Note that this function won't run because a lot of things (like injectedCurrent and ENa) aren't defined.  A function like this one can be very hard to make both human readable and run quickly.  So I have written preprocessor createCell.m which takes the human readable template function above and creates machine readable MATLAB Code function, based on a key function, hh.m.
+Note that this function won't run because a lot of things (like injectedCurrent and ENa) aren't defined.  A function like this one can be very hard to make both human readable and run quickly.  So I have written preprocessor CreateCell.m which takes the human readable template function above and creates machine readable MATLAB Code function, based on a key function, HH.m.
 Before we discuss the key function the nextState equation requires explanation:

@@ Line 5: / Line 5: @@
 Moving on to today's material, recall that we have looked at the action potential with the Hodgkin-Huxley model using the textbook software, Neurons in Action.  Today we are going to use MATLAB.  We will generate data, then change parameters, then calculate the likelihood that the model (with different parameters) produced the data.
-== Step Function ==
+== Time Step Function ==
 Here is the function that simulates the model (one step at a time):

← Older revision		Revision as of 17:18, 24 February 2009
Line 229:		Line 229:

	== Homework ==		== Homework ==
		+
		+	The first 4 questions are worth 1 point each. You are encouraged to check with your classmates and with me to see that we are all getting the same results.
		+
		+	* '''Homework I.1:''' Calculate the log likelihood with the default values in the key (follow directions above).
		+
		+	* '''Homework I.2:''' Repeat the log-likelihood calculation but change the key so that the fitting makes all correct assumptions (change the values of key.assume to match their values higher up. If there is no assumption about a variable it is assumed correct. You can add or remove assumptions, but you need at least one.
		+
		+	* '''Homework I.3:''' Calculate the log-likelihood that an RC circuit (i.e. a cell with just a leak current), produces the action potential data from the Hodgkin-Huxley model. To do this set key.assume.gNa = 0 and key.assume.gK = 0, and remove all other assumptions, and run the code. Please try to understand what you are doing.
		+
		+	* '''Homework I.4:''' Calculate the log-likelihood that the voltage trace from a Hodgkin-Huxley model looks identical to one from an RC-circuit. Make key.assume for gNa and gK be the default Hodgkin-Huxley parameters, but for generating the data key.gen.gNa, key.gen.gK, set these to zero.
		+
		+	The last question is worth 6 points and full credit is not automatic. Review question.
		+
		+	* '''Homework I.5''' Concisely and effectively explain the mechanisms behind the action potential.

← Older revision		Revision as of 17:04, 24 February 2009
Line 227:		Line 227:

	These are the intermediate variables to save while generating data.		These are the intermediate variables to save while generating data.
		+
		+	== Homework ==

← Older revision		Revision as of 16:57, 24 February 2009
Line 113:		Line 113:
	CreateData(HH)		CreateData(HH)

		+	This creates and plots data (input and measurements as a function of time). You can plot other things (like the state variable, stateM) with the commands
		+
		+	load HH
		+	plot(out.time,out.stateM)
		+
		+	After loading HH, type
		+
		+	out
		+
		+	For a list of things you can plot.
	The final step of the process is the likelihood calculation. For this you need two functions, plus [http://www.mathworks.com/matlabcentral/fileexchange/15235 Freeware code] that it uses.		The final step of the process is the likelihood calculation. For this you need two functions, plus [http://www.mathworks.com/matlabcentral/fileexchange/15235 Freeware code] that it uses.

← Older revision		Revision as of 16:55, 24 February 2009
Line 129:		Line 129:

	== Changing the Key File ==		== Changing the Key File ==
		+
		+	Let's look at the key file:
		+
		+	function key = HH
		+
		+	% PREFIX TO START FILE NAMES
		+	key.prefix = 'HH';
		+
		+	The first item is the prefix of the files associated with the key (not including the templates). When you change the key, change the name and the prefix. For example change HH.m to HHA.m and prefix to 'HHA'.
		+
		+	% TEMPLATES TO CONVERT TO FAST RUNNING CODE
		+	key.steptemplate = 'HH_step_template.m';
		+	key.meastemplate = 'HH_meas_template.m';
		+
		+	These are the templates. A future version will have separate templates for generation and fitting.
		+
		+	% PARAMETERS FOR GENERATING DATA
		+	key.gen.gNa = 120;
		+	key.gen.gK = 36;
		+	key.gen.gL = 0.3;
		+	key.gen.ENa = 115; % mV
		+	key.gen.EK = -12; % mV
		+	key.gen.EL = 10.6; % mV
		+	key.gen.CAP = 1; % uF/cm^2
		+	key.gen.PNoiseLevel = 0.01;
		+	key.gen.MNoiseLevel = 0.001;
		+
		+	These are the parameters for generating the data (not necessarily fitting).
		+
		+	% INITIAL CONDITIONS FOR STATE VARIABLES
		+	key.state.stateV = 0;
		+	key.state.stateM = 0.05293421762087;
		+	key.state.stateN = 0.31768116757978;
		+	key.state.stateH = 0.59611104634676;
		+
		+	These are the state variables and their initial conditions.
		+
		+	% WHICH PARAMETERS TO FIT
		+	key.fit = {'gNa','gK'};
		+
		+	These are the parameters to tweak for finding the maximum likelihood.
		+
		+	% ASSUMPTIONS ABOUT PARAMETERS & STATES, IF NOT SPECIFIED ASSUMED CORRECT
		+	key.assume.gNa = 125;
		+	key.assume.gL = 0.5;
		+	key.assume.stateV = 1;
		+
		+	These are the (possibly) incorrect assumptions about the parameters and initial conditions for fitting.
		+
		+	% INPUT VARIABES AND CODE FOR CREATING INPUT
		+	key.input = {'injectedCurrent'};
		+	key.inputcreate = {@StepCurrent};
		+	key.inputparams(1).holding = 0;
		+	key.inputparams(1).step = 10;
		+	key.inputparams(1).start = 10;
		+	key.inputparams(1).stop = 25;
		+
		+	This specifies the injected current input.
		+
		+	% NOISE VARIABLES
		+	key.noise.process = {'PNoise'};
		+	key.noise.measurement = {'MNoise'};
		+
		+	This specifies the number and names of the noise variables.
		+
		+	% MEASUREMENTS
		+	key.meas = {'measuredVoltage'};
		+
		+	This specifies the number and names of of the measured variables
		+
		+	% TRAJECTORY TIME PARAMETERS
		+	key.time.oneDT = 0.01; % msec
		+	key.time.sqrtDT = 0.1; % msec^(1/2)
		+	key.time.TMAX = 30; % msec
		+	key.time.fitStart = 9; % msec
		+
		+	These specify trajectory parrameters. sqrtDT must be the square root of oneDT.
		+
		+	% RANDOM SEED
		+	key.seed = 0;
		+
		+	This specifies the seed of the random number generator when generating data.
		+
		+	% DEBUGGING
		+	key.debug = {'ionicCurrent','alpha_m','alpha_n','alpha_h', ...
		+	'beta_m','beta_n','beta_h'};
		+
		+	These are the intermediate variables to save while generating data.