Assignment 9, Part 1: model function

This is Part 1 of Assignment 9.

In the Assignment 9 Overview, we provided a way to model the sample temperature based on the block temperature:

function SimulatedTemperatureOutput = SimulateLowPass( TimeConstant, InputData, TimeVector )
    if( nargin < 3 )
        TimeVector = (0:(length(InputData)-1))/10;
    end

    transferFunction = tf( 1, [TimeConstant, 1] );

    initalTemperature = InputData(1);
    InputData = InputData - initalTemperature;

    SimulatedTemperatureOutput = lsim( transferFunction, InputData, TimeVector' ) + initalTemperature;
end

In a similar fashion, write functions in MATLAB for S(t), the expression for photobleaching, and Q(t), the expression for thermal quenching. You are welcome to use the following templates as a guide, but note that you may need to alter the input and/or output parameters of these functions to suit your final purpose.

function SimulatedBleachingOutput = SimulatePhotobleaching( Kbleach, InputData )

    ...

end

function SimulatedQuenchingOutput = SimulateThermalQuenching( Kquench, InputData )
    
    ...

end

Once you have all the pieces, put everything together into a single model function representing:

$ \left . V_{f,model}(t) = K_{gain} S(t) Q(t) C_{ds}(T_{sample}(t), \Delta H^\circ, \Delta S^\circ) + K_{offset}\right . $

Here, C_ds is the model melting curve produced by the DnaFraction function from part 1 of the lab.

In order for the function to be compatible with MATLAB's nlinfit, the first input argument must be a vector containing all the parameters to be fitted, and the second argument must contain a vector/matrix of the independent variable(s). Don't forget to include parameters for the instrument gain and offset, and $ \Delta H^\circ, \Delta S^\circ $, as well as the bleaching, quenching, and thermal time constants.

function SimulatedOutput = Vfmodel( Parameters, InputData )
    tauThermal = Parameters(1);
    Kbleach = Parameters(2);

    ...

end

your code (after having tested it in part 2)

Navigation

• Assignment 9 Overview
• Part 1: model function
• Part 2: test your code with simulated data
• Part 3: fitting your data

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