# Difference between revisions of "Assignment 9, Part 1: model function"

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− | Finally, put everything together into a single model function that | + | Finally, put everything together into a single model function that represents |

+ | <math>\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 .</math> | ||

+ | |||

+ | ''S(t)'' is the expression for photobleaching, ''Q(t)'' is the expression for thermal quenching, and ''C<sub>ds</sub>'' is the model melting curve produced by the <code>DnaFraction</code> function from part 1 of the lab. | ||

+ | |||

+ | |||

+ | In order for the function to be compatible with MATLAB's <tt>nlinfit</tt>, 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 <math>\Delta H^\circ, \Delta S^\circ</math>, as well as the bleaching, quenching, and thermal time constants. | ||

<pre> | <pre> |

## Revision as of 14:29, 21 August 2017

This is Part 1 of Assignment 9.

The wiki page on the DNA model function outlines 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 the following functions in MATLAB which model the phenomena of photobleaching and thermal quenching:

function SimulatedBleachingOutput = SimulatePhotobleaching( Kbleach, InputData ) ... end function SimulatedQuenchingOutput = SimulateThermalQuenching( Kquench, InputData ) ... end

Finally, put everything together into a single model function that represents $ \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 . $

*S(t)* is the expression for photobleaching, *Q(t)* is the expression for thermal quenching, and *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) |