Spring 2012:Leanna Morinishi Lab 1

Lab 1: Optical Trapping

What I wanted to accomplish

• Complete a button that takes in data from a tethered microbead and adjusts the stage position to center it on the tether
  • Try to get nicer calibration data
  • Function that finds the center
  • Feed in recorded data in a simulation
• Look at the properties of the tether, to calculate the persistence and contour lengths

What I have learned

• How to talk to the DAQ and ActiveX controls
• More about QPD and piezo-electric
• How to put a button on a UI in Matlab!!

How I did it

Centering Function

• First, I learned how to activate channels, and talk to the DAQ
• I created a sine wave and had it repeat infinitely, then acquired that same data from the DAQ
• In the actual code, we decided to integrate into OTKB.m, so the following is just the functions within that code
• We begin by establishing a waveform in the x-direction, calculating the center position
  • Repeat in y-direction, then x-direction 4 times
• Take the mean calculated center positions and use that as the final centering position
• Invoke piezos to reset the center voltage at our calculated position

• The centering function itself required only that I bin and average my data, smooth it, then find the indices of the max and min and take the point in the middle of them.

Results

Proof of Concept for Center Calculation

Force/Stretching Estimation using nlinfit

(Calculated contour and persistence lengths are in nm)

Code

Centering Function

function pushbuttonDNATetherCenter_Callback(hObject, eventdata, handles)
    dnaTetherCentering(handles, uiSettings)

function DNATetherCentering(handles, uiSettings)
    accuracy = 1;
    accuracyY = 1;
    setParams = false;
    xcenter = false;
    ycenter = false;
    while accuracy < 4;
        if ~setParams
            xaxisPiezoDriver = handles.PiezoDriverDescriptorList{1};
            yaxisPiezoDriver = handles.PiezoDriverDescriptorList{2};
            handles.SamplesToSave = uiSettings.numberofSeconds*uiSettings.sampleRate;

            Amplitude = uiSettings.stageOscillationAmplitude;
            waveformFreq = round(uiSettings.sampleRate / uiSettings.stageOscillationFrequency);
            time = linspace(0:length(numberOfSamples)-1,numberOfSamples);
            centeringcycle = Amplitude*sin(2*pi*waveformFreq * time)';
            waveform = [centeringcycle zeros(length(centeringcycle),1)]; 
            numberOfSamples = sampleRate * duration; %set sampleRate and duration;

            set(handles.DaqInput.ObjectHandle,'SampleRate',400);
            set(handles.DaqInput.ObjectHandle,'Trigger','Manual');
            set(handles.DaqInput.ObjectHandle,'SamplesPerTrigger',numberOfSamples);

            set(handles.DaqOutput.ObjectHandle,'Trigger','Manual');
            set(handles.DaqOutput.ObjectHandle,'RepeatOutput',3);
    % 
            setParams = true;
        end
        start(handles.DaqInput.ObjectHandle);
        data = getdata(handles.DaqInputHandle);
        Trigger(handles.DaqInput.Output.ObjectHandle);
        putdata(handles.DaqOutput.ObjectHandle,waveform);
        start(handles.DaqOutput.ObjectHandle);
        Trigger(handles.DaqOutput.ObjectHandle);
        waveform = findCenter(data, xcenter, ycenter, waveform);
        stop(handles.DaqInput.ObjectHandle);
        stop(handles.DaqOutput.ObjectHandle);
    end
        
        
    function waveform = findCenter(data, xcenter, ycenter, waveform)

        [quantizedXAxisx BinnedDatax StandardDeviationx Countx] = BinData( ...
         data, 'XColumn', 3, 'YColumn', 1);
        [quantizedXAxisy BinnedDatay StandardDeviationy County] = BinData( ...
         data, 'XColumn', 4, 'YColumn', 2);
        data = [BinnedDatax' BinnedDatay' quantizedXAxisx' quantizedXAxisy']; % qpdx qpdy piezx piezy

        centeredPosition = (positionOfMaxVoltage + positionOfMinVoltage)/2;
        fprintf('The position of the stage is %d',centeredPosition);

        if ~xcenter && ~ycenter
            [MaxValue MaxVoltageIndex] = max(data(:,1));
            positionOfMaxVoltage = centeringcycle(MaxVoltageIndex(1));
            [MinValue MinVoltageIndex] = min(data(:,1));
            positionOfMinVoltage = centeringcycle(MinVoltageIndex(1));
            centeredPosition = (positionOfMaxVoltage + positionOfMinVoltage)/2;
            invoke(handles.PiezoDriverDescriptorList{1}.DriverActiveXControl,...
             'SetPosOutput', 0, centeredPosition);
            xcenter = true;
            waveform = [zeros(length(centeringcycle),1) centeringcycle ]; 

        elseif xcenter && ~ycenter
            [MaxValue MaxVoltageIndex] = max(data(:,2));
            positionOfMaxVoltage = centeringcycle(MaxVoltageIndex(1));
            [MinValue MinVoltageIndex] = min(data(:,2));
            positionOfMinVoltage = centeringcycle(MinVoltageIndex(1));
            centeredPosition = (positionOfMaxVoltage + positionOfMinVoltage)/2;
            invoke(handles.PiezoDriverDescriptorList{2}.DriverActiveXControl,...
             'SetPosOutput', 0, centeredPosition);
            fprintf('The position of the stage is %d',centeredPosition);
            waveform = [ centeringcycle zeros(length(centeringcycle),1)]; 
            if accuracyY == 4;
               centeredPosition = mean(CheckaccuracyYposition);
               invoke(handles.PiezoDriverDescriptorList{2}.DriverActiveXControl,...
                'SetPosOutput', 0, centeredPosition);
            end
            CheckaccuracyYposition(accuracyY) = centeredPosition;
            accuracyY = accuracyY + 1;
            ycenter = true;

        elseif xcenter && ycenter 
            [MaxValue MaxVoltageIndex] = max(data(:,1));
            positionOfMaxVoltage = centeringcycle(MaxVoltageIndex(1));
            [MinValue MinVoltageIndex] = min(data(:,1));
            positionOfMinVoltage = centeringcycle(MinVoltageIndex(1));
            centeredPosition = (positionOfMaxVoltage + positionOfMinVoltage)/2;
            CheckaccuracyXposition(accuracy) = centeredPosition;
            waveform = [ centeringcycle zeros(length(centeringcycle),1)];
            % center to mean value of all checkaccuracyXposition
            if accuracy == 4;
               centeredPosition = mean(CheckaccuracyXposition);
               invoke(handles.PiezoDriverDescriptorList{1}.DriverActiveXControl,...
                'SetPosOutput', 0, centeredPosition);
            end
            accuracy = accuracy +1;
            ycenter = false;
        end

Persistence and Contour Length Estimation

Y = 1;          % Young's modulus
I = 1;          % moment of inertia
T = 293;        % Temperature K
k_B = 1.38e-23; % Boltzmann's constant (m^2 kg)/(s^2 K)
x = 10;         % end to end extension of DNA tether

l_p = 45;       % persistence length nm (Y * I)/(k_B * T);
l_c = 1180;     % contour length nm

datax = load('pretty nice DNA tether 20mw 1.txt');

datax(:,3) = datax(:,3)*2.22; % 2.22 um/V
datax(:,1) = datax(:,1)/(.5); % .5 V/um

location = [1 1];

edgesx = linspace(min(datax(:,3)), max(datax(:,3)), 1e3);
[l, whichbinx] = histc(datax(:,3), edgesx);
binmeansx = zeros(1, length(edgesx-1));

for i = 1:length(edgesx)-1
    flagmembers = (whichbinx == i);
    members = datax(flagmembers,1);
    binmeansx(i) = mean(members);
end

smoothedx = smooth(binmeansx,200);
[xmin xminindex] = min(smoothedx);
[xmax xmaxindex] = max(smoothedx);
middlex = ceil(mean([xminindex xmaxindex]));

x_stage = edgesx(xmaxindex:xminindex); %, smoothedx(xmaxindex:xminindex)
x_bead = 1e3*abs(smoothedx(middlex) - smoothedx(xmaxindex:xminindex))';

y = x_bead*5e-5; % 5e-5 N/um
myFunction = @ (x, xdata)  forceApplied(Y, I, T, x_bead, x(1), x(2));
 
beta = nlinfit(x_bead, y, myFunction, [45, 1180]);

figure()
semilogx(x_bead, forceApplied(Y, I, T, x_bead, beta(1), beta(2)))
ylabel('Force [pN]')
xlabel('Tether Extension [nm]')
title(['DNA Tether Stretching - L_p: ', num2str(beta(1)), ' L_c: ', num2str(beta(2))])</nowiki