Revision as of 08:46, 28 February 2012

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 We 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.

Estimating contour and persistence lengths

$ F = \frac{k_{B}}{l_{p}}[(\frac{1}{4}(1 - \frac{x}{l_{c}})^{-2} - \frac{1}{4} +\frac{x}{l_{c}}] $

where k_{B} is the Boltzmann constant, l_{c} is the contour length and l_{p} is the persistence length.

Results

Proof of Concept for Center Calculation

The following data is one example, taken from tethered bead data at 20 mW.

Force/Stretching Estimation using nlinfit

(Calculated contour and persistence lengths are in nm at 20mW)

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