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<!DOCTYPE html>
<html ng-app='ITC'>
<head>
<meta charset="utf-8">
<meta http-equiv="X-UA-Compatible" content="IE=edge">
<meta name="viewport" content="width=device-width, initial-scale=1.0">
<script src="https://oss.maxcdn.com/html5shiv/3.7.2/html5shiv.min.js"></script>
<script src="https://oss.maxcdn.com/respond/1.4.2/respond.min.js"></script>
<title>Oxford Chemistry - ITC Experimental Design Strategy Puzzle</title>
<meta property="og:url" content="https://learntech.imsu.ox.ac.uk/SPR/" />
<meta property="og:type" content="website" />
<meta property="og:title" content="Experimental Design Strategy Puzzle (SPR) - Oxford Biochemistry" />
<meta property="og:description" content="Learn experimental design through playing with a simulation of surface plasmon resonance. Created by Oxford Biochemistry Department." />
<meta property="og:image" content="http://www.your-domain.com/path/image.jpg" /
<!-- Angular Libraries & Credits -->
<script type="text/javascript" src="libraries/angular/angular.js"></script>
<script src="https://ajax.googleapis.com/ajax/libs/angularjs/1.4.8/angular-route.js"></script>
<script type="text/javascript" src="libraries/angular/angular-cookies.min.js"></script>
<!-- jQuery Libraries & Credits, load before Bootstrap & Flot since they requires it -->
<script type="text/javascript" src="libraries/jquery/jquery-1.11.3.min.js"></script>
<!-- Bootstrap Libraries -->
<link rel="stylesheet" href="libraries/bootstrap/bootstrap.min.css">
<link rel="stylesheet" href="libraries/bootstrap/bootstrap-theme.min.css">
<script type="text/javascript" src="libraries/bootstrap/bootstrap.min.js"></script>
<!-- Angular Flot Chart Libraries & Credits -->
<script type="text/javascript" src="libraries/flot/jquery.flot.js"></script>
<script type="text/javascript" src="libraries/flot/angular-flot.js"></script>
<script type="text/javascript" src="libraries/flot/jquery.flot.tooltip.min.js"></script>
<script type="text/javascript" src="libraries/flot/jquery.flot.axislabels.js"></script>
<script type="text/javascript" src="libraries/flot/jquery.flot.selection.js"></script>
<script type="text/javascript" src="scripts/services/chart-config.js"></script>
<!-- Ui-grid Libraries & Credits -->
<link rel="stylesheet" href="libraries/ui-grid/ui-grid.min.css">
<script type="text/javascript" src="libraries/ui-grid/ui-grid.min.js"></script>
<script type="text/javascript" src="libraries/ui-grid/exporter.js"></script>
<script type="text/javascript" src="libraries/ui-grid/selection.js"></script>
<script type="text/javascript" src="libraries/random.js"></script>
<script type="text/javascript" src="scripts/services/table-config.js"></script>
<!-- Google Fonts Web Font Embedding & Credits
<link rel='stylesheet' type='text/css' href='https://fonts.googleapis.com/css?family=PT+Sans:700'>
<link rel='stylesheet' type='text/css' href='https://fonts.googleapis.com/css?family=Work+Sans:300,500'>-->
<!-- Personal libraries, load last since these files will be referencing to those previous libraries too -->
<script type="text/javascript" src="scripts/index_modules.js"></script>
<script type="text/javascript" src="scripts/services/system_model.js"></script>
<script type="text/javascript" src="scripts/services/experiment_status.js"></script>
<script type="text/javascript" src="scripts/services/output_model.js"></script>
<script type="text/javascript" src="scripts/filters/time_filter.js"></script>
<script type="text/javascript" src="scripts/filters/keylength.js"></script>
<!-- <script type="text/javascript" src="scripts/filters/mw_filter.js"></script>
<script type="text/javascript" src="scripts/filters/uM_filter.js"></script> -->
<script type="text/javascript" src="scripts/index_controller.js"></script>
<link rel="stylesheet" href="styles/main.css">
<title>ITC SIMULATION</title>
</head>
<body ng-controller="viewControl as view">
<!-- Distinguishing content for small device size media query -->
<div class="smallDevice">
<h1 class="smallDevice-heading">Oh No!</h1><br>
<h4 class="smallDevice-message">We know you are excited to start the practical</h4>
<h4 class="smallDevice-message">However, for the best experience</h4>
<h4 class="smallDevice-message">we would suggest switching to a device with larger screen size <br><font color="red">(at least an iPad viewing in landscape)</font></h4>
<h4 class="smallDevice-message">See you there!</h4>
</div>
<!-- Distinguishing content for large device size media query -->
<div class="largeDevice" style="min-height: 100%; padding-bottom: 150px; position:relative;">
<!-- 1. Navigation Bar -->
<nav id="oxonHeaderFooter" class="navbar navbar-fixed-top navbar-custom">
<div class="navbar-menu">
<!--a href="" class="navbar-text navbar-link">HOME</a>
<a href="" class="navbar-text navbar-link">OBJECTIVES</a>
<a href="" class="navbar-text navbar-link">SPR</a>
<a href="" class="navbar-text navbar-link">EXPERIMENT DESIGN</a>
<a href="" class="navbar-text navbar-link">CRITIQUE</a>
<div class="navbar-text navbar-clicked">SIMULATION</div>
<a href="" class="navbar-text navbar-link">SUMMARY</a>
<a href="" class="navbar-text navbar-link">CONTACT</a-->
<div id="navbar-placeholder">Goal: Complete the tutorial to teach yourself Isothermal Titration Calorimetry and practice experimental design skills.</div>
</div>
</nav>
<!--MODALS-->
<!-- INITIALIZATION MODAL -->
<div id="initialising_modal" class="modal fade in" tabindex="-1" role="dialog">
<div class="modal-dialog" role="document">
<div class="modal-content">
<div class="modal-header">
<!--button type="button" class="close" data-dismiss="modal" aria-label="Close"><span class="modal-cross" aria-hidden="true">×</span></button-->
<h4 class="modal-title" id="modalLabel">Welcome to ITClab!</h4>
</div>
<div class="modal-body">
Welcolme to the Isothermal Titration Calorimetry Laboratory - ITClab<br><br>
The aim of the lab is to teach you to characterise an association reaction by designing an ITC experiment. This software is designed to mimic an ITC machine, allowing you to control the independent variables and have access to the results.<br><br>
However, before you can begin playing the game, we want to teach you the theory and practice behind the technique. By reading the informaion available here, integrating it with your prior knowledge, and answering questions you will have a strong grounding in ITC. <br><br>
<font color="#51A7F9">Hence this lab is broken into 2 parts:</font><br>
(1) <font color="#c5b552">Exploration:</font> You explore the software and answer questions on the presented material. Answering some questions will unlock other questions and information while answering other questions will unlock aspects of the software.<br>
(2) Game: You use the knowlege you gained in exploration to design, run and analyse an ITC experiment. The game becomes avaialable on completion of Part (1) <br><br>
First, we will show you how the questions work...<br><br>
<font color="#51A7F9">QUESTION MECHANICS</font><br>
In order to unlock the game part of this tutorial, you must answer all questions throughout correctly. Questions are presented in multiple choice format. If you get the question wrong at first then you will be prompted to answer the question again, but this time you also have to write a short paragraph explaing your reasoning.
<br><br>
This example shows you how it works - take a few moments to answer the question both right and wrong (refresh the page in between):
</div>
<div class=question-box ng-show='view.experiment.questions[0].IsCorrect==null'>
<div class='modal-question-question'>Example Question</div>
<div class=modal-question-content>
{{view.experiment.questions[0].question}}<br><br>
{{view.experiment.questions[0].A}}<br>
{{view.experiment.questions[0].B}}<br>
{{view.experiment.questions[0].C}}<br>
{{view.experiment.questions[0].D}}<br>
</div>
<div class='modal-question-footer'>
<select id='mquestion' class='units_dropdown' ng-model='answer' ng-init="answer=1">
<option ng-value="1">A</option>
<option ng-value="2">B</option>
</select>
<button type='button' class='button clickable2' ng-click="view.experiment.mQuestionConfirm(answer,0)">CONFIRM ANSWER</button>
</div>
</div>
<div class=question-box ng-show='view.experiment.questions[0].IsCorrect'>
<div class='modal-question-title-correct'>Correct!</div>
<div class=modal-question-content>
Congratulations, you answered the first question right! It will get harder...<br><br>
An isothermal process is one in which the temperature of the system does not change. This can be achieved by using a large heat sink (such as a constant temperature water bath) surrounding the system. Any heat released/absorbed by the system is absorbed/released by the water bath, keeping the temperature constant.
</div>
<div class='modal-question-footer'></div>
</div>
<div class=question-box ng-show='view.experiment.questions[0].IsCorrect==false && view.experiment.questions[0].beenWrong==1'>
<div class='modal-question-title'>Example Written Question</div>
<div class=modal-question-content>
Your answer is incorrect. Please answer the question again, but this time explain your answer in the box below.<br><br>
This written answer will be checked by the demonstrator at the end of the exploration. <br><br>
<b>Contact the demonstrator now if you are having problems. If you are incorrect again the demonstrator will help you before you can continue.</b><br><br>
{{view.experiment.questions[0].question}}<br><br>
{{view.experiment.questions[0].A}}<br>
{{view.experiment.questions[0].B}}<br>
{{view.experiment.questions[0].C}}<br>
{{view.experiment.questions[0].D}}<br>
(You do not need to enter anything here for now.)
</div>
<div class='modal-question-footer'>
<form novalidate name='writtenAnswer'>
<textarea class='answer-form' name='WrittenAnswer' ng-model='WrittenAnswer' type='string' rows='4' placeholder='Written answer here...'></textarea>
<select id='mquestion' class='units_dropdown' ng-model='answer' ng-init="answer=A" >
<option ng-value="1">A</option>
<option ng-value="2">B</option>
</select>
<button type='button' class='button clickable2' ng-click="view.experiment.wQuestionConfirm(answer,WrittenAnswer,0)">CONFIRM BOTH ANSWERS</button>
</form>
</div>
</div>
<div class=question-box ng-show='view.experiment.questions[0].IsCorrect==false && view.experiment.questions[0].beenWrong==2'>
<div class='modal-question-title'>Incorrect!</div>
<div class=modal-question-content>
Your answer is incorrect for the 2nd time, please contact a demonstrator to discuss.
</div>
<div class='modal-question-footer'></div>
</div>
<div class ='modal-body'>
You may have noticed that if you answer the question wrong a second time a different prompt appears with no option to answer again (try this now). At this point you should consult the demonstrator who will help you understand where you have gone wrong. Your progress through the tutorial is monitored and questions are unlocked as you answer others correctly, so it may be necessary to ask the demonstrator to help you immediately. When the demonstrator is happy that you understand, they will change the question to 'correct', and you are free to continue.<br><br>
From here on your answers will be saved - refreshing will not reset your previous attempts...
</div>
<div class='modal-body' id='center_buttons'>
<button type="button" class="modal-button clickable2" data-dismiss="modal" ng-click='view.experiment.questions[0].IsCorrect=null'>Continue</button>
</div>
</div>
</div>
</div>
<!-- THEORY MODAL -->
<div id="basics_modal" class="modal fade" tabindex="-1" role="dialog">
<div class="modal-dialog" role="document">
<div class="modal-content">
<div class="modal-header">
<button type="button" class="close" data-dismiss="modal" aria-label="Close"><span class="modal-cross" aria-hidden="true">×</span></button>
<h4 class="modal-title" id="modalLabel">THEORY</h4>
</div>
<div class="modal-body">
WHAT IS THE PURPOSE OF AN ITC EXPERIMENT?<br><br>
ITC is a biophysical technique that is used to determine the thermodynamic parameters of association reactions. In just one well designed ITC experiment, the parameters ΔH<sub>R</sub>, K<sub>eq</sub> and the stoichiometry (n) can all be determined. From these, ΔG<sub>R</sub> and ΔS<sub>R</sub> can also easily be calculated. It is the only biophysical technique where all of these thermodynamic parameters can be determined simultaneously.<br><br>
It is achieved by measuring the heat rate (absorbed or realeased) during a binding event after an injection of titrant into the titrand. <br><br>
(add more on how useful it is vs other calorimeters - power vs total heat, sensitivity (power compensation))
</div>
<div class=question-box ng-show='view.experiment.IsCorrect[1]==null'>
<div class='modal-question-title'>Question!</div>
<div class=modal-question-content>
{{view.experiment.questions[1].question}}
</div>
<div class='modal-question-footer'>
<form novalidate name='writtenAnswer'>
<textarea class='answer-form' name='WrittenAnswer' ng-model='WrittenAnswer' type='string' rows='4' placeholder='Written answer here...'></textarea>
<button type='button' class='button clickable2' ng-click="view.experiment.wQuestionConfirm(answer,WrittenAnswer,questionnumber)">SUBMIT</button>
</form>
</div>
</div>
<div class=question-box ng-show='view.experiment.questions[1].IsCorrect==!null'>
<div class='modal-question-title-correct'>Correct!</div>
<div class=modal-question-content>
Thank you for your answer, it will be checked by the demnstrator at the end of the tutorial.<br><br>
</div>
<div class='modal-question-footer'></div>
</div>
<div class='modal-body'>
HOW ARE THE MEASUREMENTS TAKEN?<br><br>
In a standard ITC machine there are two cells (shown below): the SAMPLE CELL (filled with a sample solution) and the REFERENCE CELL (filled with buffer solution); both are in good thermal contact with a large heat sink (an ADIABATIC JACKET), and a small amount of heat power (a baseline) is applied equally to both cells via separate heaters. The ligand is injected into the sample cell with a very sensitive, programable mechanical SYRINGE. The temperature difference between the two cells is measured continuously and heat power to the sample cell is adjusted via a FEEDBACK LOOP to maintain the cells at exactly equal temperatures. Hence, if the reaction is exothermic the power applied to the SAMPLE CELL (relative to the baseline power) is reduced, and visa versa for endothermic reactions. This differential power is the direct observable of the experiment and is used to calculate how much heat is released or absorbed during each injection. <br><br>
<img src="images/itcDiagram.png" alt='Diagram of ITC machine' style="width:300px;height:260px;display:block;margin:auto"></img><br><br>
</div>
<!-- EXAMPLE: ONE INJECTION -->
<div class=question-box ng-show='view.experiment.examples[0].isComplete==false || view.experiment.examples[1].isComplete==false'>
<div class='modal-example-title'>EXAMPLE 1!</div>
<div class=modal-question-content>
Its time to run your first ITC experiment!<br><br>
In this example we want you to get used to how the machine works by running two double injection experiments with different equilibration times (injection interval/time between injections).<br><br>
Objectives:<br>
+ Learn how the inputs of the machine work.<br>
+ Understand the shape of the single injection output and how it relates to the required time between injection.<br>
+ Understand if an output is exothermic or endothermic.<br><br>
Here are the parameters we want you to enter to the input fields on the right (all stay constant apart from time between injections):<br>
Number of Injections: 1,<br>
Volume of injections: 10μl,<br>
[ligand]: 300μM<br>
[macromolecule]: 30μM<br>
Time between injections: 1 and 5<br><br>
<i>When you 'Process' the results the software integrates each individual injection peak and plots it against the molar ratio of ligand to sample. It outputs these data to the 'Results Table' below the Console. These data can be exported by clicking the menu item on the table and then clicking 'export to .csv'.<br><br>
You do not need to export the data from this experiment. </i>
</div>
<div class='modal-question-footer'>
<button type="button" class="modal-button clickable2" data-dismiss="modal" ng-click="view.runExample([0,1])">Start Example</button>
</div>
</div>
<div class=question-box ng-show='view.experiment.examples[0].isComplete==true && view.experiment.examples[1].isComplete==true'>
<div class='modal-example-title'>EXAMPLE 1 COMPLETE!</div>
<div class=modal-question-content>
Well Done!<br><br>
That was an example with just two injections. The power profile is defined by a sharp change, followed by an exponential return to equilibrium value. Initially when the ligand is injected the net rate (forwards vs reverse) is at its highest, hence the large heat output. As the mixture comes closer to equilibrium, the net rate gets closer and closer to 0 (forwards rate ≈ backwards rate) and less and less heat is released.<br><br>
During ITC, it is very important that the cell is allowed to equilibrate between injections. Equilibration time changes is due to kinetic factors - a lower rate results in longer equilibration time. It may be useful to check using a similar two injection experiment whether the time between injections is long enough to achieve equilibration. Do not just use an unneccessarily long equillibration time because the experiment will take much longer than it should!
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<!-- QUESTION: TWO INJECTIONS -->
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{{view.experiment.questions[2].D}}<br>
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<div class="modal-body">
WHAT DOTHE RESULTS OF AN ITC EXPERIMENT LOOK LIKE AND WHY?<br><br>
An ITC experiment consists of not just one or two injections but a series of injections (25-30 is normal). The molar ratio of titrant to titrand (ligand:sample) increases stepwise over the course of the experiment. The heat change is not constant for each injection due to the increasing saturation of the sample. If the experiment is well designed then the set of injections will produce very varied heats of injection over the molar ratio range. <br><br>
Lets consider why the total heat produced per injection varies over the course of the experiment (an exothermic example): on the first few injections, almost all of the ligand associates with the sample, producing the most heat for one injection. With subsequent injections, the sample already has more ligand associated to it, and hence less of the injected ligand will bind, producing less heat per injection. As the sample heads past the equivalence point and into the late stages of the experiment, less and less ligand binds to a more saturated sample, until the sample is fully saturated and no heat is released upon injection.<br><br>
The resulting graph takes a sigmoidal shape with the inflection point of the graph representing the stoichiometry of the reaction. A typical ITC experimental output is seen below. The graph on top is the raw data output. By integrating each peak, you get a total heat output per injection, which is plotted in the lower half of the figure below. It is possible to change the x-axis to molar ratio for convienience. <br><br>
The thermodynamic parameters can be extracted from this graph, either using an computer based iterative method, or a less robust manual method. <br><br>
<img src="images/itcOutput.png" style='width:300px;height:360px;display:block;margin:auto'>
ANALYSIS<br><br>
The thermodynamic parameters can be extracted from this graph, either using an computer based iterative method, or a less robust manual method. Both will breifly be discussed here: <br><br>
The stoichiometry (n) is easy: it is represented by the position of the infection point. For instance, if the inflection point is located at a molar ratio of 1, then n=1. If it is at 3, then n = 3.<br><br>
<u>(1) Iterative Method</u><br>
The method solves for ΔH<sub>R</sub> and K<sub>eq</sub> simultaneously by starting from an approximate K<sub>eq</sub> and then calculating hypothetical ΔH<sub>R</sub> for each addition of titrant. Based on the variation between these enthalpy figures, the approximate K<sub>eq</sub> value is adjusted, and the enthalpies recalculated. Over a large number of iterations, the variation between the individual ΔH<sub>R</sub> is minimised, to yield the values of K<sub>eq</sub> and ΔH<sub>R</sub>.<br><br>
<u>(2) Asymptote Method</u>
First, ΔH<sub>R</sub> is calculated from a non-zero asymptote of the sigmoidal curve binding isotherm. The complete reaction of a vanishingly small addition of titrant can be assumed (the relative extent of reaction approaches unity as the concentration approaches zero).<br><br>
Once the figure for ΔH<sub>R</sub> is known, the extent of reaction for each injection can be calculated (from total heat evolved through to that addition relative to the total moles of titrant added through that same point) and hence values for K<sub>eq</sub> can be found for each injection (from total amounts of product formed and reactant remaining based on each total extent of reaction). Importantly, the value of K<sub>eq</sub> is calculated with the least error in the inflection region of the experiment. For the earliest or latest points in the titration, there is very high relative error resulting from very little product formed or very little reactant remaining, hence the lowest-uncertainty association constant results will come from the middle part of the titration curve.<br><br>
The analysis using the asymptote method will be covered in detail later in the tutorial, when you will create a spreadsheet that will allow you to complete many sets of data analysis.
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<b>Contact the demonstrator now if you are having problems. If you are incorrect again the demonstrator will help you before you can continue.</b><br><br>
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{{view.experiment.questions[3].A}}<br>
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<!-- EXPERIMENTAL OVERVIEW MODAL -->
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<h4 class="modal-title" id="modalLabel">Experimental Overview</h4>
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The basics steps that make up an ITC experiment are laid out below:<br><br>
+ <b>Planning</b><br>
Select: concentrations, volume of injection, number of injections, time between injections<br><br>
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<div class="modal-body" ng-show="expression">
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+ <b>Solution Preparation</b><br>
Do: make solutions, ?test solutions for concenrations<br><br>
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+ <b>Collect Raw Data</b><br>
Run the experiment<br><br>
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+ <b>Correct Raw Data</b><br>
Determine other contributions to heat release and adjust raw data<br><br>
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+ <b>Process and Analyse Data</b><br>
Determine if hypothesis has been tested and/or disproved/proved<br><br>
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+ <b>Repeat</b><br>
If results are inconclusive, adjust parameters/hypothesis accordingly and re-run experiment.<br><br>
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<h4 class="modal-title" id="modalLabel">PLANNING</h4>
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<div class="modal-body">
Before you try to design a good experiment, you need to first understand the technique you are using and what you are expecting. Review your knowledge on ITC in the Theory Tab, or ask a demonstrator if you need any help.<br><br>
Planning of an ITC experiment is very important. Being able to determine ΔH<sub>R</sub> and K<sub>eq</sub> relies on choosing the correct concentrations of ligand and sample macromolecule because:<br><br>
+ finding ΔH<sub>R</sub> is constrained by the sensitivity of the instrument - if not enough heat is produced per injection because concentrations are too low (signal to noise ratio is to low) then you cannot find ΔH<sub>R</sub>.<br><br>
+ finding K<sub>eq</sub> depends on the heat change varying between injections to produce a smooth sigmoid that was discussed in 'Theory'. The shape of the curve is a function of K<sub>eq</sub> and the concentration of macromolecule in the samle cell. <br><br>
How is the shape affected by changing K<sub>eq</sub> and [Macromolecule]? Lets find out!<br><br>
Brandt's experimental parameter (c) is defined by:<br><br>
<div style='text-align: center'><i>c = K<sub>eq</sub> x [Macromolecule] x n</i> </div><br><br>
It has been determined that for the sigmoidal curve to be the correct shape to acheive characterisation, c should lie between 10 and 1000, with best results found in the middle of the range. Hence, in order to plan an ITC experiment, you need to have a rough idea of K<sub>eq</sub>, so that you can choose a concentration of macromolecule which brings c into the acceptable range. <br><br>
It seems counterintuitive that in order to design a good experiment and determine the parameters ΔH<sub>R</sub> and K<sub>eq</sub> and the stoichiometry you need to have a rough estimate of those parameters! Normally when attempting to run an ITC, data will be gathered to asertain a rough estimate of them beforehand. Techniques that are used to find estimates of K<sub>eq</sub> include:<br>
+ Fluorescence spectroscopy<br>
+ Surface plasmon resonance<br>
+ etc<br>
ITC is then used to determine a much more accurate value of K<sub>eq</sub> and ΔH<sub>R</sub>.<br><br>
So [Macromolecule] is chosen to keep c within the acceptable range based on an estimate of K<sub>eq</sub>. How then, do you select the [ligand]? If you consider the stoichiometry of the reaction then it should become clear. We want the equivalence point of the reaction to occur halfway though the experiment, so select the concentrations that will achive this based on the stoichiometry. You will get some practice determining these concentrations shortly.<br><br>
When researchers were looking into the effect of c on the shape of the ITC curve, they simulated many ITC runs to work out exactly the acceptable range. Lets run a range of experiments to show the effect directly. From these results, we can discuss how best to select c values, and the specific limitations of high and low K<sub>eq</sub> values.<br><br>
But first, we need to be sure that we can calculate the concentrations of ligand and macromolecule required based on the Brandt's c parameter...
</div>
<!-- WORKED EXAMPLE 1 -->
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<div class='modal-example-title-'>Worked Example 1</div>
<div class=modal-question-content>
N.B. In this ITC machine the following is true:<br>
Volume sample cell = 0.000994l (994μl)<br>
Volume syringe = 0.000250l (250μl)<br><br>
In this example:<br>
K<sub>eq</sub> ≈ 4.0 x 10<sup>6</sup><br>
ΔH<sub>R</sub> ≈ -10 kJ/mol<br><br>
1) Calculate a suitable concentration for the macromolecule solution.<br>
2) Calculate a suitable concentration for the ligand solution.<br><br>
1) Recall that ideal conditions are 10<c<1000, where c = K<sub>eq</sub> x [Macromolecule] x n</i>. We select c = 50.<br><br>
c = 50 = (4.0 x 10<sup>6</sup>) x [macromolecule],<br>
[macromolecule] = 50/(4.0 x 10<sup>6</sup>) = 12.5μM<br><br>
2) We want the equivalence point to occur halfway through the titration, so moles of titrant should be twice the moles of ligand n<sub>macro</sub>=994μl*12.5μM = 12.425nM, thus n<sub>ligand</sub>=24.85nM.<br><br>
Assuming that we use the total volume of the syringe for the titration: [ligand] = 24.85nM/250μl = 99.4μM<br><br>
When you are happy with this calculation click continue, you will be asked to complete a similar calculation before we move on.
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<div class='modal-example-title-'>Calculation 1a</div>
<div class='modal-question-content'>
N.B. In this ITC machine the following is true:<br>
Volume sample cell = 0.000994l,<br>
Volume syringe = 0.000250l<br><br>
In this example:<br>
K<sub>eq</sub> ≈ 2.0 x 10<sup>9</sup><br>
ΔH<sub>R</sub> ≈ -21 kJ/mol<br><br>
<b>1) Calculate a suitable concentration for the macromolecule solution.</b><br>
afterwards you will be asked to:<br>
2) Calculate a suitable concentration for the ligand solution.<br><br>
Select c = 50 as previously.<br>
YOUR ANSWER SHOULD BE ENTERED IN MOLAR UNITS
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Macromolecule<br>
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<!-- CORRECT -->
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Congratulations, you answered the question right! <br><br>
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<div class='modal-example-title-'>Calculation 1a <b>Incorrect</b></div>
<div class='modal-question-content'>
<b>Your answer is wrong - please try again!</b><br><br>
N.B. In this ITC machine the following is true:<br>
Volume sample cell = 0.000994l,<br>
Volume syringe = 0.000250l<br><br>
In this example:<br>
K<sub>eq</sub> ≈ 2.0 x 10<sup>9</sup><br>
ΔH<sub>R</sub> ≈ -21 kJ/mol<br><br>
<b>1) Calculate a suitable concentration for the macromolecule solution.</b></b><br>
afterwards you will be asked to:<br>
2) Calculate a suitable concentration for the ligand solution.<br><br>
Select c = 50 as previously.<br>
YOUR ANSWER SHOULD BE ENTERED IN MOLAR UNITS
</div>
<div class='modal-question-footer'>
<form novalidate name='answer_form'>
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Please try again - Macromolecule<br>
<input class="form" name="macroConc" ng-model='macroConc' type="number" required>
<button type="button" class="modal-button clickable2" ng-click="view.mQuestion(macroConc,4)">Answer</button>
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<!-- WRONG 2X -->
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<div class='modal-question-title'>Incorrect!</div>
<div class=modal-question-content>
Your answer is incorrect for the 2nd time. The worked example can be found below:<br><br>
c = 50 = (2.0 x 10⁹) x [macromolecule],
[macromolecule] = 50/(2.0 x 1⁹) = 25nM
You will have to perfrom this calculation multiple times from here on.
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<div class='modal-example-title-'>Calculation 1b</div>
<div class='modal-question-content'>
N.B. In this ITC machine the following is true:<br>
Volume sample cell = 0.000994l,<br>
Volume syringe = 0.000250l<br><br>
In this example:<br>
K<sub>eq</sub> ≈ 2.0 x 10<sup>9</sup><br>
ΔH<sub>R</sub> ≈ -21 kJ/mol<br><br>
1) Calculate a suitable concentration for the macromolecule solution.<br>
answer to 1): {{view.experiment.questions[4].answer}}<br>
<b>2) Calculate a suitable concentration for the ligand solution.</b><br><br>
Select c = 50 as previously.<br>
YOUR ANSWER SHOULD BE ENTERED IN MOLAR UNITS
</div>
<div class='modal-question-footer'>
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Ligand Concentration<br>
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<!-- CORRECT -->
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Congratulations, you answered the question right! <br><br>
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<div class='modal-example-title-'>Calculation 1b <b>Incorrect</b></div>
<div class='modal-question-content'>
Your answer is wrong - please try again!<br><br>
N.B. In this ITC machine the following is true:<br>
Volume sample cell = 0.000994l,<br>
Volume syringe = 0.000250l<br><br>
In this example:<br>
K<sub>eq</sub> ≈ 2.0 x 10<sup>9</sup><br>
ΔH<sub>R</sub> ≈ -21 kJ/mol<br><br>
1) Calculate a suitable concentration for the macromolecule solution.<br>
afterwards you will be asked to:
<b>2) Calculate a suitable concentration for the ligand solution.</b><br><br>
Select c = 50 as previously.<br>
YOUR ANSWER SHOULD BE ENTERED IN MOLAR UNITS
</div>
<div class='modal-question-footer'>
<form novalidate name='answer_form'>
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Please try again - Macromolecule<br>
<input class="form" name="macroConc" ng-model='ligandConc' type="number" required>
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<!-- WRONG 2x -->
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<div class='modal-question-title'>Incorrect!</div>
<div class=modal-question-content>
Your answer is incorrect for the 2nd time. The worked example can be found below:<br><br>
We want the equivalence point to occur halfway through the titration, so moles of titrant should be twice the moles of ligand n<sub>macro</sub>=994μl*25nM = 24.85pmol, thus n<sub>ligand</sub>=49.7pmol.<br><br>
Assuming that we use the total volume of the syringe for the titration: [ligand] = 49.9pmol/250μl = 0.1988μM<br><br>
You will have to perfrom this calculation multiple times from here on so please study it.
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<div class='modal-example-title-'>Calculation 1b</div>
<div class='modal-question-content'>
N.B. In this ITC machine the following is true:<br>
Volume sample cell = 0.000994l,<br>
Volume syringe = 0.000250l<br><br>
In the previous examples we assumed that the stoichiometry (n) ≈ 1.0. Consider the case with higher n.<br><br>
In this example:<br>
K<sub>eq</sub> ≈ 2.0 x 10<sup>9</sup><br>
ΔH<sub>R</sub> ≈ -21 kJ/mol<br><br>
The stoichiometry (n) ≈ 3.0
1) Calculate a suitable concentration for the macromolecule solution.<br>
answer to 1): {{view.experiment.questions[4].answer}}<br>
<b>2) Calculate a suitable concentration for the ligand solution.</b><br><br>
Select c = 50 as previously.<br>
YOUR ANSWER SHOULD BE ENTERED IN MOLAR UNITS
</div>
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Ligand Concentration<br>
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<!-- CORRECT -->
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<div class='modal-question-title-correct'>Correct!</div>
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Congratulations, you answered the question right! <br><br>
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<!-- WRONG -->
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<div class='modal-example-title-'>Calculation 1b <b>Incorrect</b></div>
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Your answer is wrong - please try again!<br><br>
N.B. In this ITC machine the following is true:<br>
Volume sample cell = 0.000994l,<br>
Volume syringe = 0.000250l<br><br>
In the previous examples we assumed that the stoichiometry (n) ≈ 1.0. Consider the case with higher n.<br><br>
In this example:<br>
K<sub>eq</sub> ≈ 2.0 x 10<sup>9</sup><br>
ΔH<sub>R</sub> ≈ -21 kJ/mol<br><br>
The stoichiometry (n) ≈ 3.0
1) Calculate a suitable concentration for the macromolecule solution.<br>
afterwards you will be asked to:
<b>2) Calculate a suitable concentration for the ligand solution.</b><br><br>
Select c = 50 as previously.<br>
YOUR ANSWER SHOULD BE ENTERED IN MOLAR UNITS
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Please try again - Macromolecule<br>
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<div class='modal-question-title'>Incorrect!</div>
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Your answer is incorrect for the 2nd time. The worked example can be found below:<br><br>
We want the equivalence point to occur halfway through the titration, so moles of titrant should be six times (n.b. n=3) the moles of ligand:<br> n<sub>macro</sub>=994μl*25nM = 24.85pmol, thus n<sub>ligand</sub>=0.1491nmol.<br><br>
Assuming that we use the total volume of the syringe for the titration: [ligand] = 0.1491pmol/250μl = 0.5964μM<br><br>
You will have to perfrom this calculation multiple times from here on so please study it.
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<!-- EXAMPLE 1A - 4x, 5x, 1x-->
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<div class='modal-example-title'>EXAMPLE 1a!</div>
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Now that we have shown you how to perform the calculations to select suitable concentrations based on c, lets run some experiments to have a look at the effect that changing c has on the results. Then we can use this data to inform future decisions on the value of c.<br><br>
We want to know:<br>
(1) how changing c affects the shape of the curve,<br>
(2) whether these changes are consistent across more than one K<sub>eq</sub> value.<br><br>
So lets run 8 experiments:<br>
4 with a value of K<sub>eq</sub> ≈ 4.0 x 10<sup>6</sup> with c values of 1, 10, 100, 1000,<br>
4 with a value of K<sub>eq</sub> ≈ 4.0 x 10<sup>9</sup> with c values of 1, 10, 100, 1000.<br><br>
Lets run these experiments!<br><br>
<i>In order to complete this example, you must run the 4 experiments with a K<sub>eq</sub> ≈ 4.0 x 10<sup>6</sup>. You will know you have completed each experiment correctly when a 'Success' reading is displayed on the console. This time we are going to plot the data in excel, so make sure you use the 'export to .csv' function after <b>EACH RUN</b> - the data is not maintained in the results table after that. </i><br><br>
The remaining parameters are set out below:<br>
Number of injections: 25<br>
Volume of Injections: 10μl<br>
Time bewtween injections: 5s<br><br>
ENSURE YOU EXPORT THE DATA FROM EACH RUN TO EXCEL!<br><br>
When you are successfull with all four, <b>return here to start the next four runs!</b>
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<div class='modal-example-title'>EXAMPLE 1a COMPLETE!</div>
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<i>HAVE YOU EXPORTED ALL THE DATA TO EXCEL? IF NOT, RETURN TO THE MAIN PAGE AND MAKE SURE THAT YOU DO BEFORE CLICKING CONTINUE.</i><br><br>
Well Done!<br><br>
Now we need to run the next 4 experiments with K<sub>eq</sub> ≈ 2.0 x 10<sup>9</sup> to compare.<br><br>
The remaining parameters are the same as before:<br>
Number of injections: 25<br>
Volume of Injections: 10μl<br>
Time bewtween injections: 5s<br><br>
When you are successful with the next four, return here!<br><br>
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<div class='modal-example-title'>EXAMPLE 1b COMPLETE!</div>
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Well Done!<br><br>
Now you have run 8 ITC experiments, with 4 different c values, and 2 different K<sub>eq</sub> values. You should have also exported all of the data to excel. Notice that when exporting, the software exports three columns of data:<br>
(1) Injection numben<br>
(2) Heat for injection.<br>
(3) Heat for injection per mole of injectant.<br><br>
So the third column is a version of the second column, normalised for moles of injectant. This normailies the two sets of 4 runs, since they occur at different concentrations.<br><br>
First, plot the normailised data into a scatter graph - all on the same graph.<br>
Then plot the non-normalised data into a scatter graph - all on the same graph.<br><br>
You can add connecting lines between the points for clarity, but remember that these lines are simply connectors, not a trendline or line of best fit!<br><br>
Take a look at the graphs. What do you notice?<br>
+ How does changing c effect the shape of the curve?<br>
+ Are these changes consistent over different values of K<sub>eq</sub>?<br><br>
Click continue when you are ready.
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Lets look at the normalised graphs first. The answer to our second question is hopefully straightforward when we see what has happened. The normalised heats of injection are identical for both values of K<sub>eq</sub>. Hence, the graphs at each c both follow exactly the same shape - they are exactly the same points on the graph!<br><br>
Now lets consider how the shape changes with c, looking at the normalised graphs again:<br>
<u>c=1:</u><br>
These are flat, featureless lines whose values slowly decrease in magnitude from low molar ratio to high. It is not possible to determine the K<sub>eq</sub> value from these graphs, since there is no sigmoidal shape. However, it is possible to determine the ΔH<sub>R</sub> values (more on how later).<br>
<u>c=10:</u><br>
The sigmaoid shape is slightly more pronounced in this example. You would still struggle to calculate K<sub>eq</sub> though, as the change in heats is not that big.<br>
<u>c=100:</u><br>
A significant sigmoid shape. All thermodynamics could be characterised.<br>
<u>c=1000:</u><br>
Very steep sigmoid function. Not many points in the infection region, so difficult to characterise c. As values of c get larger, the sigmoid become more and more like a step function - the inflection region occurs all in one injection so is not well defined. In these cases, it can be impossible to discern between two ligand-macromlecule pairs with K<sub>eq</sub> values even as far apart as an order of magnitude - the step functions are not different enough - both are simple step functions.<br><br>
Does it seem strange that we are talking about potentially using a range of c values equivalent to 2 orders of magnitude? Why do we not just used a value of c=100 every time?<br><br>
Consider the Example of K<sub>eq</sub> ≈ 4.0 x 10<sup>9</sup>, ΔH<sub>R</sub> = -10kJmol<sup>-1</sup>, c=100 that you just ran.
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{{view.experiment.questions[6].question}}<br><br>
K<sub>eq</sub> ≈ 4.0 x 10<sup>9</sup><br>
ΔH<sub>R</sub> ≈ -10 kJ/mol<br>
[Macromolecule] = 0.000000025<br>
[Ligand] = 0.000198<br>
c = 100<br><br>
Do you see any reason why this experiment would not provide suitable results?<br><br>
{{view.experiment.questions[6].A}}<br>
{{view.experiment.questions[6].B}}<br>
{{view.experiment.questions[6].C}}<br>
{{view.experiment.questions[6].D}}<br>
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<div class='modal-question-title-correct'>Correct!</div>
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Congratulations, you answered the question right! <br><br>
Because the value of k<sub>eq</sub> is much higher, and therefore the concentrations are much lower, the signal to noise ratio of the calorimeter will be TOO LOW to gather any useful data. In this case, we must choose a much higher value of c, so that the concentrations used cause a larger heat change upon addition.
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<div class='modal-question-title'>Incorrect!</div>
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Your answer is incorrect. <br><br>
Lets run another experiment to show why.
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<div class='modal-example-title'>EXAMPLE!</div>
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In this example we will investigate the effects of noise on the readings. In previous examples, the machine has produced 'perfect' results, that is results with no added noise, based on the mathmatics behind ITC. In the next experiments, a level of experimental noise has been added. The noise is absolute not relative (the standard deviation is constant, not based on the value of the mean).<br><br>
Objectives:<br>
+ Learn how noise effects the results.<br>
+ Understand how we must adjust our solution concentration selection to account for noise.<br><br>