Team:Imperial/CBD Kinetics Model

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                    <h1>CBD Kinetics Model</h1>
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                    <div id="navWrap">
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                        <div id="subNav">
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                            <ul>
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                                <li><a href="#introduction" class="smoothScroll">Introduction</a>
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                                </li>
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                                <li><a href="#maths" class="smoothScroll">Mathematical Background</a>
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                                </li>
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                                <li><a href="#lab" class="smoothScroll">Wet-Lab Interaction</a>
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                                </li>
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                                <li><a href="#results" class="smoothScroll">Results & Conclusions</a>
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                                </li>
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                                <li><a href="#references" class="smoothScroll">References</a>
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                                </li>
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                                                <li><a href="#code" class="smoothScroll">Code</a>
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                    <section id="introduction">
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                        <h2>Introduction</h2>
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                        <p>Based on a set of ordinary differential equations describing the kinetics of cellulose-binding modules (CBM) binding to bacterial cellulose, the model is designed to predict the efficiency and affinity of the binding process. Given an initial concentration of CBM injected into the system, the model is enabled to calculate the time allowed for a certain percentage of protein binding sites on bacterial cellulose to be saturated.</p>
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                    </section>
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                    <section id="maths">
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                        <h2>Mathematical Background</h2>
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                        <h3>Model I</h3>
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                        <ul>
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                            <li>Variables:
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                                <ul>
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                                    <li>CBS(0): initial concentration of cellulose binding sites (CBS)</li>
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<li>CBS(t): concentration of unoccupied CBS at time t</li>
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<li>CBM(0): initial concentration of CBM injected into the system</li>
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<li>CBM(t): concentration of unbound CBM</li>
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<li>CBS_CBM(t): concentration of binding complex (CBS bounded with CBM)</li>
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                                </ul>
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                            </li>
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                            <li>Parameters:
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                            <ul>
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                                <li>k<sub>on</sub>: association rate constant</li>
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<li>k<sub>off</sub>: dissociation rate constant</li>
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                                <li>K<sub>D</sub> = k<sub>off</sub>/k<sub>on</sub>: equilibrium dissociation constant</li>
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                                </ul>
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                            </li>
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                            <li>Binding Kinetics:
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                                <ul>
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                                    <li><img class="content-image " src="https://static.igem.org/mediawiki/2014/8/89/IC14-modelling-kinetics-binding1.png" height=250></li>
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                                    <li>Assume CBM(t) = CBM(0) due to large concentration of CBM injected into the system compared to initial concentration of cellulose binding sites.</li>
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                                    <li>With the boundary conditions:
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                                    <ul>
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                                        <li>CBS_CBM(0) = 0</li>
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                                        <li>CBS_CBM(∞) = CBS(0)</li>
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                                        </ul></li>
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                                    <li>The ODE can be solved as:
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                                    <ul>
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                                        <li><img class="content-image " src="https://static.igem.org/mediawiki/2014/a/ac/IC14-modelling-kinetics-binding2.png" height=60></li>
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                                        <li>where k<sub>on</sub> CBM(0) &gt;&gt; k<sub>>off</sub</li>
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                                        </ul></li>
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                                </ul>
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                            </li>
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                        </ul>
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                    </section>
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                    <section id="lab">
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                        <h2>Lab Interaction</h2>
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                        <figure class="content-image image-right image-small">
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                            <img class="image-full" src="https://static.igem.org/mediawiki/2014/8/8c/IC14-modelling-kinetics-synergy.png">
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                            <figcaption>How our model and the wetlab interact with each other</figcaption>
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                        </figure>
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                        <p>Parameters in the previous expression are determined by assay experiments where k<sub>off</sub> and k<sub>d</sub> are found, from which k<sub>on</sub> is calculated: k<sub>on</sub>=k<sub>off</sub>/k<sub>d</sub>.</p>
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                        <p>LAB RESULTS HERE
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</p>
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                        <p>With the parameters obtained from the experiments, the model is then enabled to predict an exact time period for the binding sites to be saturated, where the validity of the model is further confirmed by the experiments (refer to CBD expression experiments in the drive).
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                    </section>
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                    <section id="results">
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                        <h2>Results and Conclusions</h2>
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                        <figure class="content-image image-half">
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                            <img class="image-full" src="https://static.igem.org/mediawiki/2014/7/7c/IC14-modelling-kinetics-results1.png">
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                            <figcaption>Labelled points represent 70% saturation of bacterial cellulose binding sites.
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</figcaption>
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                        </figure>
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                        <figure class="content-image image-half">
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                            <img class="image-full" src="https://static.igem.org/mediawiki/2014/8/81/IC14-modelling-kinetics-results2.png">
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                            <figcaption>It could be observed from the graph that the CBM binding capacity reduces when initial CBM concentration increases beyond 15µM; therefore, an initial CBM concentration of 15 µM would be optimum to functionalise the bacterial cellulose.</figcaption>
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                        </figure>
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                    </section>
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                    <section id="references">
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                        <h3>References</h3>
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                        <ol>
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                            <li>Zhang, Mengmeng; Wang, Bin; Xu, Bingqian Mapping Single Molecular Binding Kinetics of Carbohydrate-Binding Module with Crystalline Cellulose by Atomic Force Microscopy Recognition Imaging J. Phys. Chem. B 2014, 118, 6714−6720s
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                    </section>
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                    <section id="code">
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                        <h3>Code</h3>
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                    </section>
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Revision as of 10:42, 8 October 2014

Imperial iGEM 2014

Aqualose

CBD Kinetics Model

Introduction

Based on a set of ordinary differential equations describing the kinetics of cellulose-binding modules (CBM) binding to bacterial cellulose, the model is designed to predict the efficiency and affinity of the binding process. Given an initial concentration of CBM injected into the system, the model is enabled to calculate the time allowed for a certain percentage of protein binding sites on bacterial cellulose to be saturated.

Mathematical Background

Model I

  • Variables:
    • CBS(0): initial concentration of cellulose binding sites (CBS)
    • CBS(t): concentration of unoccupied CBS at time t
    • CBM(0): initial concentration of CBM injected into the system
    • CBM(t): concentration of unbound CBM
    • CBS_CBM(t): concentration of binding complex (CBS bounded with CBM)
  • Parameters:
    • kon: association rate constant
    • koff: dissociation rate constant
    • KD = koff/kon: equilibrium dissociation constant
  • Binding Kinetics:
    • Assume CBM(t) = CBM(0) due to large concentration of CBM injected into the system compared to initial concentration of cellulose binding sites.
    • With the boundary conditions:
      • CBS_CBM(0) = 0
      • CBS_CBM(∞) = CBS(0)
    • The ODE can be solved as:
      • where kon CBM(0) >> k>off

Lab Interaction

How our model and the wetlab interact with each other

Parameters in the previous expression are determined by assay experiments where koff and kd are found, from which kon is calculated: kon=koff/kd.

LAB RESULTS HERE

With the parameters obtained from the experiments, the model is then enabled to predict an exact time period for the binding sites to be saturated, where the validity of the model is further confirmed by the experiments (refer to CBD expression experiments in the drive).

Results and Conclusions

Labelled points represent 70% saturation of bacterial cellulose binding sites.
It could be observed from the graph that the CBM binding capacity reduces when initial CBM concentration increases beyond 15µM; therefore, an initial CBM concentration of 15 µM would be optimum to functionalise the bacterial cellulose.

References

  1. Zhang, Mengmeng; Wang, Bin; Xu, Bingqian Mapping Single Molecular Binding Kinetics of Carbohydrate-Binding Module with Crystalline Cellulose by Atomic Force Microscopy Recognition Imaging J. Phys. Chem. B 2014, 118, 6714−6720s

Code

Retrieved from "http://2014.igem.org/Team:Imperial/CBD_Kinetics_Model"