Difference between revisions of "Team:Thessaloniki/Model"

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                 <circle-content title="Theory">
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                 <circle-content title="Workflow">
 
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                             <div class="col-xs-12 col-sm-10 col-md-9 col-lg-8">
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                                <h3>Dry Lab Workflow</h3>
 +
                                <p>
 +
                                    As Dry Lab our work consists of:
 +
                                    <ul>
 +
                                        <li>Accurately describe the mathematical representation
 +
                                            of
 +
                                            the biological system.</li>
 +
                                        <li>Create simulations that predict the behaviour of
 +
                                            the
 +
                                            system.</li>
 +
                                        <li>
 +
                                            Characterize system parameters by:
 +
                                            <ul>
 +
                                                <li>working with previous studies.</li>
 +
                                                <li>analyzing and prioritizing the effect that
 +
                                                    parameters have on the system output.</li>
 +
                                                <li>analyzing the robustness of the system and
 +
                                                    make
 +
                                                    observations.</li>
 +
                                            </ul>
 +
                                        </li>
 +
                                    </ul>
 +
                                </p>
 +
                                <p>
 +
                                    All of the above are going to be useful for your project,
 +
                                    as
 +
                                    you need to have a model, that can estimate the in vivo
 +
                                    system
 +
                                    behaviour of the system, in order to be able to make and
 +
                                    test
 +
                                    hypotheses that you and the Wet Lab poses.
 +
                                </p>
 +
                                <p>
 +
                                    <b>In this section</b> we our going to <b>share the
 +
                                        knowledge</b>
 +
                                    that we
 +
                                    gained, from our experience working for our project, in
 +
                                    designing and working on biological network motifs. You can
 +
                                    also view this section as <b>brief introduction on all the
 +
                                        things
 +
                                        we did</b>, as we put links as examples in the
 +
                                    workflow,
 +
                                    that take
 +
                                    you to our models.
 +
                                </p>
 +
                                <p class="text-center">
 +
                                    In Figure 1, we present a flowchart, that summarizes our
 +
                                    understanding regarding how you should approach the
 +
                                    modelling
 +
                                    of a biological network.
 +
                                    <img class="responsive-image" src="https://static.igem.org/mediawiki/2018/a/a2/T--Thessaloniki--model-flowchart.png"
 +
                                        alt="workflow explaining">
 +
                                    <small class="text-grey-5">Figure 1: Dry Lab workflow summarized in a
 +
                                        flowchart.</small>
 +
                                </p>
 +
                                <p>
 +
                                    The most important part is that you need to understand
 +
                                    perfectly how the system should work and what each
 +
                                    component of
 +
                                    the system does. This means, that you have to arrange
 +
                                    sessions
 +
                                    with Wet lab where you will discuss about the system and
 +
                                    you
 +
                                    ask as many questions as you have. These sessions will
 +
                                    never
 +
                                    end, but it’s important to arrange as many as you can when
 +
                                    starting off, in order to build a strong foundation on
 +
                                    understanding your system and what it has to offer.
 +
                                </p>
 +
 
 +
                                <p>
 +
                                    After that you will be confident enough to showcase the
 +
                                    interactions happening in the system and create a
 +
                                    mathematical
 +
                                    representation of it. The mathematical representation in
 +
                                    our
 +
                                    case, were the Ordinary Differential Equations of the
 +
                                    system
 +
                                    and the chemical reactions happening between different
 +
                                    components in the cell.
 +
                                </p>
 +
                                <p>
 +
                                    Furthermore, for the model to be accurate it has to have
 +
                                    well
 +
                                    characterized parameters. For this, you can actually do
 +
                                    many
 +
                                    things. We combined sensitivity and robustness analysis
 +
                                    alongside with a very extensive bibliography search. Our
 +
                                    methods are described later in this section and you can
 +
                                    find
 +
                                    implementations of them on both TALE and dcas9-sgRNA
 +
                                    models. As
 +
                                    shown in Figure 1, it is important to take into account,
 +
                                    that
 +
                                    the condition that will break the characterization loop is
 +
                                    different for each project and depends on what you want
 +
                                    from
 +
                                    your model and how accurate should it be.
 +
                                </p>
 +
                                <p>
 +
                                    And that’s it. After all these things, you have a model
 +
                                    that
 +
                                    tries its best to describe your system behaviour and
 +
                                    estimate
 +
                                    the concentration of the different components. But, we are
 +
                                    not
 +
                                    finished yet. Now you have to arrange new sessions with Wet
 +
                                    lab, show them your system, describe to them what you did
 +
                                    and
 +
                                    answer all the questions they have, and most importantly,
 +
                                    make
 +
                                    decisions about the system design that you could not answer
 +
                                    before. Now you can make any hypothesis for the system and
 +
                                    actually test it with your model. You should though, take
 +
                                    into
 +
                                    consideration, that the model is an estimation of the
 +
                                    reality
 +
                                    and depending on the effort you put in the designing and
 +
                                    characterizing it, you will get better or worse
 +
                                    estimations. As
 +
                                    an example, of how we used our models to help in the system
 +
                                    design, you can take a look at TALE tuning with IPTG-LacI,
 +
                                    dcas9-sgRNA repressor analysis, and dcas9 expression site
 +
                                    decision. As a last part of our model, we also tested the
 +
                                    implementation of IFFL in RNA level. On the other hand, an
 +
                                    example of how we integrated Wet lab’s feedback into our
 +
                                    model
 +
                                    is shown in Dcas9 subsystem.
 +
                                </p>
 +
                                <p>
 +
                                    Finally, when the experiments are finished you will have
 +
                                    the
 +
                                    chance to take the experimental data and the model
 +
                                    parameters
 +
                                    into them. This could be as simple as using the data
 +
                                    produced
 +
                                    by robustness analysis and finding the parameter set with
 +
                                    the
 +
                                    minimum distance from the experimental data, as we did in
 +
                                    TALE
 +
                                    robustness analysis, or using methods like linear/non
 +
                                    linear
 +
                                    regression, bayesian estimation etc. The most experimental
 +
                                    data
 +
                                    you have, the better for the model characterization. In our
 +
                                    case, the data we used [1] to fit the model was the system
 +
                                    error and for this reason, we had limited options regarding
 +
                                    what parameters we should fit to achieve the better
 +
                                    results. To
 +
                                    overpass this obstacle, we used the result from TALE
 +
                                    sensitivity analysis that showed as what was the most
 +
                                    influential parameters for the output and fitted them while
 +
                                    fixing the others.
 +
                                </p>
 +
                                <p>
 +
                                    Now you have a model, that is fitted to experimental
 +
                                    results
 +
                                    and you can use that model, if you want to continue your
 +
                                    work
 +
                                    in the system. If the experimental results, are not as
 +
                                    expected, after fitting your model to them, you can
 +
                                    optimize
 +
                                    the parameters or use new components and continue by giving
 +
                                    new
 +
                                    feedback to Wet lab. Again for optimizing you can perform a
 +
                                    new
 +
                                    robustness analysis, because with it you can test
 +
                                    extensively
 +
                                    different sets from the parametric space save and analyze
 +
                                    all
 +
                                    the results as you want. Another option that we considered,
 +
                                    is
 +
                                    a gradient descend algorithm but as we didn’t used it in
 +
                                    the
 +
                                    end, we will not discuss further about it. If computational
 +
                                    cost is not a problem for you, we would recommend
 +
                                    robustness
 +
                                    analysis, otherwise gradient descent algorithms or other
 +
                                    Artificial Intelligence algorithms are the way to go.
 +
                                </p>
 +
 
 +
                                <h4>Sensitivity analysis</h4>
 +
                                <h5>What is sensitivity analysis?</h5>
 +
                                <p>
 +
                                    The study of how uncertainty in the output of a model
 +
                                    (numerical or otherwise) can be apportioned to different
 +
                                    sources of uncertainty in the model input [3].
 +
                                </p>
 +
                                <h5>Why we use sensitivity analysis?</h5>
 +
                                <p>
 +
                                    When we construct a computational model, there are many
 +
                                    parameters that can not be identified, because it is likely
 +
                                    that a similar experiment has not been carried out. Also,
 +
                                    there is a chance where a similar experiment has been
 +
                                    carried out, but for minor variations of the experimental
 +
                                    arrangements, the changes in each parameter are large. It
 +
                                    is therefore extremely useful to use a mathematical
 +
                                    tool,the sensitivity analysis, with which we can come to
 +
                                    many conclusions that will help us to evolve the model. The
 +
                                    most important of them are[3]:
 +
                                </p>
 +
                                <p>
 +
                                    <b>Factor prioritization:</b> One reason for using
 +
                                    sensitivity analysis is to study the parameters in order to
 +
                                    identify the most important ones. The most important ones,
 +
                                    i.e. those with the highest sensitivity, are the ones that
 +
                                    cause the greatest variation in the final output. By
 +
                                    knowing what these are, we can focus on their precise
 +
                                    measurement to reduce the variance of the final system,
 +
                                    while providing a model that best approaches reality.
 +
                                </p>
 +
                                <p>
 +
                                    <b>Factor Fixing:</b> Having ranked parameters from the
 +
                                    most important to the less important, we can choose a fixed
 +
                                    point for the non-critical parameters that lies within the
 +
                                    originally defined range since it does not contribute much
 +
                                    to the output variance. In this way, we can better observe
 +
                                    the inter-relationships of important parameters in many
 +
                                    system subunits that contain a large set of kinetic
 +
                                    equations.
 +
                                </p>
 +
                                <p>
 +
                                    <b>Variance cutting:</b> To reduce the variance of the
 +
                                    output, we
 +
                                    can apply a series of sensitivity analyses, starting from
 +
                                    all system inputs and investigating each time which
 +
                                    parameters lead to greater sensitivity in output variance.
 +
                                    By removing the parameters, that are the most influential,
 +
                                    as long as they are characterized well for the biological
 +
                                    system we are studying, then the output variance that
 +
                                    remains is the sum of variations caused by the
 +
                                    non-important parameters which is not big. This leads the
 +
                                    system to fewer input parameters with less output variation
 +
                                    and simultaneous reduction of computational cost.
 +
                                </p>
 +
                                <p>
 +
                                    <b>Factor Mapping:</b> To achieve concrete outputs, we need
 +
                                    to
 +
                                    evaluate the relationships between inputs and which
 +
                                    parameter combinations lead to undue variation in output.
 +
                                    There are parameter interactions that for a particular
 +
                                    system cannot achieve system response within strictly set
 +
                                    limits and certain conditions. For example, in a system
 +
                                    that controls the amount of a toxic substance that, if
 +
                                    present in large quantities, can lead to cell destruction,
 +
                                    we need to explore the system's parameters, and find which
 +
                                    combinations lead to the desired results.
 +
                                </p>
 +
 
 +
                                <h4>Global vs Local Sensitivity analysis</h4>
 +
                                <p>Sensitivity analysis can be applied in 2 variations:</p>
 +
 
 +
                                <p>
 +
                                    Local sensitivity analysis evaluates changes in model
 +
                                    outputs with respect to variations in single parameter
 +
                                    input [3] [4]. In particular, a small change is made,
 +
                                    accompanied by a calculation of the local sensitivity
 +
                                    index, for each parameter separately. The local sensitivity
 +
                                    index of a parameter p is calculated by the partial output
 +
                                    of the system relative to the parameter for a very small
 +
                                    change of the parameter value.
 +
                                </p>
 +
 
 +
                                <p>
 +
                                    On the contrary, Global sensitivity analysis simultaneously
 +
                                    varies all parameters over the entire parameter space,
 +
                                    which allows to simultaneously evaluate the relative
 +
                                    contributions of each individual parameter as well as the
 +
                                    interactions between parameters to the model output
 +
                                    variance [3]. Because of this, global sensitivity is more
 +
                                    capable of approaching the parameters when non-linear
 +
                                    phenomena occur in the system.
 +
                                </p>
 +
 
 +
                                <p>
 +
                                    The biological systems that we study in synthetic biology
 +
                                    show many non-linear phenomena among their components and
 +
                                    the range of parameter values cannot always be found in
 +
                                    bibliography and is often considered large. For this
 +
                                    reason, it is proposed to explore the importance of the
 +
                                    parameters globally.
 +
                                </p>
 +
 
 +
                                <h4>Sobol sensitivity analysis</h4>
 +
 
 +
                                <p>
 +
                                    Below we describe the procedure followed by the Sobol
 +
                                    sensitivity analysis to calculate:
 +
                                    <ul>
 +
                                        <li>First and second order indices referring to the
 +
                                            contribution of a particular parameter to the
 +
                                            output and to the contribution of the interaction
 +
                                            between the pair of parameters respectively.</li>
 +
                                        <li>Total-effect indices to calculate the contribution
 +
                                            of a parameter in combination with its contribution
 +
                                            from its interactions with other parameters.</li>
 +
                                    </ul>
 +
                                    The algorithmic analysis process begins by producing a
 +
                                    sample from the input space of each parameter. This is done
 +
                                    by quasi-random sequences that produce samples that are
 +
                                    uniformly distributed in the area with small differences
 +
                                    between them and are often used for monte carlo integration
 +
                                    [3]. Then, for each set of parameters, the output of the
 +
                                    system is calculated. Finally, Sobol indices are calculated
 +
                                    by the procedure described below and the results are
 +
                                    analyzed in first, second and total sensitivity indices
 +
                                    [4].
 +
                                </p>
 +
 
 +
                                <p>For a system, the output of which is characterized by a
 +
                                    function f(x), which is integrable and its inputs are
 +
                                    x(x1,x2,x3). The first move is to decompose into the sums
 +
                                    of the effect, that the various components of the system
 +
                                    have.</p>
 +
 
 +
                                <p>Defined as <span id="fo-eq"></span>, is the average of f(x)
 +
                                    for different parameter sets values</p>
 +
                                <p>
 +
                                    f(x) Decomposition:
 +
                                    <div id="f-dec-eq"></div>
 +
                                </p>
 +
                                <p>
 +
                                    We can generalize (1) as follows
 +
                                    <div id="fx-eq"></div>
 +
                                    where n is the number of system inputs and i &lt; j,
 +
                                    because fij(xi,xj) = fji(xj,xi).
 +
                                </p>
 +
                                <p>
 +
                                    Then we define the variance D of the output function, of
 +
                                    the total sums and the average of each parameter as a
 +
                                    random variable, that is evenly distributed over an
 +
                                    interval [4] and the result is the sum of the variance
 +
                                    caused by each parameter or a combination of these in each
 +
                                    set of parameters describing the total variance of the
 +
                                    output as the following sum:
 +
 
 +
                                    <div id="d-eq"></div>
 +
                                    where f(x) is square-integrable, therefore as total sums of
 +
                                    the contribution of all the differences between the set
 +
                                    parameters,
 +
                                    <div id="d2-eq"></div>
 +
                                    Equation (3) is analyzed as (1), and shows how much each
 +
                                    variable has contributed, as well as their combined
 +
                                    interactions in the final overall system variance.
 +
                                    <div id="d3-eq"></div>
 +
                                    where <span id="d1s-eq"></span> is the variance we have
 +
                                    from specific parameters. For example, if we wanted the
 +
                                    first order sensitivity index of variable we would use as a
 +
                                    numerator only <span id="d1x-eq"></span>.
 +
                                </p>
 +
                                <p>
 +
                                    Computational cost is proportional to the type of problem,
 +
                                    the number of parameters and the non-linear phenomena that
 +
                                    appear in the relationship between the interacting
 +
                                    parameters. For small numbers of parameters like the model
 +
                                    we have performed, variance-based methods are considered
 +
                                    satisfactory and relatively quick. As the order of
 +
                                    sensitivity indices increases, the cost increases
 +
                                    accordingly. As mentioned above, one way to use a
 +
                                    variance-based method like Sobol is to reduce the number of
 +
                                    parameters (variance cutting) by excluding for each
 +
                                    calculation those that do not affect.
 +
                                </p>
 +
                                <h3>Robustness analysis</h3>
 +
                                <p>
 +
                                    When we start building a model, its structure contains many
 +
                                    uncertainties that are not easy to assess. Such
 +
                                    uncertainties are the mathematical expression of kinetic
 +
                                    equations, stoichiometric coefficients of kinetics, and the
 +
                                    simplifications made from a more complex network to a more
 +
                                    simplified model. In addition, the complexity of biological
 +
                                    systems makes it impossible to fully analyze all the
 +
                                    reactions that occur inside and outside the environment,
 +
                                    among the various components that they consist of.
 +
                                    Robustness analysis is a tool useful for studying the
 +
                                    general behavior of a system, despite the uncertainties
 +
                                    that exist in it.
 +
                                </p>
 +
                                <p>
 +
                                    Applying robustness analysis to the mathematical model
 +
                                    under study, we set price ranges for each parameter that we
 +
                                    do not know, setting maximum and minimum values ​​that are
 +
                                    considered realistic within the biological system, which
 +
                                    are estimated from bibliography and experimental data. Then
 +
                                    the model is exhaustively simulated in many sets of
 +
                                    parameters created by sampling. The sampling method used is
 +
                                    the Latin hypercube, which generates random numbers divided
 +
                                    into equal intervals within the range given for each
 +
                                    parameter. Within each interval a value is randomly
 +
                                    selected.
 +
                                </p>
 +
                                <p>
 +
                                    We use error bars in order to show the output variation
 +
                                    around the mean value. They may correspond to a large range
 +
                                    of parameter values that are spaced apart to several orders
 +
                                    of magnitude between them. The error bars were calculated
 +
                                    either by standard deviation of all concentrations for each
 +
                                    copy number or by the corresponding standard error.
 +
                                </p>
 +
                                <p>
 +
                                    Once, the sensitivity analysis described above, has been
 +
                                    applied to reduce the number of uncertain parameters in the
 +
                                    system, and robustness analysis to output values ​​that are
 +
                                    highly variable, we can evaluate the results and better
 +
                                    study the behavior of the system. In our system we studied
 +
                                    the uncertainty of protein of interest concentrations at a
 +
                                    time when all components of the system are stabilized in
 +
                                    steady-state, relative to the copy number of the plasmids.
 +
                                </p>
 +
 
 +
                                <h3>Implementation</h3>
 +
                                <h5>Simbiology Matlab®</h5>
 +
                                <p>
 +
                                    We created the biological networks, building -up the
 +
                                    dynamic
 +
                                    systems using the MATLAB®language, specifically Simbiology®
 +
                                    toolbox that allowed as to analyze easily the kinetic
 +
                                    equations
 +
                                    with species, reactions and doses-response with it’s simple
 +
                                    to
 +
                                    use Graphical interface. We chose to solve the ordinary
 +
                                    differential equations with variable-step continuous solver
 +
                                    ode15s . The ode15s is a good choice for stiff problems and
 +
                                    in
 +
                                    our simulations settings we set absolute tolerance <span id="ten6-eq"></span>
 +
                                    and
 +
                                    relative tolerance <span id="ten3-eq"></span> . Υου can see
 +
                                    our simbiology diagrams
 +
                                    here.
 +
                                </p>
 +
                                <h5>Python packages </h5>
 +
                                <p>
 +
                                    After the usage of Simbiology for the chemical interaction
 +
                                    modelling we use scipy’s odeint for the construction of our
 +
                                    systems ODE equations. We use python because we wanted to
 +
                                    integrate other packages (e.g for sensitivity analysis)
 +
                                    that help us to extend our analysis, and compare the
 +
                                    results. The interaction between simbiology and python help
 +
                                    us to understand the differences that exist between them
 +
                                    and to practice in both environments.
 +
                                </p>
 +
                                <p>
 +
                                    In addition to that, we used Python’s built in
 +
                                    multiprocessing module in order to increase the
 +
                                    computational speed by dividing the tasks of robustness and
 +
                                    sensitivity analysis to many processes (as many as the
 +
                                    cores of each PC).
 +
                                </p>
 +
 
 +
                                <h5>SALib - Sensitivity Analysis Library in Python</h5>
 +
                                <p>
 +
                                    This library helped us to incorporate sensitivity analysis
 +
                                    in all systems calculating the effects of model input
 +
                                    (different parameters in each model) regarding variation of
 +
                                    model output (concentration of sfGFP). We specifically used
 +
                                    Sobol Sensitivity analysis that calculates the sensitivity
 +
                                    index generating model inputs using Saltelli’s extension of
 +
                                    the Sobol sequence sampling []. This way, we were able to
 +
                                    understand which parameters are the most affected and
 +
                                    discuss with wet lab if and what changes are needed. You
 +
                                    can see here[] all our simulation code.
 +
                                </p>
 +
 
 +
                                <h5>Robustness analysis</h5>
 +
                                <p>
 +
                                    For robustness analysis, we use python packages and
 +
                                    SALib.sample package to produce the sampling. The sampling
 +
                                    uses the Latin hypercube method (LHS), that generates a
 +
                                    random sample of N points for each uncertain input
 +
                                    parameter. The number of parameter sets is 10.000 unless
 +
                                    otherwise mentioned and the parameter ranges take the same
 +
                                    values as in sensitivity analysis. For each result,
 +
                                    robustness analysis measures the standard deviation, and
 +
                                    the mean for every copy number as well as the error between
 +
                                    input-output and prints these results in a csv.
 +
                                </p>
 +
 
 +
                                <h5>Digital Ocean</h5>
 +
                                <p>
 +
                                    Furthermore, in order to increase the computational speed of the analysis as well as running more experiments together, we used Digital Ocean cloud computing platform[].
 +
                                </p>
 +
 
 +
                                <h5>Salis calculator RBS</h5>
 +
                                <p>
 +
                                        We used RBS calculator from Salis Lab [5] to estimate the mRNA’ s translation rate for all proteins on our systems. The calculations are described in each model’s page. See translation rate estimation.
 +
                                </p>
 +
 
 +
                                <h6>REFERENCES</h6>
 +
 
 +
                                <div class="row justify-center q-mb-md q-mt-md" :class="rM('text-dark', 'text-light')">
 +
                                    <small class="row q-mb-sm">
 +
                                        [1] Segall-Shapiro, T., Sontag, E. and Voigt, C. (2018). Engineered promoters enable constant gene expression at any copy number in bacteria. Nature Biotechnology, 36(4), pp.352-358.
 +
                                    </small>
 +
                                    <small class="row q-mb-sm">
 +
                                        [2] Herman, J. and Usher, W. (2017) SALib: An open-source Python library for sensitivity analysis. Journal of Open Source Software, 2(9). doi:10.21105/joss.00097
 +
                                    </small>
 +
                                    <small class="row q-mb-sm">
 +
                                        [3] Ratto, M., Andres, T., Campolongo, F., Cariboni, J., Gatelli, D., Saisana, M. and Tarantola, S. (2008). Global Sensitivity Analysis. John Wiley & Sons.
 +
                                    </small>
 +
                                    <small class="row q-mb-sm">
 +
                                        [4] Zhang, X., Trame, M., Lesko, L. and Schmidt, S. (2015). Sobol Sensitivity Analysis: A Tool to Guide the Development and Evaluation of Systems Pharmacology Models. CPT: Pharmacometrics & Systems Pharmacology, 4(2), pp.69-79.
 +
                                    </small>
 +
                                    <small class="row q-mb-sm">
 +
                                        [5] Espah Borujeni, A., Channarasappa, A. and Salis, H. (2013). Translation rate is controlled by coupled trade-offs between site accessibility, selective RNA unfolding and sliding at upstream standby sites. Nucleic Acids Research, 42(4), pp.2646-2659.
 +
                                    </small>
 +
                                </div>
 +
                            </div>
 
                         </div>
 
                         </div>
 
                     </template>
 
                     </template>
Line 63: Line 570:
 
                         <div class="row justify-center">
 
                         <div class="row justify-center">
 
                             <a href="https://2018.igem.org/Team:Thessaloniki/Model/Tale">
 
                             <a href="https://2018.igem.org/Team:Thessaloniki/Model/Tale">
−
                                 <q-btn style="width: 150px; height: 150px; border: 4px solid cornflowerblue; border-radius: 100%" label="TALE"></q-btn>
+
                                 <q-btn style="width: 150px; height: 150px; border: 4px solid cornflowerblue; border-radius: 100%"
 +
                                    label="TALE"></q-btn>
 
                             </a>
 
                             </a>
 
                         </div>
 
                         </div>
Line 70: Line 578:
 
                         <div class="row justify-center">
 
                         <div class="row justify-center">
 
                             <a href="https://2018.igem.org/Team:Thessaloniki/Model/dCas9">
 
                             <a href="https://2018.igem.org/Team:Thessaloniki/Model/dCas9">
−
                                 <q-btn style="width: 150px; height: 150px; border: 4px solid cornflowerblue; border-radius: 100%" label="dCas9"></q-btn>
+
                                 <q-btn style="width: 150px; height: 150px; border: 4px solid cornflowerblue; border-radius: 100%"
 +
                                    label="dCas9"></q-btn>
 
                             </a>
 
                             </a>
 
                         </div>
 
                         </div>
Line 77: Line 586:
 
                         <div class="row justify-center">
 
                         <div class="row justify-center">
 
                             <a href="https://2018.igem.org/Team:Thessaloniki/Model/NAR">
 
                             <a href="https://2018.igem.org/Team:Thessaloniki/Model/NAR">
−
                                 <q-btn style="width: 150px; height: 150px; border: 4px solid cornflowerblue; border-radius: 100%" label="NAR"></q-btn>
+
                                 <q-btn style="width: 150px; height: 150px; border: 4px solid cornflowerblue; border-radius: 100%"
 +
                                    label="NAR"></q-btn>
 
                             </a>
 
                             </a>
 
                         </div>
 
                         </div>
Line 152: Line 662:
 
         })
 
         })
  
−
         let equatations = [
+
         let equatations = [{
−
         ]
+
            id: 'fo-eq',
 +
            eq: `f_0`
 +
        }, {
 +
            id: 'f-dec-eq',
 +
            eq: `f(x) = f_0 + f_1(x_1) + f_2(x_2) + f_3(x_3) + f_{12}(x_1,x_2) +f_{13}(x_1,x_3)+f_{23}(x_2,x_3) + f_{123}(x_1,x_2,x_3)`
 +
        }, {
 +
            id: 'fx-eq',
 +
            eq: `
 +
                \\begin{array}{lr}
 +
                f(x) = f_0 + \\sum_{i=1}^{n} f_i(x_i) + \\sum_{i<j}^{n} f_{ij}(x_{ij}) + f_i..._n(x_i...x_n) & (1)
 +
                \\end{array}
 +
            `
 +
        }, {
 +
            id: 'd-eq',
 +
            eq: `
 +
            \\begin{array}{lr}
 +
            D = \\int f(x)^2 - f_0^2 & (2)
 +
            \\end{array}
 +
            `
 +
        }, {
 +
            id: 'd2-eq',
 +
            eq: `
 +
            \\begin{array}{lr}
 +
                D = \\sum_{s=1}^{n} \\sum_{i_1<...<i_s}^{n} D_{i1}..._{is} & (3)
 +
            \\end{array}
 +
            `
 +
        }, {
 +
            id: 'd2-eq',
 +
            eq: `
 +
            \\begin{array}{lr}
 +
            S_{i1}..._{is}= \\frac{ D_{i1}..._{is}}{D} & (4)
 +
            \\end{array}
 +
            `
 +
        }, {
 +
            id: 'd1s-eq',
 +
            eq: `D_{i1}..._{is}`
 +
        }, {
 +
            id: 'd1x-eq',
 +
            eq: `D_1(x1)`
 +
        }, {
 +
            id: 'ten3-eq',
 +
            eq: `10^-3`
 +
        }, {
 +
            id: 'ten6-eq',
 +
            eq: `10^-6`
 +
         }]
  
 
         iGEM.parseLatex(equatations)
 
         iGEM.parseLatex(equatations)

Revision as of 02:31, 17 October 2018

The goal of the model is to study the Incoherent Feed Forward Loop (IFFL) as a network type in three systems that use different components critical to the proper network operation. This function aims at balancing the final product to a specific steady state, regardless of the input disruption. We then responded to questions raised by the wet lab, thus helping towards the right course of thought during experimental planning, as well as a better understanding of the systems and the different choices that emerged. We applied a sensitivity analysis to classify system parameters according to their significance, and finally, we explored the robustness of our system predictions by indentifying parameter sets and evaluating their cellular behavior.

How IFFL works

The stability of a system in which IFFL is applied is represented by the staying of its output at a constant level in the equilibrium state for each change of input. In this type of network, the number of plasmids is the input, which is variable and the final protein is the output of the system that must remain constant at each change of input.

In the following figure, the input X is shown to be responsible for the continuously increasing production of the gene of interest Z, as well as for the production of the internal variable Y, which suppresses the production of Z. As mentioned in [], the system is represented by a logical AND gate, which expresses the effect of input X and suppressor Y on output Z.