Difference between revisions of "Team:Waterloo/Modeling/Intercellular Spread"

 
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     <section id="motivation" title="Motivation">
 
     <section id="motivation" title="Motivation">
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        <h2>Motivation</h2>
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<div class="row">
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        <p>
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    <div class="col-sm-8">
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            The spread of infection between cells and among populations has been modelling extensively, but the middle ground of intercellular spread is relatively unexplored. We investigated whether our defense system would protect individual <em>Arabidopsis</em> plants using an agent-based approach. Briefly, each plant cell is treated an agent that may become infected by CaMV or resistant to infection due to plant defense signalling. Infected cells run an instance <a href="https://2015.igem.org/Team:Waterloo/Modeling/CaMV_Replication">ODE model that was created to study viral replication</a> and then may pass infection to their neighbours. The spread through the stems and leaves of the plant can be tracked with and without the CRISPR/Cas9 system.
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    <p>Viral spread has been modeled extensively on very <a href = "https://2015.igem.org/Team:Waterloo/Modeling/CaMV_Replication">small scales</a> and on large (population) scales, but, surprisingly, the middle ground of intercellular spread is relatively unexplored <cite ref="Rodrigo2014"></cite><cite ref="Tromas2014"></cite>. First, we had to make a model on this scale. Then, we used this model to investigate whether our defense system would protect individual <em>Arabidopsis</em> plants. </p>
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        </p>
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        [insert screenshot of the simulation]
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<p>  This is an agent-based approach. Briefly, each plant cell is treated an agent that may become infected by CaMV or resistant to infection due to plant defense signalling. Infected cells run an instance of our ODE model for viral replication; they may also pass infection to their neighbors. The spread through the stems and leaves of the plant can be tracked with and without the CRISPR/Cas9 system.</p>
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    </div>
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        [insert diagram of the plant’s plasmodesmata and vascular system]
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    <div class="col-sm-4">
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         <figure>
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         <p>
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             <img src="/wiki/images/d/da/Waterloo_mathVS_graphic.svg" alt="Stylized plant leaves" style="width:200px;"/>
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             As a reaction to the presence of the virus, the plant cells will destroy infected cells through apoptosis as well as signal to the rest of the plant to begin production of defensive chemicals in preparation for attack. This signaling causes systemic required resistance, a broad, long-term increased resistant to future infections.<cite ref="Ryals1994"></cite>
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            <figcaption class="model-caption">Plant Leaves</figcaption>
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        </p>
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        </figure>
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    </div>
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    </div>
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<p>This leads to our second goal which is to integrate the intracellular replication and intercellular spread models to fully understand impact of CRISPR/Cas9. Altogether, we are attempting to demonstrate the feasibility of our anti-viral system and use our findings to direct the project design.</p>
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        <p>As a reaction to the presence of the virus, the plant cells will destroy infected cells through apoptosis as well as signal to the rest of the plant to begin production of defensive chemicals in preparation for attack. This signaling causes systemic required resistance, a broad, long-term increased resistant to future infections.<cite ref="Ryals1994"></cite>.</p>
  
 
         <ul>
 
         <ul>
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         <h3>Biology of Viral Infection Spread</h3>
 
         <h3>Biology of Viral Infection Spread</h3>
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<p> For information on this, please see the Intercellular Spread section of the CaMV biology page <a href = "https://2015.igem.org/Team:Waterloo/Modeling/CaMV_Biology">here</a>. </p>
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        <h4>Intercellular</h4>
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        <p> For information on this, please see the Intercellular Spread section of the CaMV biology page <a href = "https://2015.igem.org/Team:Waterloo/Modeling/CaMV_Biology">here</a>. </p>
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        <h4>Systemic Infection</h4>
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        <p>Phloem/Vascular System</p>
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        <h3>Plant Defense Mechanisms</h3>
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    <h4>Hypersensitive Response (HR)</h4>
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        <p>
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            Interplant signaling plays an important role in the hypersensitive response of plants, where plant cells selectively undergo apoptosis in order to destroy infected or damaged cells, such as in the event of pathogen attacks like CaMV.
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        </p>
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        <p>
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            A main intercellular signaling molecule is hydrogen peroxide (H2O2), formed during electron transport processes <cite ref="Neill2002"></cite>. This is produced in elevated levels the event of pathogen attack and other stresses, and can damage DNA and proteins <cite ref="Neill2002"></cite>. It allows for the localization of apoptosis which occurs as a result of the hypersensitive response as well as increased expression of defense genes, which it modulates during defense response <cite ref="Neill2002"></cite>. H<sub>2</sub>O<sub>2</sub> has been observed in tobacco plants to induce the production of proteasomes linked to the degradation of cells in programmed cell death <cite ref="Neill2002"></cite>. In Arabidopsis thaliana, it has been observed that increased generation of H2O2 leads to an increase of calcium ions in the form of cytosolic calcium, which, triggering a cascade of reactions leading to the apoptosis of infected cells <cite ref="Neill2002"></cite>. H<sub>2</sub>O<sub>2</sub> has also been observed inducing the expression of glutathione S-transferase (GST) and phenylalanine ammonia‐lyase (PAL), both of which are defense-related genes, as well as genes involved in the production and degradation of H2O2 <cite ref="Neill2002"></cite>. Additionally, it has been observed to cause the stomatal closure of cells <cite ref="Neill2002"></cite>.
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        </p>
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        <p>
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            Another intercellular signaling molecule is nitric oxide (NO), found primarily in its gaseous form, which may be produced at the same time as (H2O2) after pathogen challenge, and induces a similar defense response as (H2O2). <cite ref="Neill2002"></cite> It increases the gene expression of defensive genes such as PAL1 and GST. <cite ref="Neill2002"></cite> Additionally, NO may have a role in iron-level regulation in plants, and redox signaling through its potential involvement with pathogen-induced oxygenase. <cite ref="Neill2002"></cite> There is limited research for NO as a plant signal, however, it has been researched extensively as a signaling molecule in mammalian cells <cite ref="Neill2002"></cite>. Like in mammalian cells, NO has been observed increasing levels of cyclic GMP in the event of pathogen challenge and inducing programmed cell death. <cite ref="Neill2002"></cite>
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        </p>
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        <p>
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            In additional to working concurrently with each other, NO and H2O2 also interact with a whole host of other signaling molecules, such as jasmonic acid, ethylene, and salicylic acid <cite ref="Neill2002"></cite>, which have to be taken into consideration when studying intercellular plant signaling as a whole.
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        </p>
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        <h3>Systemic  Acquired Resistance (SAR)</h3>
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        <p>
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            The systemic acquired resistance (SAR) defense mechanism, or immunization of plants, is a broad, long-term increased resistant to future infections. <cite ref="Ryals1994"></cite> This is similar to the increased resistance against diseases in mammals, after having been infected. <cite ref="Ryals1994"></cite> It is important to note that this resistance is not triggered by mechanical damage caused by factors such as herbivore attack. <cite ref="Ryals1994"></cite> This mechanism is only activated after a pathogen is detected within the plant, triggering defenses through signals <cite ref="Ryals1994"></cite> Salicylic acid (SA) has been identified as a molecule with an indispensable role in the pathway to systemic acquired resistance. <cite ref="Klessig2000"></cite> Additionally, NO also has an important role in activating systemic acquired resistance. <cite ref="Klessig2000"></cite> During the initial wave of defense after pathogen detection, there is an “oxidative burst” wherein levels of oxidative species suddenly increase. <cite ref="Klessig2000"></cite> This is accompanied by cell wall protein linkage, the activation of kinase and increased gene expression defensive genes. <cite ref="Klessig2000"></cite> A second wave of defense is found in the hypersensitive response, wherein lesions form (from programmed cell death). <cite ref="Klessig2000"></cite> NO and SA play an interconnected role with each other, where reactive oxygen species (ROS) such as NO have been observed accumulating SA, and in turn, SA triggers ROS production (including NO and H2O2). <cite ref="Klessig2000"></cite>
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        </p>
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        <h4>Plant Defense Signalling and Spread</h4>
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As a response to attacks by pathogens, plants can signal this to other plants through chemical emissions in the air. Additionally, plants may also potentially be able to communicate through common mycorrhizal networks (CMN) created by mycorrhizal fungi, connecting the roots of different plants together . Mycorrhizal fungi found in the soil have a symbiotic relationship between them and the roots and the roots of the plants, as well as giving additional defense to the plant itself <cite ref="Song2010"></cite>. They allow nutrients, carbon and water to travel from plant to plant <cite ref="Song2010"></cite>. Song et al studied the potential of the CMN carry plant communication signals in tomato plants. The reception of these signals from infected plants is highly advantageous to non-infected, neighbouring plants, as it allows the non-infected plant to increase their defenses, including increased levels of defends enzymes, and the expression of genes related to their defenses <cite ref="Song2010"></cite>. In Song et al, they measured the levels of six defense enzymes in tomato plants: peroxidase (POD), polyphenol oxidase (PPO), chitinase, β-1,3-glucanase, phenylalanine ammonia-lyase (PAL) and lipoxygenase (LOX). The levels of all of the of the measured defense enzymes as well as gene expression encoding for these enzymes increased in CMN connected plants in the presence of a A.solani pathogen challenge <cite ref="Song2010"></cite>). It was proposed in the study that the speed of intercellular signals is faster than the transfer of signal molecules in the CMN, and that it gives a greater advantage over air-spread chemical signals due to the different factors such as the unpredictability of the wind and the space between plants. <cite ref="Song2010"></cite>.
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         <h3>Agent-Based Model Design</h3>
 
         <h3>Agent-Based Model Design</h3>
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        <p><em>Include Model Assumptions!!!</em></p>
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  <p>To trace the spread of the virus through the leaf, we used an agent-based model. Each cell produces and spreads the virus</p>
 +
        <ul>
 +
            <li></li>
 +
            <li>Explain reasons for the parameters</li>
 +
        </ul>
 +
      <h3>Plant Structure</h3>
 +
        <ul>
 +
            <li>Cells are groups into leaves. Cells are only connected by plasmodesmata to other cells in the same leaf.</li>
 +
            <li>Each leaf also has one phloem (stem) that links to the central vasculature of the plant. These phloem cannot produce either viral particles or resistance molecules themselves; they only act as conduits to pass them along.</li>
 +
        </ul>
 +
 
  
 +
      <h4>Model Assumptions</h4>
 +
        <ul>
 +
                  <li>Viral Spread Chance - each time step, infected cells have a small probability of passing a virion to a neighboring cell. It is unbiological to have each cell's infection spread at every timestep, as this leads rapidly to 100% infection, contrary to observations <cite ref="Tromas2014"></cite>. Unfortunately, no number for this infection probability could be found in literature, so a reasonable approximation of this value was implemented in order to emulate normal viral spread.</li>
 +
                  <li>Cas9 is already at a steady state at time of infection</li>
 +
        </ul>
 
         <h4>Plant Structure</h4>
 
         <h4>Plant Structure</h4>
 
         <ul>
 
         <ul>
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         <h4>Virus</h4>
 
         <h4>Virus</h4>
 
         <ul>
 
         <ul>
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             <li><b>Initial Infection Site</b> is a user-selected integer representing the number of lesions on a plant leaf for the application of the virus</li>
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             <li><b>Initial Infection Sites</b> is a user-selected integer representing the number of lesions on a plant leaf for the application of the virus</li>
 
             <li><b>Founder Population</b> represents the number of viruses in each of the lesions, or the multiplicity of infection, which should be between 2 and 13 <cite ref="Gutierrez2010"></cite></li>
 
             <li><b>Founder Population</b> represents the number of viruses in each of the lesions, or the multiplicity of infection, which should be between 2 and 13 <cite ref="Gutierrez2010"></cite></li>
 
             <li><b>Viral Spread Rates</b> the virus spreads at a rate of about 3 cells per day, but it takes longer for the cell to begin actively producing and exporting virions<cite ref="Khelifa2010"></cite></li>
 
             <li><b>Viral Spread Rates</b> the virus spreads at a rate of about 3 cells per day, but it takes longer for the cell to begin actively producing and exporting virions<cite ref="Khelifa2010"></cite></li>
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             <li>Viral Spread Chance</li>
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             <li><b>Viral Spread Chance</b></li>
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             <li>Viral Assembly</li>
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             <li><b>Viral Assembly</b></li>
 +
            <li><b>Modify Virus</b> "On" runs the simulation with Cas9, "Off" is without</li>
 +
 
 
         </ul>
 
         </ul>
  
 
         <h4>Plant Response</h4>
 
         <h4>Plant Response</h4>
 
         <ul>
 
         <ul>
−
<li><b>SAR</b> or Systemic Acquired Response, is a form of acquired immunity. The plant produces signalling molecules and enables cells to become resistant or lyse themselves</li>
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<li><b>SAR</b> or Systemic Acquired Response, is a form of acquired immunity. The plant produces signalling molecules and enables cells to become resistant or lyse themselves</li>
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        <li><b>Resistance Threshold</b> is the level of SA signalling molecule required for a cell to become resistant to the pathogen</li>
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            <li><b>Resistance Threshold</b> is the level of SA signalling molecule required for a cell to become resistant to the pathogen</li>
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        <li><b>Lysis Threshold</b> is the level of SA signalling molecule required for a cell to undergo apoptosis to protect the rest of the organism</li>
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            <li><b>Lysis Threshold</b> is the level of SA signalling molecule required for a cell to undergo apoptosis to protect the rest of the organism</li>
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        <li><b>SA Signalling Molecule</b> is generated by resistant or susceptible cells neighbouring infected or resistant cells at a rate of one per minute, after those neighbours have been infected/resistant for 8hrs</li>
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            <li><b>Signalling Molecule</b> is generated by resistant or susceptible cells neighbouring infected or resistant cells at a rate of one per minute, after those neighbours have been infected/resistant for 8hrs. The model has been simplified to have both HR and SAR spread through the plant using one signalling chemical instead of the complex interactions between several different signalling molecules separately .</li>
 
         </ul>
 
         </ul>
  
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         <h3>Modelling Software Choice</h3>
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         <h3>Agent-Based Modelling Software</h3>
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         <p>
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            The agent-based modelling software for the simulation had several different criteria needed to be fulfilled: the ability to create different kinds of agents, control over the connections between agents (e.g. plasmodesmata betweeen cells), an option to have complex rules within each agent, being able to have an arbitrary number of model states and keep track of time since infection, as well as being easy to use. Originally, three different software packages (MASON, MESA and Netlogo) were chosen out of several as the top candidates to create the viral spread simulation due to their fulfillment of the above criteria. All of the languages required were unfamiliar, and thus would have to be learned from scratch. Netlogo was chosen to create the final simulation due to a variety of its strengths as well as time constraints. Although Netlogo was the most unfamiliar-looking language, it presented itself as the simulation package with the smallest learning curve. Additionally, it had readily-available documentation and a built-in GUI. MESA was a Python-based simulation package and ultimately was not chosen due to its documentation not being as detailed or as readily available as MASON or Netlogo’s, as well as the level of familiarity with Python required to create the model being too high to achieve within the time constraints. MASON, a Java-based simulation package, despite having excellent, easily-found documentation did not have a built-in GUI, and did not have as many built in-functions as the Netlogo, thus requiring more work to get off the ground. Although in some cases the fewer amount of built-in functions could have proved to be an advantage (it would have added more flexibility and customization to the simulation), due to the time constraints and the demand of a level familiarity with Java (as with MESA) to create a simulation with MASON, Netlogo was thus chosen over MASON.
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      <div class="row vertical-align">
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        </p>
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          <div class="col-sm-8">
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            <p>We identified several requirements for the software used in our agent-based model:</p>
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        <h4>Software Downloads</h4>
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            <ul>
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        <div class="row vertical-align">
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                <li>Ability to create different kinds of agents (cells, vasculature, and others).</li>
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            <div class= "col-sm-4">
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                <li>Control over connections between agents (e.g. plasmodesmata betweeen cells)</li>
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                <li>Support for complex rules (e.g. ODE simulations) within each agent</li>
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                <li>Arbitrary number of model states</li>
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                <li>Tracking of time since infection</li>
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                <li>Ease of use</li>
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            </ul>
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          </div>
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          <div class= "col-sm-4">
 
                 <figure>
 
                 <figure>
 
                     <a href="https://ccl.northwestern.edu/netlogo/"><img src="https://static.igem.org/mediawiki/2015/1/16/Waterloo_Math_ViralSpread_NetlogoIcon.png" style="width:200px;"/></a>
 
                     <a href="https://ccl.northwestern.edu/netlogo/"><img src="https://static.igem.org/mediawiki/2015/1/16/Waterloo_Math_ViralSpread_NetlogoIcon.png" style="width:200px;"/></a>
  
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                     <figcaption>Link to Download Netlogo</figcaption>
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                     <figcaption>NetLogo, the chosen agent-based modelling software</figcaption>
 
                     <div class="img-att">i
 
                     <div class="img-att">i
 
                         <ul class="img-att-bubble">
 
                         <ul class="img-att-bubble">
 
                             <li>Photo &copy; <a href="https://ccl.northwestern.edu/netlogo/">Uri Wilensky</a></li>
 
                             <li>Photo &copy; <a href="https://ccl.northwestern.edu/netlogo/">Uri Wilensky</a></li>
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                             <li><a href="http://www.macupdate.com/app/mac/21469/netlogo">Original Photo</a></li>
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                             <li><a href= "http://www.macupdate.com/images/icons256/21469.png">Original Photo</a></li>
 
                         </ul>
 
                         </ul>
 
                     </div>
 
                     </div>
 
                 </figure>
 
                 </figure>
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            </div>
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          </div>       
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        </div>
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      <p>Three different software packages (<a href="https://cs.gmu.edu/~eclab/projects/mason/">MASON</a>, <a href=""https://pypi.python.org/pypi/Mesa/">MESA</a> and <a href="https://ccl.northwestern.edu/netlogo/">Netlogo</a>) were considered in depth. <a href=""https://pypi.python.org/pypi/Mesa/">MESA</a> is a Python-based simulation package and was not used due to its poor documentation and the level of familiarity with Python required to create the model. <a href="https://cs.gmu.edu/~eclab/projects/mason/">MASON</a>, a Java-based simulation package, has excellent, easily-found documentation but no GUI and fewer built-in functions. Although fewer built-in functions could be an advantage (adding more flexibility and customization to the simulation), time constraints and unfamiliarity with Java pushed us to use <a href="https://ccl.northwestern.edu/netlogo/">NetLogo</a> instead of MASON. NetLogo was easy to learn, well-documented and had a built in GUI. These were essential for rapid prototyping -- while some other choices would have been better able to handle large simulations, they would have had much longer development time for small changes, ultimately impeding our efforts to make a quality model. </p>
  
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            <div class= "col-sm-4">
 
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                <figure>
 
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                    <a href= "https://pypi.python.org/pypi/Mesa/"><img src="https://static.igem.org/mediawiki/2015/4/4b/Waterloo_Math_ViralSpread_MESAIcon.svg" style="width:200px;"/></a>
 
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                    <figcaption>Link to Download MESA</figcaption>
 
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                </figure>
 
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            </div>
 
  
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            <div class= "col-sm-4">
 
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                <figure>
 
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                    <a href= "https://cs.gmu.edu/~eclab/projects/mason/"><img src="https://static.igem.org/mediawiki/2015/a/a2/Waterloo_Math_ViralSpread_MASONIcon.svg "style="width:200px;"/></a>
 
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                    <figcaption>Link to Download MASON</figcaption>
 
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                </figure>
 
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            </div>
 
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        </div>
 
 
     </section>
 
     </section>
  
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         <h2>Results</h2>
 
         <h2>Results</h2>
 
     </section>
 
     </section>
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 +
<h3>Normal -- no intervention</h3>
 +
 +
        <figure>
 +
            <img src="/wiki/images/0/0f/Waterloo_mathVSnocrispr.gif" alt="Video of spread in plant without CRISPR" style="max-width: 400px;" />
 +
            <figcaption>Agent-based Netlogo model shows the spread of infection (red) and acquired resistance (blue) in a leaf where each agent simulates an ODE replication model. Without CRISPR, one leaf is entirely overwhelmed.</figcaption>
 +
        </figure>
 +
 +
 +
<p>
 +
We were quite successful in making a reasonable representation of the normal process of viral spread. A typical model run proceeds as follows:</p>
 +
<ul>
 +
<li>The virus quickly spreads to most of the initially infected lead, with only a small amount of resistance developing.</li>
 +
<li>Once it has spread to this entire leaf, it spreads into the plant’s vascular system and the main stem.</li>
 +
<li>Soon, all of the vascular structure is carrying the virus. But the infection runs its own course in each leaf.</li>
 +
<li>In some cases, resistance builds up and seals off the point of initial infection. In others, the infection spreads into the leaf, but a sizable fraction of it becomes resistant.</li>
 +
<li>Apoptosis occurs near the boundaries between infected and resistant regions, often cutting off these regions from the rest of the plant. </li>
 +
</ul>
 +
 +
<p>In a few cases, the plant is lucky & the initial infection was small, so the infection did not spread beyond the first leaf. However, most simulation runs result in over half the plant being infected.</p>
 +
 +
 +
<h3>CRISPR/Cas9 – our intervention</h3>
 +
 +
        <figure>
 +
            <img src="/wiki/images/9/95/Waterloo_mathVSwithcrispr.gif" alt="Video of spread in plant with CRISPR" style="max-width: 400px;"/>
 +
            <figcaption>Agent-based Netlogo model shows the spread of infection (red) and acquired resistance (blue) in a leaf where each agent simulates an ODE replication model. The CRISPR effect parameter (t1/2) is captured in the ODE.</figcaption>
 +
        </figure>
 +
 +
<p>
 +
When we introduce our CRISPR/Cas9 mechanism, and hold all other parameters constant, we see that the infection is stopped remarkably quickly. It rarely spreads into the vasculature.
 +
The level of resistance is correspondingly lower, since the plant detects less of a threat.</p>
 +
 +
<p>This effective prevention of viral spread is maintained even with moderate increases in other viral parameters and/or decrease in resistance.</p>
 +
  
 
     <section id="discussion" title="Discussion">
 
     <section id="discussion" title="Discussion">
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        <h2>Discussion</h2>
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 +
  <h2>Discussion</h2>
 +
<p>As with many projects in mathematical biology, one of the biggest challenges is finding accurate parameter values. Our slider-based approach was a creative solution that enables us to investigate the balance of different factors in viral spread and resistance, but it was quite arbitrary. Our results remain fundamentally qualitative – we can tell our intervention helps, but we can’t say by how much.</p>
 +
 
 +
<p>There are two main ways this could be improved. One is simply to more systematically explore this parameter space. Computationally, this would take a long time, since there are many variables with very large feasible ranges, but it is conceptually simple. However, there is a risk that this would not be particularly illuminating.</p>
 +
 
 +
<p>A better solution is to push for inventive experiments that can better determine these parameters. Tromas and colleagues make excellent use of flow cytometry to get this kind of data </cite><cite ref="Tromas2014"></cite>. This allows them to determine the infectivity of cells as a function of time. While this doesn’t quite give the probability per time of <em>attempted</em> spread events, it’s a very promising line of inquiry.</p>
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<p>A different direction in which this model could be improved is having a more detailed and faithful plant architecture. There are many types of cells in plant leaves, for example, as well as multiple interconnectin plant defense mechanisms. There are also orders of magnitude more cells than we rendered. These changes would be needed to make our model more accurate; they would also entail running it on different software.</p>
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Latest revision as of 01:45, 21 November 2015

Viral Spread Model

Viral spread has been modeled extensively on very small scales and on large (population) scales, but, surprisingly, the middle ground of intercellular spread is relatively unexplored . First, we had to make a model on this scale. Then, we used this model to investigate whether our defense system would protect individual Arabidopsis plants.

This is an agent-based approach. Briefly, each plant cell is treated an agent that may become infected by CaMV or resistant to infection due to plant defense signalling. Infected cells run an instance of our ODE model for viral replication; they may also pass infection to their neighbors. The spread through the stems and leaves of the plant can be tracked with and without the CRISPR/Cas9 system.

Stylized plant leaves
Plant Leaves

This leads to our second goal which is to integrate the intracellular replication and intercellular spread models to fully understand impact of CRISPR/Cas9. Altogether, we are attempting to demonstrate the feasibility of our anti-viral system and use our findings to direct the project design.

As a reaction to the presence of the virus, the plant cells will destroy infected cells through apoptosis as well as signal to the rest of the plant to begin production of defensive chemicals in preparation for attack. This signaling causes systemic required resistance, a broad, long-term increased resistant to future infections..

  • Explain and link this to the parameters in the model once the parameters are finalized
  • Explain reasons for the parameters

Model Formation

Biology of Viral Infection Spread

For information on this, please see the Intercellular Spread section of the CaMV biology page here.

Agent-Based Model Design

To trace the spread of the virus through the leaf, we used an agent-based model. Each cell produces and spreads the virus

  • Explain reasons for the parameters

Plant Structure

  • Cells are groups into leaves. Cells are only connected by plasmodesmata to other cells in the same leaf.
  • Each leaf also has one phloem (stem) that links to the central vasculature of the plant. These phloem cannot produce either viral particles or resistance molecules themselves; they only act as conduits to pass them along.

Model Assumptions

  • Viral Spread Chance - each time step, infected cells have a small probability of passing a virion to a neighboring cell. It is unbiological to have each cell's infection spread at every timestep, as this leads rapidly to 100% infection, contrary to observations . Unfortunately, no number for this infection probability could be found in literature, so a reasonable approximation of this value was implemented in order to emulate normal viral spread.
  • Cas9 is already at a steady state at time of infection

Plant Structure

  • Plasmodesmata
  • Phloems and Vascular System

Virus

  • Initial Infection Sites is a user-selected integer representing the number of lesions on a plant leaf for the application of the virus
  • Founder Population represents the number of viruses in each of the lesions, or the multiplicity of infection, which should be between 2 and 13
  • Viral Spread Rates the virus spreads at a rate of about 3 cells per day, but it takes longer for the cell to begin actively producing and exporting virions
  • Viral Spread Chance
  • Viral Assembly
  • Modify Virus "On" runs the simulation with Cas9, "Off" is without

Plant Response

  • SAR or Systemic Acquired Response, is a form of acquired immunity. The plant produces signalling molecules and enables cells to become resistant or lyse themselves
  • Resistance Threshold is the level of SA signalling molecule required for a cell to become resistant to the pathogen
  • Lysis Threshold is the level of SA signalling molecule required for a cell to undergo apoptosis to protect the rest of the organism
  • Signalling Molecule is generated by resistant or susceptible cells neighbouring infected or resistant cells at a rate of one per minute, after those neighbours have been infected/resistant for 8hrs. The model has been simplified to have both HR and SAR spread through the plant using one signalling chemical instead of the complex interactions between several different signalling molecules separately .

Agent-Based Modelling Software

We identified several requirements for the software used in our agent-based model:

  • Ability to create different kinds of agents (cells, vasculature, and others).
  • Control over connections between agents (e.g. plasmodesmata betweeen cells)
  • Support for complex rules (e.g. ODE simulations) within each agent
  • Arbitrary number of model states
  • Tracking of time since infection
  • Ease of use
NetLogo, the chosen agent-based modelling software
i

Three different software packages (MASON, MESA and Netlogo) were considered in depth. MESA is a Python-based simulation package and was not used due to its poor documentation and the level of familiarity with Python required to create the model. MASON, a Java-based simulation package, has excellent, easily-found documentation but no GUI and fewer built-in functions. Although fewer built-in functions could be an advantage (adding more flexibility and customization to the simulation), time constraints and unfamiliarity with Java pushed us to use NetLogo instead of MASON. NetLogo was easy to learn, well-documented and had a built in GUI. These were essential for rapid prototyping -- while some other choices would have been better able to handle large simulations, they would have had much longer development time for small changes, ultimately impeding our efforts to make a quality model.

Results

Normal -- no intervention

Video of spread in plant without CRISPR
Agent-based Netlogo model shows the spread of infection (red) and acquired resistance (blue) in a leaf where each agent simulates an ODE replication model. Without CRISPR, one leaf is entirely overwhelmed.

We were quite successful in making a reasonable representation of the normal process of viral spread. A typical model run proceeds as follows:

  • The virus quickly spreads to most of the initially infected lead, with only a small amount of resistance developing.
  • Once it has spread to this entire leaf, it spreads into the plant’s vascular system and the main stem.
  • Soon, all of the vascular structure is carrying the virus. But the infection runs its own course in each leaf.
  • In some cases, resistance builds up and seals off the point of initial infection. In others, the infection spreads into the leaf, but a sizable fraction of it becomes resistant.
  • Apoptosis occurs near the boundaries between infected and resistant regions, often cutting off these regions from the rest of the plant.

In a few cases, the plant is lucky & the initial infection was small, so the infection did not spread beyond the first leaf. However, most simulation runs result in over half the plant being infected.

CRISPR/Cas9 – our intervention

Video of spread in plant with CRISPR
Agent-based Netlogo model shows the spread of infection (red) and acquired resistance (blue) in a leaf where each agent simulates an ODE replication model. The CRISPR effect parameter (t1/2) is captured in the ODE.

When we introduce our CRISPR/Cas9 mechanism, and hold all other parameters constant, we see that the infection is stopped remarkably quickly. It rarely spreads into the vasculature. The level of resistance is correspondingly lower, since the plant detects less of a threat.

This effective prevention of viral spread is maintained even with moderate increases in other viral parameters and/or decrease in resistance.

Discussion

As with many projects in mathematical biology, one of the biggest challenges is finding accurate parameter values. Our slider-based approach was a creative solution that enables us to investigate the balance of different factors in viral spread and resistance, but it was quite arbitrary. Our results remain fundamentally qualitative – we can tell our intervention helps, but we can’t say by how much.

There are two main ways this could be improved. One is simply to more systematically explore this parameter space. Computationally, this would take a long time, since there are many variables with very large feasible ranges, but it is conceptually simple. However, there is a risk that this would not be particularly illuminating.

A better solution is to push for inventive experiments that can better determine these parameters. Tromas and colleagues make excellent use of flow cytometry to get this kind of data . This allows them to determine the infectivity of cells as a function of time. While this doesn’t quite give the probability per time of attempted spread events, it’s a very promising line of inquiry.

A different direction in which this model could be improved is having a more detailed and faithful plant architecture. There are many types of cells in plant leaves, for example, as well as multiple interconnectin plant defense mechanisms. There are also orders of magnitude more cells than we rendered. These changes would be needed to make our model more accurate; they would also entail running it on different software.

References

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