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| <header><strong class='sub_headers' style='font-size: 55px;'>CFD – Large Intestine (Colon) Model</strong></header> | | <header><strong class='sub_headers' style='font-size: 55px;'>CFD – Large Intestine (Colon) Model</strong></header> |
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− | <!-- Section 1 -->
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− | <button id='Section_a_collapsable' class='accordion' style='font-size: 20px; letter-spacing: 1.5px;'>Overview – Goals</button>
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− | <div id='panelCCFDa' class='panel' style='text-align: justify; padding: 20px 0px 0px 0px;'>
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| + | <!-- Section 1 --> |
| <article> | | <article> |
| + | <div style='text-align:center'><header><strong class='sub_headers'>Overview</strong></header></div> |
| <section class='sub_sections'> | | <section class='sub_sections'> |
| <div style='text-align: justify;'> | | <div style='text-align: justify;'> |
− | <p>Let's imagine that the classifier plasmids are ready to be used in vivo, thus, in clinical trials.</p> | + | <p><i>“Design is the distinguishing activity of synthetic biology”</i></p></br> |
− | <ul>
| + | <p>This paraphrased quote, originally coined by Herbert A. Simon to describe engineering, perfectly outlines the cornerstone of synthetic biology and the iGEM competition: the rational design of biological circuits by modular parts. Fueled by pure excitement for the promising and novel field of synthetic biology, we embarked on a multi-faceted journey into the world of iGEM and designed a bimodal project. The principal pillar of our efforts has been pANDORRA; a programmable AND OR RNAi Assembly platform engineered to optimize logic circuit design and implementation. We applied our modular assembly platform to build a multi-input RNAi based logic circuit to specifically target colorectal cancer cells. Adjuvantly, we concocted a bactofection system performing cell-specific adhesion and bacterial density dependent invasion and plasmid transference.</p> |
− | <li>How can we predict the path, which the genetically engineered bacteria will follow inside the large intestine?</li>
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− | <li>How can we be certain that our bacteria will eventually reach the area around the cancerous tissue?</li>
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− | <li>Will our bacteria attach to the carcinoma or will the Colon Chyme wash them out? </li>
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− | </ul>
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− | <p>The purpose of our Colon Fluid Dynamics model is to give an answer to those questions and to further explore the unknown and chaotic world of the human large intestine.</p>
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| </div> | | </div> |
| </section> | | </section> |
| </article> | | </article> |
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− | </div>
| + | <!-- Section 2 --> |
− | <!-- Section 2 -->
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− | <button id='Section_b_collapsable' class='accordion' style='font-size: 20px; letter-spacing: 1.5px;'>The Large Intestine</button>
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− | <div id='panelCCFDb' class='panel' style='text-align: justify; padding: 20px 0px 0px 0px;'>
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− |
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| <article> | | <article> |
| + | <div style='text-align: center'><header><strong class='sub_headers'>pANDORRA pipeline</br>a re-invention of the engineering cycle</strong></header></div> |
| <section class='sub_sections'> | | <section class='sub_sections'> |
| <div style='text-align: justify;'> | | <div style='text-align: justify;'> |
− | <p>In our project, the RNAi-based apoptotic circuit is to be eventually distributed via the gastrointestinal system towards the tumor inside the large intestine. Thus, it is essential that we examined carefully the properties of the colon's environment. </p> | + | <span><b>RNAi-based logic circuits</b></span> |
− | <p>The large intestine is the last section of the gastrointestinal tract that is responsible for absorbing water and nutrients and concurrently converting digested food into feces. (Even though the length of the colon is considerably smaller than the small intestine's, the thickness of the walls as well as its diameter are bigger.) The length of the colon approaches the mean value of 1.5m and 6-7cm in diameter in most humans.</p>
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− | <p>The Chyme (intestinal fluid containing the digested food) is transported from the small intestine towards the large intestine via the ileocecal sphincter. Chyme “settles” in the cecum, after its entrance into the large bowel, where it is mixed with bacteria which naturally reside in it constituting the gut's flora and contribute to much of the large intestine's functionality. The chyme is transferred consequently from one haustra to another by slow peristaltic waves. Those waves can be either mass movements, which are very slow and widespread movements happening a few times throughout the day and associated with food consumption by means of the gastrocolic and duodenocolic reflex or segmentation movements that mostly serve to chop and mix the intestinal content.</p> | + | <p>We aimed to develop a fully-predictable regulatory program, exploiting the distributed cellular availability of specific molecular input to differentiate various cell types by the production of a protein output. Following the engineering cycle, as described in [1], our first step was “Specification”. Our end goal at the beginning, was quite singular: create a molecular logic circuit, a biocomputer, that can trigger cell death or produce fluorescence when a certain expression profile is found in a cell. Before delving deeper into the inner working of our logic circuit design, let’s review two fundamental notions concerning the computing of such circuits:</p> |
− | <p>Peristalsis is a radially symmetrical contraction and relaxation of muscles that propagates as a wave down the tube (in our case the intestinal tube), in an anterograde direction. In the case of the human intestinal tract, smooth muscle tissue contracts in sequence to produce a peristaltic wave, which propels fecal aggregates along the tract. This is the main kind of movement that will be taken into account in our model. More technical details on the physical model of peristalsis are presented in the Human Colon Fluid Dynamics section of our model.</p>
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− | <p>The large intestine can be considered a mechanical propulsion system implying that one should determine its elastic and viscous properties before proceeding with the model. </p>
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− | <p>Some primitive tensile properties of the human large intestine are the maximal stress and destructive strain, valued at 0.9 MPa and 180% respectively<sup>[<a href='#ref1'>1</a>]</sup>. In addition, to gauge the elastic properties of the intestinal wall one needs to determine the elastic modulus (Young's modulus) as well as the Poisson Ratio.</p>
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− | <p>Young's modulus (E) is a numerical constant that describes the elastic properties of an elastic material undergoing tension or compression unidirectionally and functions as ameasure of the material's capacity to withstand alterations in its shape. The mathematical formula describing this physical entity is the following:</p></br>
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− | <span class='equation'>\[E = \frac{{stress}}{{strain}} = \frac{{F{L_0}}}{{A({L_n} - {L_0})}}\]</span>
| + | |
− | <p>The physical units of E in the metric system are Newtons per square meter (N/m<sup>2</sup>).</p>
| + | |
− | <p>Poisson's Ratio (σ) is the ratio of transverse contraction strain to longitudinal extension strain in the direction of the stretching force applied on the material's surface. The large intestinal tissue is commonly considered as soft tissue and the mathematical formula describing its Poisson's ratio is the following:</p>
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− | <span class='equation'>\[\sigma = - \frac{{d{\varepsilon _{trans}}}}{{d{\varepsilon _{axial}}}}\]</span>
| + | |
− | <p>Those values exist in the literature; as a mean value across all locations of the colon (distal, medial and proximal) as well as in every possible orientation (circumferental and longtitudinal) for the Elastic Modulus equal to 5.18 MPa and as a commonly accepted value of 0.5 for incompressible materials for soft tissue, such as the colon.[<a href='#ref2'>2</a>,<a href='#ref3'>3</a>]</p>
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− | </div>
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− | </section>
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− | </article>
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− | </div>
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− | <!-- Section 3 -->
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− | <button id='Section_c_collapsable' class='accordion' style='font-size: 20px; letter-spacing: 1.5px;'>Human Colon Fluid Dynamics</button>
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− | <div id='panelCCFDc' class='panel' style='text-align: justify; padding: 20px 0px 0px 0px;'>
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− |
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− | <article>
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− | <header><strong class='sub_headers'>Human Colon Fluid Dynamics </strong></header>
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− | <section class='sub_sections'>
| + | |
− | <div style='text-align: justify;'>
| + | |
− | <span>Our genetically engineered bacteria are supposed to navigate towards the cancerous tissue inside the large intestine via the gastrointestinal tract's chyme. As mentioned before, chyme is a fluid consisting of partly digested food flowing through the digestive tract. Thus, in order to determine the bacterial flow characteristics, a fluid dynamics analysis is mandatory. </span>
| + | |
− | <article>
| + | |
− | <div style='text-align: left'><header><strong class='sub_headers'>GEOMETRY</strong></header></div>
| + | |
− | <p>Colon cancer constitutes one of the most commonly diagnosed cancers worldwide, thus one could easily consider the importance of determining its morphology. More often than not, colorectal cancer emerges as a malignant transition of a polyp, therefore one could assume that they share their macroscopic geometry, particularly in the early stages.</p>
| + | |
− | <p>In our Colon Cancer CFD model, we assumed that the polyp, which evolved to cancer, is found in the proximal ascending colon of the large intestine as it is one of the most common colon regions where carcinomas are found (together with the Sigmoid Colon). Thus, the geometry of our model represents the caecum and a major part of the ascending colon. The CAD file for the geometry was designed with the “Autodesk – Inventor Professional” software.</p>
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− | <table>
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− | <tr>
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− | <td><img alt='One' title='one' class='sub_images' /></td>
| + | |
− | <td><p>It contains 2D identical structures which were then revolved into 3D objects and unified as an assembly so that they form a 3D solid structure.
| + | |
− | The round surface on the left of the solid represents the fluid inlet, thus it could be considered as the final part of the caecum </p></td>
| + | |
− | </tr>
| + | |
− | </table>
| + | |
− | <p>region close to the ileocecal sphincter. After the inlet, one could see the characteristic “curved cylindrical” shapes which represent the intestinal haustra. On the upper right side of the image is the fluid outlet which could be considered as the section close to the hepatic flexure which then continues to the transverse colon. </p>
| + | |
− | <p>After the construction of the outer intestinal geometry, the geometry of the cancerous polyp was added to the structure. By adding a 2D sketch on a working plane parallel to one of the haustra and by constructing a mushroom-like shaped solid, we were able to design the tumor inside the colon.</p>
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− | <table>
| + | |
− | <tr>
| + | |
− | <td><img alt='One' title='one' class='sub_images' /></td><td><p>The tumor is the blue object shown on the diagram. The solid which we created is very similar to the anatomical morphology of a human polyp. </p></td>
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− | </tr>
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− | </table>
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− | </article>
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− | </div>
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− | </section>
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− | </article>
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− | <!-- Section 4 -->
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− | <article>
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− | <div style='text-align: left'><header><strong class='sub_headers'>FLUID DYNAMICS GOVERNING EQUATIONS</strong></header></div>
| + | |
− | <section class='sub_sections'>
| + | |
− | <div style='text-align: justify'>
| + | |
− | <p>In this section we examine the physical laws behind the flow of the gastrointestinal fluids.</p>
| + | |
− | <p>The basic differential equations that govern the flow of fluids are the Navier – Stokes equations and the continuity equation. The mathematical form of those equations is as follows:</p>
| + | |
− | <span class='equation'>\[\rho \left( {\frac{{\partial {\bf{V}}}}{{\partial t}} + {\bf{V}} \cdot \nabla {\bf{V}}} \right) = - \nabla p + \rho {\bf{g}} + \nabla \cdot \left( {\mu (\nabla {\bf{V}} + {{(\nabla {\bf{V}})}^T})} \right) - \frac{2}{3}\mu (\nabla \cdot {\bf{V}}){\bf{I}})\]</span>
| + | |
− | <span class='equation'>\[\rho \nabla \cdot {\bf{V}} = 0\]</span>
| + | |
− | <p>where <strong>ρ</strong> (rho) stands for fluid density, <strong>V</strong> is the velocity vector of the fluid which produces a velocity field and <strong>μ</strong> (mu) stands for dynamic viscosity of the fluid. Let's analyze further each term in the equations:</p>
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| <ul> | | <ul> |
− | <li><span class='equation'>\[\rho \left( {\frac{{\partial {\bf{V}}}}{{\partial t}} + {\bf{V}} \cdot \nabla {\bf{V}}} \right)\] </span>: This term represents all the inertial forces.</li> | + | <li style='list-style: decimal'>The nature of the biological switches. Switches are the physical entities that implement a universal set of logic gates, thus enabling computation. A plethora of biomolecules can be utilized upon which to build switches. Between gene-based, RNA-based, protein-based etc. biological switches we chose trans-acting RNA switches and specifically miRNAs. Thanks to their ability to regulate a large fraction of the human transcriptome and natural implementation NOR logic [2] when multiple ones regulate the same gene, miRNAs have been extensively studied in mammalian systems. Moreover, they are excellent internal inputs since miRNAs are found to play crucial roles in the disease spectrum [3].</li> |
− | <li><span class='equation'>\[ - \nabla p\] </span>: This term all the pressure forces.</li> | + | <li style='list-style: decimal'>The rudimentary circuit abstraction. In order for a miRNA-based cell profiling to function, in accordance with seminal papers of the field [2, 4-7], a number of miRNA markers is selected and the circuit computes an AND gate with these markers in order to perform a classification task.Since miRNAs are molecules exerting solely inhibitory effects on expression, a repressor is required to repress the output, “linking” the high miRNA-markers that inhibit (directly or indirectly) the production of the repressor and the low miRNA-markers that typically target the output gene. As a result, we needed to select the nature of the repressor, with options including a transcriptional one such as LacI, a post-transcriptional one like a synthetic shRNA or both, as well as the in-depth topology, by determining the layers of the circuit (two or more). More elaborate architectures can be employed by utilizing this basic architecture</li> |
− | <li><span class='equation'>\[\nabla \cdot \left( {\mu (\nabla {\bf{V}} + {{(\nabla {\bf{V}})}^T})} \right) - \frac{2}{3}\mu (\nabla \cdot {\bf{V}}){\bf{I}})\] </span>: This term all the viscous forces.</li>
| + | |
− | <li><span class='equation'>\[\rho {\bf{g}}\] </span>: This term represents the external gravitational force of weight.</li>
| + | |
| </ul> | | </ul> |
− | <p>All these terms combined together, comprise the well-known Navier-Stokes which represent the conservation of momentum. The continuity equation for incompressible fluids represents the conservation of mass in the system. Another way of writing the Navier – Stokes equations for incompressible fluids is the following one:</p> | + | <p>In conclusion, we’ ve set our “classification” task as follows:</p> |
− | <span class='equation'>\[\rho \left( {\frac{{\partial {\bf{V}}}}{{\partial t}} + {\bf{V}} \cdot \nabla {\bf{V}}} \right) = - \nabla p + \rho {\bf{g}} + \mu {\nabla ^2}{\bf{V}}\]</span>
| + | |
− | <p>These equations generally hold for incompressible Newtonian fluids. In the case of fecal matter, we consider the fluid to be Newtonian as it is composed mainly of liquid water (close to 90%) while inside the caecum and ascending colon and because the relationship between the viscous stresses and the local strain rate is linear.</p>
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− | <p>Once we know the velocity field <strong>V</strong> as well as the pressure <strong>p</strong> in every spatial point of our geometry, we can determine the stress tensor, which in mathematical terms stands as follows:</p>
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− | <span class='equation'>\[{\bf{\sigma }} = - p{\bf{I}} + \eta [\nabla {\bf{V}} + {(\nabla {\bf{V}})^T}]\]</span>
| + | |
− | <p>From the stress tensor one could determine the values of two other important fluid mechanical quantities, the hydrodynamic force and the hydrodynamic torque, which are expressed mathematically as follows:</p>
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− | <ul>
| + | |
− | <li>Hydrodynamic Force: <span class='equation'>\[F(t) = \iint\limits_S(\[{{\bf{\sigma }} \cdot {\bf{n}}}\]) dS]</span></li>
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− | <li>Hydrodynamic Torque: <span class='equation'>\[L(t) = \iint\limits_S(\[{{\bf{x}} \times ({\bf{\sigma }} \cdot {\bf{n}})}\]) dS]</span></li>
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− | </ul>
| + | |
− | <p>These two integrals are calculated on the surface S and x stands for the positions on that surface.</p>
| + | |
− | <p>We should refer to a common dimensionless group in fluid dynamics that we used in our model. The ratio of inertial forces to viscous forces, Reynold's number (Re), is one of the most important dimensionless groups in fluid dynamics. The mathematical representation of Re is the following one:</p>
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− | <span class='equation'>\[{\mathop{\rm Re}\nolimits} = \frac{{\rho Vl}}{\mu }\]</span>
| + | |
− | <p>where <strong>ρ</strong> is the fluid density, <strong>V</strong> the fluid velocity, <strong>l</strong> the characteristic length (characteristic area in 3D objects) and μ the dynamic viscosity. The Reynold's number could be used as an indicator in order to determine whether a specific kind of fluid motion is laminar or turbulent of even transitional. In our case, the Reynold's number has a very low value equal to 0.00003 and thus, the viscous effects dominate the fluid. The reason why Reynold's number takes such a low value is that if we zoomed in the fluid we could see bacteria swimming at the same velocity as the fluid velocity field. Assuming that the size of a bacterium is about 10<sup>-6</sup>m, their swimming velocity is 30x10<sup>-6</sup> m/s and the density of the fluid in which the bacteria swim is 1000 kg/m<sup>3</sup> and the dynamic viscosity is around 0.001 Pa.s, the Reynold's number turns out to be equal to 1x10<sup>-5</sup>.</p>
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− |
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− | <button onclick='sizeWindowCCFD()' class='accordion' style='font-size: 30px; letter-spacing: 1.5px'>Life at low Reynolds numbers</button>
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− | <div class='panel' id='panelCCFD' style='font-size: 25px; text-align: justify; color: orange; margin: 10px;'>
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− | <i><p>Life at low Reynold's numbers: In environments such as a fluid with a very low Reynold's number, the particles which “live” inside the fluid are considered “swimmers” as they deform their surface to sustain their movement. In our case, the E. coli bacteria, which constitute an important part of the gut's flora, have helical flagella to help them with their locomotion. </p>
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− | <p>If a bacterium suddenly stops deforming its body, it will become a “victim” of the inertial forces of the fluid and thus, it will decelerate. At low Reynold's numbers, the drag force acting on the bacterium takes the form of viscous forces, <span class='equation'>\[{f_{drag}}\mathop \eta \limits^\~ UL\]</span> , and the bacterium can reach a distance of about 0.1 nm before stopping its movement. In contrast, at high Reynold numbers the distance is longer and thus, Re at low values can be interpreted as a non-dimensional coasting distance.</p>
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− | <p>One could describe the locomotion of a bacterium in low Re as a function of the swimming gait <strong>\[{u_s}(t)\] </strong>(velocity field on the body surface). At every instant, it can be assumed that the body is solid with unknown velocity <strong>\[U(t)\] </strong> and rotation rate <strong>\[\Omega (t)\]</strong>. Thus, the instantaneous velocity on the body surface is <span class='equation'>\[u = {\bf{U}} + {\bf{\Omega }} \times {\bf{x}} + {{\bf{u}}_s}\]</span>. To calculate in every time step the values of <strong>\[U(t)\] </strong> and <strong>\[\Omega (t)\]</strong>, one needs to determine both the velocity and stress fields in the problem in order to utilize the following integral:</p>
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− | | + | |
− | <span class='equation'>\[{\bf{\hat F}} \cdot U + {\bf{\hat L}} \cdot \Omega = - \iint\limits_S(\[{{u_s} \cdot \hat \sigma \cdot n}\]) dS]</span>
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− | | + | |
− | <p>Assuming that the swimmer is a bacterium with filament, what makes its movement in low Re possible is mainly the existence of drag forces perpendicular to the motion of the filament. The propulsive force generated along the filament (length L and deformation amplitude y(x,t)) is given by:</p>
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− | | + | |
− | <span class='equation'>\[{{\bf{F}}_{prop}} \approx ({\xi _ \bot } - {\xi _\parallel })\int_0^L {\left( {\frac{{\partial y}}{{\partial t}}\frac{{\partial y}}{{\partial x}}} \right)dx{e_x}} \]</span>
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− | | + | |
− | <p>This equation is a consequence of Purcell's Scallop Theorem and is derived for Re -> 0<sup>[<a href='#ref4'>4</a>]</sup>. </p></i>
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− | </div>
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| </div> | | </div> |
| </section> | | </section> |
| </article> | | </article> |
− | <!-- Section 5 -->
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| + | <!-- Section 3 --> |
| <article> | | <article> |
− | <div style='text-align: left'><header><strong class='sub_headers'>MESHING & NUMERICAL SIMULATION</strong></header></div> | + | <div style='text-align: center'><header><strong class='sub_headers'>Produce fluorescence or induce apoptosis when a specific miRNA expression profile* is found in colorectal cancer cells (Caco-2).</strong></header></div> |
| <section class='sub_sections'> | | <section class='sub_sections'> |
− | <div style='text-align: justify'> | + | <div style='text-align: justify;'> |
− | <p>The software for the model's numerical simulations is Comsol Multiphysics (v. 5.0) thus, the numerical method utilized is Finite Element Method (FEM).</p> | + | <p>*The miRNA expression profile should be predetermined in order to discriminate Caco-2 cells from healthy cells.</p> |
− | <p>The number of physical problems that can be solved analytically is very small compared to all the real world physical systems that can be solved only by approximations. One way to find a solution to a complex physical problem such as fluid flow in the human large intestine is to utilize discretization methods that lead to numerical solutions. An example of space discretization method is the Finite Element Method which considers an analytical function as a linear combination of basis functions. </p>
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− | <!-- EQUATION -->
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− | <p>Comsol Multiphysics uses this method in order to compute the numerical solutions of f<sub>ap</sub> in every single node of the space discretization. However, in order for such calculations to be possible one needs to discretize the problem geometry into nodes and elements. The grid that is being produced by the software user is called a “Mesh” and the shape of its elements can vary. In our model, the tetrahedron mesh was utilized, which is the 3D representation of the 2D triangle mesh. Although the meshing was implemented by the software itself by using “physics-based” mesh, the discretization method was tetrahedral as it is easy and quick to create but it also creates an unstructured grid which in our case is helpful as there are domain regions with large difference in the required scales. For instance, in the proximity of the tumor we needed a finer meshing as the numerical solutions would converge to more accurate values that way.</p>
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− | <table>
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− | <tr>
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− | <td><img alt='' title='' class='sub_images' src='' /></td><td><p>The mesh generated by Comsol Multiphysics is a physics-controlled mesh with finer elements. The tetrahedral space discretization is visible on the mesh plot. We present here two mesh plots; the first shows the tetrahedral meshing of the intestinal geometry and the second one depicts the interior region where the tumor meshing is visible.</p></td>
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− | </tr>
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− | <tr>
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− | <td><img alt='' title='' class='sub_images' src='' /></td>
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− | </tr>
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− | </table>
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| </div> | | </div> |
| </section> | | </section> |
| </article> | | </article> |
− |
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− | <!-- Section 6 -->
| + | <!-- Section 4 --> |
| <article> | | <article> |
− | <div style='text-align: left'><header><strong class='sub_headers'>Initial Parameters & Boundary Conditions</strong></header></div> | + | <div style='text-align: center'><header><strong class='sub_headers'>Circuit topology optimization & miRNA Boolean expression selection</strong></header></div> |
| <section class='sub_sections'> | | <section class='sub_sections'> |
− | <div style='text-align: justify'> | + | <div style='text-align: justify;'> |
− | <p>In CFD models one needs to determine the initial values of the parameters as well as the boundary conditions of the problem in order to get an accurate result from the solver.</p> | + | <p>Εxperimental classifiers have been designed by trial-and-error, by tweaking the parameters of the network in order to identify the optimal architecture and Boolean expression, or in a semi-manual fashion, via ranking and manual selection of differentially expressed miRNAs retrieved from databases produced by large scale studies. [8] There are several constraints that dictated theses approaches, for example the inadequacy of basic building blocks to better assemble and characterize various mammalian classifiers and the lack of powerful tools to automate logic circuit design based on miRNA molecular switches. Although daunting as a task, we set off to address both of these issues by:</p> |
− | <p>The normal velocity of Chyme inside the small intestine is below 1 cm/s and inside the large intestine it's even slower. Thus, we assumed that a logical value for the inlet normal velocity is 0.5 cm/s. The outlet boundary condition is pressure and its value is 101.16 kPa, close to 1 atm <sup>[<a href='#ref5'>5</a>]</sup>.</p> | + | <p>-Creating pANDORRA (programmable AND OR RNAi Assembly) in order to produce a large number of mammalian parts, which can be used for a bottom-up construction of any conceivable logic circuit based on universal logic gates</p> |
− | <p>The intestinal “tube” in our geometry is considered to be a no-slip wall in our study which implies that the velocity of the fluid particles close to the wall will tend to zero. The tumor region is a no-slip interior wall. </p> | + | <p>-Increasing the functionality and directionality of our assembly process by following a step-by-step cloning workflow and using standardized primers or overhangs after the integration of extensive technical feedback received by Stamatis Damalas. Click <a href=’https://2017.igem.org/Team:Greece/HP/Gold_Integrated’>here</a> to check it out.</p> |
| + | <p>-Employing a computational framework to facilitate the selection of circuit inputs (miRNAs), form the logic expression and simulate optimal circuit-performance in different topologies. Check out<a href=’https://2017.igem.org/Team:Greece/RNAi%20Classifier%20Desig#'>our model</a> |
| + | <p>As in mature engineering clades, models simplify the real work and facilitate design in ideal conditions. Other models then evaluate the proposed designs more thoroughly and either send the designers back to the drawing board or to the test bench; that is the essence of our design approach: a progressive dance where modelling and design come ever closer together.</p> |
| </div> | | </div> |
| </section> | | </section> |
| </article> | | </article> |
− | </div>
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− | <!-- Section 7 -->
| + | </section> |
− | <button id='Section_k_collapsable' class='accordion' style='font-size: 20px; letter-spacing: 1.5px;'>Results</button>
| + | </article> |
− | <div id='panelCCFDk' class='panel' style='text-align: justify; padding: 20px 0px 0px 0px;'>
| + | <!-- A. THE BASIC COMPONENTS OF THE CIRCUIT --> |
− | | + | <article> |
| + | <header><strong class='sub_headers' style='font-size: 55px;'>A. THE BASIC COMPONENTS OF THE CIRCUIT</strong></header> |
| + | <section> |
| + | <!-- Section 1 --> |
| <article> | | <article> |
| + | <div style='text-align:left'><header><strong class='sub_headers'>Wet Lab Input</strong></header></div> |
| <section class='sub_sections'> | | <section class='sub_sections'> |
| <div style='text-align: justify;'> | | <div style='text-align: justify;'> |
− | <p>The velocity field of the fluid flow inside the large intestine is quite complex, when peristalsis occurs, as the intestinal walls contract in a periodical manner in order to forward the colon contents towards the rectum where they are being secreted. However, that kind of study is beyond the scope of our model. In our model the inlet velocity is a consequence of the contraction of the caecum but we assume that the time scale of the peristalsis is bigger than the fluid movement's; thus, no peristaltic waves occur throughout our model and the fluid is driven by its inlet velocity and a pressure outlet which is close to 1 atm.</p> | + | <p>The sequences of the plasmids used for the construction of the cell-type classifier between HeLa cells and healthy cells described in [4] were kindly provided by Prof. Xie. We've used these plasmids as a starting point to “detach” three different mammalian promoters, three different protein coding regions and two polyA signals-terminators, codon-optimize them in order to make them BioBrick compatible and order them for de novo gene synthesis. Analytically:</p> |
− | <p>Also, viscosity is a rather important factor when it comes to fluid flow. The intestinal fluid, due to nutrients and water absorption, doesn't possess a constant viscosity value; although the site of absorption and phase change of Chyme is the Transverse Colon and not the Caecum and Ascending Colon, the digested food determines to a high degree the success of nutrients and water absorption. Thus, we considered essential to examine the fluid flow under different dynamic viscosity values.</p> | + | <ul> |
| + | <li style='list-style: decimal'>Promoters |
| + | <ul> |
| + | <li style='list-style: none'>-CMV (strong constitutive promoter from the human cytomegalovirus)</li> |
| + | <li style='list-style: none'>-TRE (inducible tetracycline response element promoter)</li> |
| + | <li style='list-style: none'>-CAGop (strong hybrid CAG promoter followed by an intron with two LacO sites [2]</li> |
| + | </ul> |
| + | </li> |
| + | <li style='list-style: decimal'>Protein Coding Regions |
| + | <ul> |
| + | <li style='list-style: none'>-rtTA (reverse tetracycline-controlled transactivator by fusing rTetR with VP16, utilized in Tet-On systems) [10]</li> |
| + | <li style='list-style: none'>-LacI (DNA-binding transcription factor that binds to LacO sites) </li> |
| + | <li style='list-style: none'><strong>- Transcriptional repressor </strong></li> |
| + | <li style='list-style: none'>-DsRed (Discosoma sp. red fluorescent protein)</li> |
| + | <li style='list-style: none'>-Apoptin </li> |
| + | </ul> |
| + | </li> |
| + | <li>polyA signals & terminators (include the motif AAUAAA which promotes both polyadenylation and termination) |
| + | <ul> |
| + | <li style='list-style: none'>-SV40 polyA</li> |
| + | <li style='list-style: none'>-rbGlob polyA*</li> |
| + | </ul> |
| + | </li> |
| + | </ul> |
| + | <p>*Next to the rbGlob polyA (upstream) there is a sequence coding for a synthetic miRNA, targeting a region of firefly luciferase [11]. Named FF4, it is a <strong>posttranscriptional repressor</strong>.</p> |
| + | <p>As a result, using these <a href='https://2017.igem.org/Team:Greece/Basic_Part'>Basic Parts</a>, a large number of circuit topologies can be envisioned.</p> |
| </div> | | </div> |
| </section> | | </section> |
| </article> | | </article> |
− | <!-- Section 8 -->
| + | <!-- Section 2 --> |
| <article> | | <article> |
− | <div style='text-align: left'><header><strong class='sub_headers'>Velocity Field – Dynamic Viscosity μ=0.6913 mPa∙s</strong></header></div> | + | <div style='text-align: center'><header><strong class='sub_headers'>Dry Lab Input</strong></header></div> |
| <section class='sub_sections'> | | <section class='sub_sections'> |
− | <p>The dynamic viscosity in this section is the value of Water Dynamic Viscosity at T = 37<sup>o</sup>C. The following diagram shows the velocity field distribution inside the colon geometry.</p> | + | <div style='text-align: justify;'> |
− | <img alt='' title='' class='sub_images' />
| + | <p>There is an ongoing debate regarding the choice of using transcriptional repressors (LacI) that act as a roadblock to RNA Polymerase or posttranscriptional repressors (FF4 and other synthetic intronic miRNAs) that act by a completely different mechanism by mRNA degradation. Experimental evidence [4] support the combination of transcriptional and post-trascriptional repression as a boost in circuit performance. However, we wanted to proceed to a more detailed analysis regarding the selection of an appropriate repressor. You can check the results of this analysis <a href='https://2017.igem.org/Team:Greece/RNAi%20Classifier%20Design'>here</a>.</p> |
− | <img alt='' title='' class='sub_images' />
| + | </div> |
− | <img alt='' title='' class='sub_images' /> | + | |
| </section> | | </section> |
| </article> | | </article> |
− | <!-- Section 9 -->
| + | <!-- Section 3 --> |
| <article> | | <article> |
− | <div style='text-align: left'><header><strong class='sub_headers'>Velocity Field – Dynamic Viscosity μ=0.01 Pa∙s</strong></header></div> | + | <div style='text-align: center'><header><strong class='sub_headers'>AND Logic Implementation & Output</strong></header></div> |
| <section class='sub_sections'> | | <section class='sub_sections'> |
− | <div style='text-align: justify'> | + | <div style='text-align: justify;'> |
− | <p>The following diagram shows the velocity field distribution inside the colon geometry.</p> | + | <p>Thanks to this combined analysis, we have designed the Biobricks to use in the experiments/simulations and made a strong case for the case-by-case use of a transcriptioal or post-trascriptional repressor according to a the miRNA dataset.</p> |
− | \[\mathop {\lim }\limits_{x \to \infty } x\]
| + | |
− | <img alt='' title='' class='sub_images' />
| + | |
− | <img alt='' title='' class='sub_images' />
| + | |
| </div> | | </div> |
| </section> | | </section> |
| </article> | | </article> |
− | <!-- Section 10 --> | + | </section> |
| + | </article> |
| + | <!-- B. MODULAR CIRCUIT ASSEMBLY & OPTIMIZATION ALGORITHM --> |
| + | <article> |
| + | <header><strong class='sub_headers' style='font-size: 55px;'>B. MODULAR CIRCUIT ASSEMBLY & OPTIMIZATION ALGORITHM</strong></header> |
| + | <section> |
| + | <!-- Section 1 --> |
| <article> | | <article> |
− | <div style='text-align: left'><header><strong class='sub_headers'>Velocity Field – Dynamic Viscosity μ=1 Pa∙s</strong></header></div> | + | <div style='text-align:left'><header><strong class='sub_headers'>Wet Lab Input</strong></header></div> |
| <section class='sub_sections'> | | <section class='sub_sections'> |
− | <div style='text-align: justify'> | + | <div style='text-align: justify;'> |
− | <p>The dynamic viscosity in this section is the value of Water Dynamic Viscosity at T = 37<sup>o</sup>C. The following diagram shows the velocity field distribution inside the colon geometry.</p> | + | <p>We envisage pANDORRA as a cloning toolkit with standard parts (designed in the previous step) that can be easily applicable to the construction of a wide range of transcriptional/posttranscriptional synthetic circuits. In this endeavor, we focused on two aspects, interoperability and modularity, by <a href='https://2017.igem.org/Team:Greece/HP/Gold_Integrated'>integrating extensive technical feedback from experts in the field.</a></p> |
− | <img alt='' title='' class='sub_images' /> | + | <p>According to Benenson et al., 2012 [9], an effective molecular switch or gate is characterized by:</p> |
− | <img alt='' title='' class='sub_images' /> | + | <ul> |
| + | <li style='list-style: disc'>The existence of a robust digital regime (that is, input levels that produce either a very low or a very high (saturated) output)</li> |
| + | <li style='list-style: disc'>Gate scalability, which is the capacity to receive an increasing number of inputs without dramatic design alterations</li> |
| + | <li style='list-style: disc'>Composability, which is the capacity to operate together with other gates in parallel and/or in cascades in a predictable manner</li> |
| + | </ul> |
| + | <p>In order to add the aforementioned features to our toolkit and to aid in the cloning process, we created various Composite Parts, that can be used to create multi-layered classifiers. At first glance, the constructs have the following general structure:</p> |
| + | <p>Promoter + Protein Coding Region + <a href='http://parts.igem.org/Part:BBa_K515105'>BBa_K515105</a> + polyA signal & terminator</p> |
| + | <p>Analytically, <a href='http://parts.igem.org/Part:BBa_K515105'>BBa_K515105</a> consists of superfolder GFP (sfGFP), a very brightly fluorescent protein under the control of the bacterial constitutive promoter J23100 and is used as a reporter to simplify the validation process during cloning. </p> |
| + | <img class='sub_image' src='' /> |
| + | <p>It is flanked by two recognition sites for BbsI, a type IIS restriction enzyme and two annealing sites for a universal M13 forward & reverse primer. As type IIS restriction enzymes recognize asymmetric DNA sequences and cleave outside of their recognition sequence, they are central to our approach for fusing miRNA target sequences into the 3’-untranslated region, as described in the next section. Examples of these constructs include:</p> |
| + | <table> |
| + | <tr><td><img class='sub_image' src='https://static.igem.org/mediawiki/2017/5/58/Greekom_Design_Composite1.png' /></td></tr> |
| + | <tr><td><img class='sub_image' src='https://static.igem.org/mediawiki/2017/c/c3/Greekom_Design_Composite2.png' /></td></tr> |
| + | <tr><td><img class='sub_image' src='https://static.igem.org/mediawiki/2017/4/4c/Greekom_Design_Composite3.png' /></td></tr> |
| + | <tr><td><img class='sub_image' src='https://static.igem.org/mediawiki/2017/b/b3/Greekom_Design_Composite4.png' /></td></tr> |
| + | <tr><td><img class='sub_image' src='https://static.igem.org/mediawiki/2017/9/98/Greekom_Design_Composite5.png' /></td></tr> |
| + | </table> |
| + | <p>Notably, the output module can include either a coding region for a fluorescent protein, DsRed or a toxin, Apoptin (<a href='http://parts.igem.org/Part:BBa_K1061001'>BBa_K1061001</a>), a selective cancer cell killer derived from the Chicken Anemia Virus (CAV) known to cause p53-independent apoptosis in more than 70 human cancer cell lines while leaving normal cells unharmed [12]. The use of Apoptin instead of hbax [4] was a change incorporated for increased cytotoxicity and an additional safety fail-safe after discussing with <a href='https://2017.igem.org/Team:Greece/HP/Gold_Integrated'>Prof. JD Keasling and interpreting OSIRIS results.</a></p> |
| + | <p>The aforementioned Biobricks can be used to fuse any desired complementary miRNA binding site into the 3’-untranslated region, between the BbsI restriction sites hardcoded into the coding and the terminator sequences to control the expression of each module by specific miRNAs. This process has the following requirements:</p> |
| + | <ul> |
| + | <li style='list-style:none'>(1) Composite Parts in the form of Promoter + Protein Coding Region + <a href='http://parts.igem.org/Part:BBa_K515105'>BBa_K515105</a> + polyA signal & terminator, BioBrick compatible format</li> |
| + | <li style='list-style:none'>(2) A number of repeated miRNA binding sites in BioBrick compatible format</li> |
| + | <li style='list-style:none'>(3) A set of standarized Extended Primers which are part of the MetaBrick Platform [13] that incorporate BsaI restriction sites to the Prefix-Suffix.</li> |
| + | </ul> |
| + | <img class='sub_image' src='https://static.igem.org/mediawiki/2017/b/bc/Greekom_Design_pANDORRA2.png' /> |
| + | <p>If the aforementioned requirements are fulfilled, then the following method is followed:</p> |
| + | <ul> |
| + | <li style='list-style:none'>(1) PCR amplification of the miRNA binding sites BioBricks</li> |
| + | <li style='list-style:none'>(2) Digestion with BbsI of the Promoter + Protein Coding Region + <a href='http://parts.igem.org/Part:BBa_K515105'>BBa_K515105</a> + polyA signal & terminator BioBricks</li> |
| + | <li style='list-style:none'>(3) Digestion with BsaI of the PCR amplified miRNA binding sites BioBricks</li> |
| + | <li style='list-style:none'>(4) The digested products have compatible sticky ends. As a result one example of the final constructs is:</li> |
| + | </ul></br> |
| + | <img class='sub_image' src='https://static.igem.org/mediawiki/2017/8/8b/Greekom_Design_pANDORRAfinal2.png' /> |
| </div> | | </div> |
| </section> | | </section> |
| </article> | | </article> |
− | <!-- Section 11 -->
| + | <!-- Section 2 --> |
| <article> | | <article> |
− | <div style='text-align: left'><header><strong class='sub_headers'>VELOCITY FIELD MAGNITUDE – TUMOR REGION </strong></header></div> | + | <div style='text-align: center'><header><strong class='sub_headers'>Dry Lab Input</strong></header></div> |
| <section class='sub_sections'> | | <section class='sub_sections'> |
− | <div style='text-align: justify'> | + | <div style='text-align: justify;'> |
− | <p>In these diagrams, the magnitude of the fluid's velocity field is given with respect to the arc length of the tumor. In the following diagram, we depict the boundary arc chosen.</p><img alt='' title='' class='sub_images' /> | + | <p>The multiple architectures that emerge from the pANDORRA toolkit can be evaluated by using the <a href='https://2017.igem.org/Team:Greece/RNAi%20Classifier%20Design'>RNAi classifier design model</a> in order to recognize the optimal one for every different classification task, for example classifying Caco-2 cells. Moreover, in our model the number of repeats for miRNA binding sites is evaluated. Another point that gets elucidated is the position of the TFF4 binding site. In our models, it is adjacent to the polyA terminator as Haefliger et al., 2016 [14] showed that when the TFF4 is upstream of other binding sites, the downstream binding sites for other miRNAs are not affected by their miRNA mimics and thus optimal knockdown efficiency isn’t observed. Check the results of this process <a href='https://2017.igem.org/Team:Greece/RNAi%20Classifier%20Design'>here</a>.</p> |
− | <img alt='' title='' class='sub_images' />
| + | |
− | <img alt='' title='' class='sub_images' />
| + | |
− | <p>One could observe that between the velocity magnitude maxima appear a few local minima which we decided to call “Velocity Field Valley Traps (VFVT)” (or Valleys of the Muses). In these regions, the velocity around them has a greater value, thus, the bacteria “swimmers” that will reach these regions will most likely stay there and attach to the tumor rather than being washed out by the fluid. We could consider those regions as local stagnation regions of the fluid. Although the local maxima for each dynamic viscosity value are found at about the same location on the arc boundary of the tumor, the local minima or VFVTs don't follow the same rule. Having said that, the VFVTs for viscosity values 0.01 Pa.s and 1 Pa.s are located on the same regions which implies that for viscosity changes in that range the regions of the tumor on which the bacteria would attach doesn't change. Those regions are:</p>
| + | |
− | <!-- TABLE --><img alt='' title='' class='sub_images' />
| + | |
− | <p>However, for viscosity value 0.6913 mPa.s the VFVTs seem to have a slight displacement from the other VFVT locations. More specifically, the first and third VFVTs “moved” towards the top arc length which implies that for low viscosities the VFVTs appear closer to more curved regions of the tumor geometry. </p>
| + | |
− | <!-- TABLE --><img alt='' title='' class='sub_images' />
| + | |
| </div> | | </div> |
| </section> | | </section> |
| </article> | | </article> |
− | <!-- Section 12 -->
| + | <!-- Section 3 --> |
| <article> | | <article> |
− | <div style='text-align: left'><header><strong class='sub_headers'>DRAG FORCES ON THE TUMOR REGION</strong></header></div> | + | <div style='text-align: center'><header><strong class='sub_headers'>AND Logic Implementation & Output</strong></header></div> |
| <section class='sub_sections'> | | <section class='sub_sections'> |
− | <div style='text-align: justify'> | + | <div style='text-align: justify;'> |
− | <p>In our study of the fluid flow near the tumor, it is essential to determine the drag forces on the tumor if we want to predict whether our ‘bactofectors' will manage to stay attached to the tumor. Thus, due to the small cohesive forces between the bacteria and the tumor surface, it is safe enough to assume that the total stress forces on the tumor due to the fluid will apply to the bacteria as well.</p> | + | <p>By this back-and-forth approach, the optimal classifier can be computationally predicted and assembled from compartmentalized modules. The architectures that emerged through this exhaustive analysis have been characterized in 3 cell lines, Caco-2, HEK-293, A549. Check the results of this process <a href='https://2017.igem.org/Team:Greece/Results'>here</a>.</p> |
− | <p>We computed the total drag forces on the tumor arc boundary (same as the velocity magnitude) by integrating the total stresses over the entire arc length. </p>
| + | |
− | <img alt='' title='' class='sub_images' />
| + | |
− | <img alt='' title='' class='sub_images' />
| + | |
− | <img alt='' title='' class='sub_images' />
| + | |
− | <p>What seems interesting in these diagrams is the fact that for different values of fluid viscosity the total stress on the boundary remains the same. Why does this happen?</p>
| + | |
− | <p>Well, let's remind ourselves that by integrating the total stresses on the arc boundary, we assume both the pressure and viscous forces. Thus, we should distinguish the two cases and examine which case is affected by the varying viscosity values.</p>
| + | |
− | <p>If we could make a prediction, it would be logical to assume that viscosity affects the viscous forces which interest us.</p>
| + | |
| </div> | | </div> |
| </section> | | </section> |
| </article> | | </article> |
− | <!-- Section 13 -->
| + | <!-- Section 4 --> |
| <article> | | <article> |
− | <div style='text-align: left'><header><strong class='sub_headers'>VISCOUS FORCES ON THE TUMOR REGION</strong></header></div> | + | <div style='text-align: center'><header><strong class='sub_headers'>Cancer-targeting and invasion module</strong></header></div> |
| <section class='sub_sections'> | | <section class='sub_sections'> |
− | <div style='text-align: justify'> | + | <div style='text-align: justify;'> |
− | <img alt='' title='' class='sub_images' /> | + | <p>Type I pilli, surface rod-shaped organelles 7nm in diameter and 1μm in length, are the best studied system of bacterial adhesion [15].They are heteropolymers of four proteins with FimA being the main structural protein of the pilli, which polymerizes approximately 1000 times to form a right-handed helix that constitutes the main axis of the structure and includes smaller concentrations of FimG, FimF and FimH [16-18]. FimH is the functional component of the structure as it alone confers the ability to bind to a-D-mannose of various eukaryotic cells and is located at the tip and the shafts of the pilus, whereas FimF and FimG seem to be responsible for docking FimH to FimA [19-20]. To achieve selective adhesion to colorectal cancer cells using type I pilli we need to disrupt their natural ability to bind to a-D-mannose and introduce a mechanism to facilitate adhesion to CRC cells by a mannose-independent mechanism. A mutation in the 49th amino acid of FimH has been demonstrated to completely abolish mannose binding [21]. In addition, a small peptide called RPMrel has been identified through phage display assays due to its ability to bind to five different colorectal cancer cell lines as well as cancerous tissues obtained by biopsies and not to other kinds of cancer [22]. Taken together these two modifications perform both the functions specified for CRC selective binding and have been successfully used by previous iGEM teams, iGEM Harvard 2015 and iGEM Ankara 2016 to that end. We employed the same part <a href=’http://parts.igem.org/Part:BBa_K1850011’>BBa_K1850011</a> that was submitted by iGEM Harvard 2015, in a fimH KO strain. Having achieved selective adhesion to colorectal cancer cells we move on to the second half of our device, internalization and transference of genetic material. Strains of the bacteria E. coli can be modified so that they will express two key proteins : invasin and listeriolysin O [23-24]. Invasin gives the bacteria, the ability to enter epithelial and other non phagocytic cells [25-26]. Listeriolysin O, on the other hand, has to do with what happens to the bacteria after they enter the target-cell. This particular protein allows the bacteria to free themselves of the vesicle that was used for their phagocytosis, without damaging the plasmatic/cell membrane of the target-cell. This happens due to the low pH of the vesicle (~5.9-6) that is also the optimal pH range for the protein listeriolysin [27-28]. The modified strains of <i>E. coli</i>, through expressing these proteins are able to not only enter non phagocytic target-cells that express b1-integrins but also to transfer their load to them, through escaping the phagolysosome [23]. Finally, we aim to put invasin and listeriolysin O under quorum control, through the use of the <i>lux</i> genetic circuit of <i>Vibrio fischeri</i>, as this operon has been utilized to achieve cell-density dependent invasion. During our communication with the safety committee, we were extremely glad to hear that we submitted a thorough and analytical Check In form and the Committee Members advised us to focus on the safe implementation of our classifier module and then consider a transfer method. As a result, we switched our focus and put great effort to characterize the components of our classifier to demonstrate the while integrating feedback from the scientific community about the health risks of our conceptual anticancer agent, formulating what we term, a <strong>5-STAR security system</strong>, which represents the culmination of our proposed modifications:</p> |
− | <img alt='' title='' class='sub_images' /> | + | <strong> |
− | <img alt='' title='' class='sub_images' /> | + | Level 1:</br> |
| + | Bacteria preferentially colonize cancer tissue compared to the adjacent healthy</br> |
| + | Level 2:</br> |
| + | Bacteria are genetically modified to express a mutated fimH, carrying a colorectal cancer-binding peptide and a point-mutation abolishing its natural substrate binding affinity.</br> |
| + | Level 3</br> |
| + | Bacteria express the invasion mechanism under the control of a lux operon, in order to achieve cell-density dependent invasion</br> |
| + | Level 4</br> |
| + | The classifier circuit, transferred by the bacteria for the final bactofection goal, is meticulously designed in order to elicit a actuation (e.g. apoptosis) selectively in cancer cells</br> |
| + | Level 5</br> |
| + | The therapeutic protein output of our classifier is Apoptin, which causes p53-independent apoptosis in more than 70 human cancer cell lines while leaving normal cells unharmed [12]</br> |
| + | </strong> |
| </div> | | </div> |
| </section> | | </section> |
| </article> | | </article> |
− | <!-- Section 14 - Conclusions -->
| + | <!-- References --> |
− | <article>
| + | |
− | <div style='text-align: left'><header><strong class='sub_headers'>Shear Rate and probability of Tumor Surface Attachment</strong></header></div>
| + | |
− | <section class='sub_sections'>
| + | |
− | <div style='text-align: justify'> | + | |
− | <p>Bacterial locomotion, in fluid flows with low Reynolds numbers, behave in a bizarre manner. To be more specific, the Navier – Stokes equation for an incompressible fluid takes the following form:</p>
| + | |
− | <span class='equation'>\[\nabla p - {\bf{f}} = \mu {\nabla ^2}{\bf{u}}\]</span>
| + | |
− | <p>In case there is an imbalance between the driving forces and the dissipation, the fluid reacts to this imbalance by altering the magnitude and direction of u in order to reach a state where there is a balance between the viscous and other forces. The imposed boundary conditions on the system determine the state of the system on the same time step as no boundary “memory” appears. Thus, the fluid depends on each time step on the boundary conditions and that implies the existence of time-reversibility [13].</p>
| + | |
− | <p>According to literature [6], surface attachment of bacteria is enhanced not in high-shear regions as one could expect but in low-shear regions. More specifically, the factor which determines the degree of bacterial attachment on a surface is the shear-induced trapping which in low-shear regions is enhanced. Thus, for small shear rates (0 – 10 s-1) one could expect sufficient bacterial surface attachment. However, in these low-shear regions chemotaxis may be compromised. Fortunately, in our Quorum Sensing Model, our bacterial communication through the AHL molecule does not affect bacterial locomotion thus chemotaxis in our case is not an issue.</p>
| + | |
− | <img alt='' title='' class='sub_image' src='' />
| + | |
− | <p>It is interesting to notice that the shear stress values on the tumor boundaries are within the low-shear region limits and thus, we expect a considerable number of our bacteria to attach to the tumor surface.</p>
| + | |
− | </div>
| + | |
− | </section>
| + | |
− | </article>
| + | |
− | </section>
| + | |
− | <!-- References -->
| + | |
| <div id='references'> | | <div id='references'> |
| <article> | | <article> |
Line 319: |
Line 263: |
| </article> | | </article> |
| </div> | | </div> |
| + | </section> |
| </article> | | </article> |
| </div> | | </div> |