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~~<div class="menulogo">MANIFOLD 2</div>~~

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~~<a class="hvr-sweep-to-right" href="https://2020.igem.org/Team:Virginia">Main</a>~~

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~~<a class="hvr-sweep-to-right" href="#abstract">Abstract</a>~~

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~~<a class="hvr-sweep-to-right" href="#problem">Problem</a>~~

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~~<a class="mainitem" href="#project">PROJECT</a>~~

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~~<a class="hvr-sweep-to-right" href="https://2020.igem.org/Team:Virginia/Inspiration">Inspiration</a>~~

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~~<a class="hvr-sweep-to-right" href="https://2020.igem.org/Team:Virginia/Description">Description</a>~~

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~~<a class="hvr-sweep-to-right" href="https://2020.igem.org/Team:Virginia/Design">Design</a>~~

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~~<a class="hvr-sweep-to-right" href="https://2020.igem.org/Team:Virginia/Experiments">Experiments</a>~~

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~~<a class="hvr-sweep-to-right" href="https://2020.igem.org/Team:Virginia/Results">Results</a>~~

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~~<a class="hvr-sweep-to-right" href="https://2020.igem.org/Team:Virginia/Modeling2">Modeling</a>~~

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~~<a class="hvr-sweep-to-right" href="https://2020.igem.org/Team:Virginia/Software">Software</a>~~

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~~Index:~~

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~~<div class="contentHolder">~~

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~~<div class="genTitle">~~

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~~<div>Modeling</div>~~

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~~<div class="sectionTitle" id="Section 1">Overview</div>~~

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~~<div class="paragraph">~~

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Our scaffold-incorporated bacterial microcompartment (BMC) system, called MANIFOLD, incorporates targeted enzyme fusions to the inner BMC shell proteins to spatially orient select enzymes to minimize metabolic flux leakage. For the Summer of 2020, the team thoroughly developed a proof-of-concept for the production of model molecule trans-resveratrol for its compact size and compatibility.

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With the onset of the global pandemic and need for quick project adaptations to a virtual environment, the modeling team sought to put a positive twist on the unprecedented circumstances and took the opportunity to flesh out a thorough multi-scale model to support experimental design in wet lab and explore various other facets of resveratrol metabolism optimization. We utilized a multitude of mathematical models in both Matlab and Python to understand the viability of our BMC system. We chose to embrace the complexities that modeling could envelop and built a multi-scale model balancing assumptions with the realistic conclusions we were to make.

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From our endeavors, we determined the optimized expression of our 14 different parts utilizing cataloged parts from the iGEM Parts Registry and the expected increase of biosynthesized trans-resveratrol when utilizing the MANIFOLD system. Our silico chronology began with a considerable amount of literature review to familiarize ourselves with recent advances in BMC research. From this, we were able to construct an optimization model for ideal part expression used in future wet lab practices. We then delved into the reaction kinetics of our system to quantify the improvement of MANIFOLD on current methods of trans-resveratrol biosynthesis.

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~~<div class="sectionTitle" id="Section 2">Research-Driven Analysis</div>~~

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The in silico investigation of MANIFOLD was guided by these questions relating to the improved assembly and efficiency of our system. In order for our design to present a significant breakthrough in metabolic engineering, we needed quantitative answers. To first construct these questions, the modeling team conducted research driven analysis to determine what parts of our system may already be characterized and which may require further modeling efforts.

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The bacterial microcompartment shell became the first topic of conversation. The [21-gene] Pdu operon (named for its natural 1,2-propanediol metabolism pathway) derived from citrobacter freundii has been only recently elucidated in literature. The shell is known to be composed of certain pdu proteins with pdu enzymes naturally localized to the interior of the compartment. The proteinaceous shell ideally forms an icosahedral shell with a mean face-to-face diameter of 117.9919 nanometers (Figure 1).[1](Apparent size and morphology of bacterial microcompartments varies with technique) Our study utilized seven pdu proteins (pduABJKNUT) which are necessary for the formation of this nanocarrier and therefore lead to BMCs of the same size.

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~~<img src="https://static.igem.org/mediawiki/2020/d/d6/T--Virginia--images--icosahedral.JPG"/>~~

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<b>Fig 1.</b> 3D rendering of the icosahedral shape of an assembled BMC. Dimensions formulated from findings in Kennedy et. al.[1] to be 117.992 nanometers with a side length of 68.123 nanometers. Note: Images represent the idealized BMC structure based on hypothesized methods of pdu protein assembly.

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Our selection of this synthetic pdu operon [2] (Synthesis of Empty Bacterial Microcompartments) was bolstered by a recent study elucidating the stoichiometric composition of these proteinaceous enclosures. [3] (Decoding the stoich) This resource quantified the ratio between pdu proteins apparent in BMC enclosures (Figure 2) which solidified the quantitative backing we needed for progression of part expression analysis. With twelve parts required for full assembly of the MANIFOLD system, the challenge of correct, relative expression became a pressing issue. With the realization of no immediate availability of in-lab practices to help in guiding these judgements through fluorescence or scanning electron microscopy methods, our attention shifted towards expanding upon methods used in literature to create an optimization model in silico.

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~~<div class="sectionTitle" id="Section 3">Relative Part Expression</div>~~

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~~<h3> BMC Background~~

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~~</h3>~~

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The pduJ protein is the most abundant protein (5212 monomers)[3] of the BMC shell. Therefore, any MANIFOLD system with correct construction of the BMC would mandate the expression of at least 5212 pduJ proteins. We therefore used the expression of pduJ as a relative lower bounded baseline for computing idealized expression of all other parts of the MANIFOLD system. These predicted relativities in part expression were deduced from theoretical relationships within the bacterial microcompartment.

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One of these key stoichiometric relationships is mediated through the pduA shell protein. The most well-researched process of inner-luminal binding is orchestrated through the pduA protein. The N-terminal of the pduD protein is hypothesized to bind with the C-terminal (luminal-facing) residues of pduA.[4] (Exploring Bacterial Organelle Interactomes: A Model of the Protein-Protein Interaction Network in the Pdu Microcompartment) MANIFOLD utilizes the first eighteen amino acids of pduD as a tag for interior localization to the BMC as has been performed before.[5] (The N-Terminal Region of the Medium Subunit (PduD) Packages Adenosylcobalamin-Dependent Diol Dehydratase (PduCDE) into the Pdu Microcompartment) This peptide sequence was combined with the zinc finger domain to enable DNA scaffold localization to the interior of the BMC for subsequent enzyme attachment. This connectivity is significant in establishing the quantified relationships between MANIFOLD components.

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~~<h3> Model Activation~~

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Correct stoichiometry between MANIFOLD parts required a method of quantification for both transcriptional and translational parameters. Due to the large number of required components, part expression would have to be carefully modulated to be in high enough quantity for a high-output system without killing the E. coli host. Transcriptional relativity had already been documented through the Anderson Promoter Library. The Anderson RBS Library has introduced several RBS combinations but the relativity in these sequences has yet to be fully elucidated. We then looked at the proclaimed RBS Calculator by the Salis Lab (https://salislab.net/software/). This software calculates the translation initiation rate (TIR) based on a thermodynamic model of free energy on and around the start codon.(https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2782888/) Using 21 Anderson RBS sequences and two others found naturally in acquired vectors, we found the calculated TIR values for our eight parts requiring an RBS. These values were used in conjunction with the relative transcriptional values of 19 Anderson Promoters to find optimized sequence combinations to achieve correct relative part expression. Due to the sheer number of combinations, the process yielded computational ratios with minimal error compared to ideal, theoretical ratios (Figure 3). Important assumptions for this model are listed below.

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~~<h3> Assumptions~~

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~~<ul>~~

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~~<li>Assume steady state with consistency in other central dogma factors (allows for transcriptional and translational rates to be multiplied)</li>~~

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~~<li>Assume ACC and HIV RT expressions may be calculated through subunit with lowest translation initiation rate</li>~~

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~~<li>Assume ribosome binding only occurs at primary stop codon less than 20 base pairs downstream of selected RBS sequence</li>~~

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~~<img src="https://i.ytimg.com/vi/NjlzcriYc8o/maxresdefault.jpg"/>~~

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~~<table border="1" cellpadding="1" cellspacing="1" class="PromCalcTable">~~

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~~<td>Part</td><td># of molecules</td><td>Ideal Ratio</td><td>RBS</td><td>Promoter</td><td>Computational Ratio</td><td>Error</td>~~

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~~<td>pduD fusion</td><td>1841</td><td>0.353</td><td>BBa_J61107</td><td>BBa_J23101</td><td>0.357</td><td>0.00335</td>~~

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~~<td>GFP fusion</td><td>3682</td><td>0.706</td><td>BBa_J61111</td><td>BBa_J23106</td><td>0.711</td><td>0.00500</td>~~

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~~<td>pduJAKBNUT</td><td>5212</td><td>1.000</td><td>Warren RBS</td><td>BBa_J23114</td><td>1.000</td><td>0</td>~~

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<b>Fig 3.</b> Results from the optimization ‘PromoterCalc’ model which detail the success in customizing Anderson Promoter and RBS sequences for individual part expression relative to pduJ. Top: The graph represents the differences between ideal and computationally-derived ratios for each part. Ideal ratios are derived from stoichiometric comparisons between parts in the idealized system. Computational ratios are derived from the model output using the quantification of Anderson promoters and translation initiation rates of Anderson RBS sequences. Bottom: The table presents sample calculations for finding both ideal and computational ratios along with the corresponding error. Note: All r_oligo parts are uniformly represented as one value and pduA’BJKNUT is omitted for simplicity.

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~~<div class="sectionTitle" id="Section 4">Exploring Model Validity</div>~~

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A supplementary model was created in complement to the optimization model to verify its findings. Specifically, the kinetics of central dogma theory in creation of our DNA Scaffolds was further investigated. The relative ratios of both Reverse Transcriptases compared to pduJ are observably low (Figure 3). Efficient functioning of the MANIFOLD system requires a sufficient amount of DNA Scaffolds to be produced and encapsulated by the BMC before the compartment becomes fully enclosed.

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~~<h3> Model Constraints~~

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Research in BMC assembly remains primarily speculative. Therefore, we used information on viral capsid assembly (a similar proteinaceous compartment) for timeline comparison. Analysis of MS2 bacteriophage viral capsid assembly details the protein shell formation required around 280 seconds for nucleation, growth, and lag time.(https://www.pnas.org/content/116/45/22485) These assembled particles are around thirty nanometers in diameter upon completion. Assuming assembly time only increases with particle size, we used this timestamp as a lower bound for our BMC formation. In addition to the expected assembly time, it is important to know the amount of DNA Scaffold we may expect to be encapsulated within the BMC upon formation. The pduD localization peptide has a measured Incorporation Efficiency of 24.7% to the lumen of the BMC.(https://onlinelibrary.wiley.com/doi/full/10.1002/mbo3.1010#mbo31010-fig-0016) Using these parameters, our system would require the presence of 37,267 (or 4.571 on the log10 scale) molecules of DNA Scaffolds before t = 280 seconds.

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We defined our relationships according to the schematic below (Figure 4). This process develops the connections between the input transcriptional/translational controlling factors (Promoter and RBS) and the output number of DNA Scaffold molecules. Our model used a numerical solver of the differential equations below to test this theory (Table I). Our assumptions are also listed below.

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~~<img src="https://wallpapercave.com/wp/wp1864652.jpg"/>~~

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<b>Fig 4.</b> Central Dogma Schematic. Where ORI represents the plasmid copy number; kr represents the transcription rate; kd represents the degradation rate; kl represents the translation rate; krHIVRT represents the HIV-RT transcription rate; and ka represents the annealing rate.

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~~last paragraph~~

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