Note that the number of repeated sequences is significantly reduced, and the closeness-of-fit to the desired codon sequence is much improved, compared to the initial random reverse-translation.
As an example of DoubleOptimizer run on a DNA sequence, a somewhat-repetitive Homo sapiens gene was arbitrarily selected from the NCBI database. Specifically, the exon sequence for Ca+2-binding protein CBP86 form VII was optimized for synthesis, again in E. coli. The same computer setup was used, and DoubleOptimizer was run for the default 10 seconds:
In this case, the sequence went from being over 47% composed of repetitive sequences 8 nucleotides or more in length to being completely non-repetitive. Also, the codon usage distribution is now a near-perfect match to the E. coli codon usage distribution.
Algorithm
DoubleOptimizer uses a genetic optimization algorithm.[4] This algorithm mimics natural selection by taking the original gene sequence and generating several variants by copying the sequence and creating random silent point mutations in each copy. Each variant is then assigned a fitness score based on its repetitiveness and closeness-of-fit to the desired codon usage distribution, and the most fit variants are kept. These are then re-copied, re-mutated and re-scored, and again only the most fit variants are kept, through several thousand rounds of selection. When optimization time runs out, the most fit member of the population after the final round of selection is displayed.
One challenge in implementing this algorithm efficiently is that scoring for repetitiveness is a time-consuming process (the time belongs to O(n2) in the length of the sequence). Because many thousands of sequences are scored in a single optimization, finding a way to reduce the computational burden of this step was a task of paramount importance. Our solution was to store for each sequence a matrix representing the locations in the sequence where repetitions are already known to occur, and to only attempt to add or remove repetitions that could by affected by the point mutations that were made. This significantly improved run-time, compared to the naive technique of independently re-scoring each modified sequence.
References
1. Several references exist that establish the link between codon usage and expression. To give some highly-cited examples:
Ikemura, T. Codon usage and tRNA content in unicellular and multicellular organisms. Mol Biol Evol (1985) 2 (1): 13-34
Gouy, M. and Gautier, C. Codon usage in bacteria: correlation with gene expressivity Nucl. Acids Res. (1982) 10 (22): 7055-7074 doi:10.1093/nar/10.22.7055
Sharp, Paul M. and Li, Wen-Hsiung. The codon adaptation index-a measure of directional synonymous codon usage bias, and its potential applications Nucl. Acids Res. (1987) 15 (3): 1281-1295 doi:10.1093/nar/15.3.1281
2. http://www.ncbi.nlm.nih.gov/protein/607359946. Original paper: Oxley PR, Ji L, Fetter-Pruneda I, McKenzie SK, Li C, Hu H, Zhang G, Kronauer DJ. The genome of the clonal raider ant Cerapachys biroi. Curr Biol. 2014 Feb 17;24(4):451-8. doi: 10.1016/j.cub.2014.01.018. Epub 2014 Feb 6. PubMed PMID: 24508170; PubMed Central PMCID: PMC3961065.
3. Kazuna DNA Research Institute. Codon Usage Database. http://www.kazusa.or.jp/codon/cgi-bin/showcodon.cgi?species=316407.
4. For a good introduction to genetic algorithms, see:
Goldberg, David E. Genetic Algorithms in Search, Optimization, and Machine Learning. Reading, Mass: Addison-Wesley Pub. Co, 1989.
CompositionSearch
A fast, local search of protein sequences against a specified amino acid distribution
When the relative proportions of amino acids in an unknown protein product have been chemically determined, it is often useful to search a proteome for proteins that have similar amino acid distributions, in order to identify this protein product. While at least one online utility for performing this task already exists (provided by the Swiss Institute of Bioinformatics ), the web-based nature of this program creates some limitations. Firstly, the SIB provides computational resources for the calculation, resulting in slower turnaround for the user (searches take about 15 minutes). Secondly, this program will only search for proteins already in the Swiss-Prot / TrEMBL databases. (At last check, only the smaller Swiss-Prot search was functional.) If an organism is being newly studied and has just been sequenced, its predicted proteome will not be in these databases. Thirdly, due to limited resources, only the top matches to a given search are provided. This does not allow for statistical comparison to the "typical" protein within a given proteome. Fourthly, for very-high-security tasks, uploading data to a third party may be undesirable.
Solution
CompositionSearch is a software tool we have created to address these issues by allowing an individual to rank all proteins in a proteome by similarity (minimum Euclidian distance) to a reference amino acid distribution locally on one's own computer. This ranking can be generated in a matter of seconds, rather than taking several minutes. Because it ranks all proteins in a proteome, CompositionSearch can also generate a figure for the significance of the similarity of a given protein to a given amino acid distribution, using the similarity of the rest of the proteome as a statistical distribution function.
Availability and Usage
CompositionSearch may be downloaded here.
CompositionSearch is a command line utility, provided as a Java jar file. It can be invoked from command line on any system with Java 7 or later installed, with the following syntax:
java -jar CompositionSearch.jar prot.fasta freqs.txt out.csv
where "prot.fasta" is a FASTA-formatted proteome, and "freqs.txt" is a file containing the desired amino distribution to match. It should be formatted as plain text, according to the following example template:
A 0.134
D 0.044
E 0.04
G 0.228
I 0.033
K 0.021
L 0.04
P 0.08
R 0.009
S 0.151
T 0.038
V 0.083
Note that this may contain as many or as few amino acids as desired. The frequencies, however, are interpreted as absolute, so if all amino acids are represented, they should add 1. (See below for discussion of how the optional -N and -X flags affect this interpretation).
"out.csv" in the above example line is the destination path to store the results of the calculation. The output will be a spreadsheet in csv format, which may be imported into your favorite desktop spreadsheet application (i.e. Microsoft Excel, LibreOffice Calc, etc.).
After execution, out.csv will contain a spreadsheet showing the reference distribution, and, in order by similarity to the reference distribution, the amino acid distributions of all proteins in the proteome. Protein name, similarity ranking, similarity score (Euclidian distance between amino acid distributions; lower is better), and similarity p-value (on the curve of other proteins in the proteome) will be listed for each protein.
The following optional flags may be used to change the program's behavior:
This will cause the program to ignore amino acids in the proteins that are not in the distribution list. In other words, this means that the frequencies given refer to frequencies relative to only the the other amino acids listed, instead of all amino acids. To clarify:
Without the -N flag, the line in the above example distribution list:
P 0.08
means that 8% of all amino acid residues in the matching protein are expected to be proline residues.
With the -N flag, the line in the above example distribution list:
P 0.08
means that 8% of amino acid residues that belong in the set {ADEGIKLPRSTV} (the amino acids with defined frequences) in the matching protein are expected to be proline residues.
Example:
java -jar CompositionSearch.jar prot.fasta freqs.txt out.csv -N
This will cause the program to completely disregard certain amino acid residue symbols in the proteome, regardless of use of the N flag.
The default value of this set of characters is 'X,' often used to represent unknown amino acid residues. Therefore the flag -XX is equivalent to normal behavior. Note that the set of characters being ignored is replaced by the -X flag, so it is always advisable to list X when using this flag.
Example:
java -jar CompositionSearch.jar prot.fasta freqs.txt out.csv -XX*-
This will cause the symbols X,*, and - to be ignored in the proteome.
Cellulose Pathway Modeling
Flux Balance Analysis
Modeling allows for efficient experimental design by optimizing specific conditions before testing with in vitro methods. Flux Balance Analysis (FBA) is used to optimize the growth medium for the bioengineered gluconacetobacter hansenii to yield bacterial cellulose to be used as biomaterial for a biodegradable drone. FBA is a mathematical method used to examine how metabolites relate to each network and makes predictions for the growth of an organism and product output. It is a direct application of linear programming to biological systems that used the stoichiometric coefficient for each reaction in the system as the set of constraints for the optimization. (add glycolysis stoichiometric picture here)
Flux Balance Analysis is perfomed under steady state conditions and requires information about the stoichiometry of metabolic pathways, metabolic demands, and strain specific parameters. At steady state, there is no accumulation or depletion of metabolites in a metabolic network, so the production rate of each metabolite in the network must equal its rate of consumption (3).
FBA will be used to optimize the growth conditions of g. hansenii in order to maximize the product output of cellulose. The exchange reactions determine the metabolites that are beneficial to the medium. Changing the composition will allow us to be able to determine the effect the composition has on the efficiency of the production media.
Model SEED- ModelView
Model SEED is an online analysis software with its own genome and media formulation database. An analysis of the G. hansenii is done with the curated model including a biomass reaction set for optimal organismal growth and a control of complete media. The biomass reaction describes the rate, which all the biomass precursors are made in correct proportions.(2) Biomass reactions include the information listed in Figure 1.(Biomass reaction picture) A biomass reactions requires a knowledge of the composition of a cell and the energy requirements that allow for the cell to grow. The biomass equation consists of three levels : macromolecular level (RNA, protein), intermediate level (biosynthetic energy), advanced level (vitamins, elements, and cofactors). The biomass equation also list to stochiometric coefficients for each part of the biomass equation. Using this biomass equation the growth rate was determined to be 66.48 gm per biomass CDW/hr was obtained. Since the flux is positive this explains that the flux of the analysis is indeed towards growth a negative or zero flux would have explained that the pathway is not used or it is impossible.
Future Directions/Modifications
Although a growth rate is obtained using Model SEED, this rate is for an environment where a complete medium is used. The growth medium being used contains dextrose, peptone, yeast extract, Na2HPO4, citric acid, agar and water. Model SEED does not have the capabilities to create a media file, so all further analysis will be done using KBase because it has the ability to customize the media used for analysis. Kbase is a software that allows for online analysis of models, where models and the corresponding media for organismal growth can be optimized. The genome database contains all genomes including the G. hansenii genome (as a JSON file). A full database for medias that exist and capabilities to create the media being used in experimentation through the IRIS interface, which is the command line environment used by Kbase. Using IRIS and the subsequent FBA tutorial, a flux balance analysis was attempted but several issue were observed because of command line issues. Kbase will allow for the majority of modifications to be done in order to obtain the correct model and medium, further help will be sought out in order to conquer the error messages seen. Once the error messages are fixed, further literature searches and consultations will be done in order to change the biomass reaction to one that will target the product growth of cellulose instead of organismal growth of G. hansenii. Again once an accurate growth rate with the proper medium is found, it will then be possible to plot the organism growth rate vs. product growth rate. Plotting this data will determine if there is a direct or inverse relationship between the two quantities.
References
1. Covert, M. W. and B. O. Palsson. Constraints-based models: regulation of gene expression reduces the steady-state solution space. J Theor Biol [Online] 2003 221(3), 309-325.
2. Feist, Adam M, and Bernhard O Palsson. The biomass objective function. Current Opinion in Microbiology. [Online] 2010,13.3, 344-349.
3. Orth, Jeffrey D, Ines Thiele, and Bernhard Ø Palsson. What is flux balance analysis? Nature Biotechnology [Online] 2010, 28.3, 245-248.
4. Schellenberger J, Que R, Fleming RMT, Thiele I, Orth JD, Feist AM, Zielinski DC, Bordbar A, Lewis NE, Rahmanian S, Kang J, Hyduke DR, Palsson BØ. Quantitative prediction of cellular metabolism with constraint-based models: the COBRA Toolbox v2.0. Nature Protocols [Online], 2011, 6:1290-1307.
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