Modeling structure-function relationships in synthetic DNA sequences using attribute grammars

Abstract

Recognizing that certain biological functions can be associated with specific DNA sequences has led various fields of biology to adopt the notion of the genetic part. This concept provides a finer level of granularity than the traditional notion of the gene. However, a method of formally relating how a set of parts relates to a function has not yet emerged. Synthetic biology both demands such a formalism and provides an ideal setting for testing hypotheses about relationships between DNA sequences and phenotypes beyond the gene-centric methods used in genetics. Attribute grammars are used in computer science to translate the text of a program source code into the computational operations it represents. By associating attributes with parts, modifying the value of these attributes using rules that describe the structure of DNA sequences, and using a multi-pass compilation process, it is possible to translate DNA sequences into molecular interaction network models. These capabilities are illustrated by simple example grammars expressing how gene expression rates are dependent upon single or multiple parts. The translation process is validated by systematically generating, translating, and simulating the phenotype of all the sequences in the design space generated by a small library of genetic parts. Attribute grammars represent a flexible framework connecting parts with models of biological function. They will be instrumental for building mathematical models of libraries of genetic constructs synthesized to characterize the function of genetic parts. This formalism is also expected to provide a solid foundation for the development of computer assisted design applications for synthetic biology.

Figure 1. Workflow of generating the gene network model encoded in a DNA sequence.

The input for this process is a DNA sequence that is first broken down into parts by the scanner. The combination of the parts is validated by the parser according to a syntactic model. After validation by the parser, the sequence is translated by applying semantic actions attached to the rules to transform the series of parts into a set of chemical equations. The resulting equations can then be solved using existing simulation engines. Each step takes the output of the previous step as input, so the workflow can start from any step if the appropriate input is provided.

Figure 2. Parse tree showing the derivation process of a two-cassette genetic construct.

In the derivation tree, terms in <> corresponds to the non-terminals in the grammar, while terms in [ ] are terminals, and the dashed lines indicate the transformation to terminals. The subscripts are used to distinguish different instances of the same category.

Figure 3. An example of attribute grammar.

Figure 4. Equation generators.

Figure 5. Chemical equations translated from a DNA sequence.

Figure 6. Mapping the behavior of 384 genetic constructs.

Each section A to F indicates a different selection of repressors within a toggle switch: (A) tetR and lacI, (B) lacI and tetR, (C) lacI and cI, (D) cI and lacI, (E) cI and tetR, and (F) tetR and cI. Other networks that cannot give rise to bistability (e.g. a construct with tetR as both genes) are excluded as are designs that only vary the GFP RBS (see text). Each pair is explored by varying the RBS (ordered by translational efficiency from low (RBS H) to high (RBS B) as determined by a qualitative fit of the results of Gardner et al. with consistent letter-based labels) and calculating the detectability ratio, defined as the steady state GFP concentration in the “on” state divided by the concentration in the “off” state. These ratios are displayed using a color map as indicated by the legend to the right. Monostable constructs have a ratio of 1 and are indicated by gray boxes. The ratio gives a measure of how easily the two steady states can be distinguished, which is important due to high experimental noise. Each pane also elucidates the traditional two-parameter bifurcation diagram of each gene pair as the translational rates are varied by changing RBSs. Constructs near the edge of the cusp operate near saddle-node bifurcations and are more prone to noise-induced switching. Thus, constructs from the cusp interior are preferred for robust behavior.