Figure 1.
Proto biocompiler architecture and example.
(a) This paper extends the Proto spatial computing language with mechanisms for genetic regulatory network design (pink). (b) An example showing how a simple high level behavioral specification is converted first into a dataflow network, then into a genetic regulatory network, and finally optimized. In this example, green fluorescence is turned ON only when both small molecule inputs aTc and IPTG are not present (aTc, anhydrotetracycline. IPTG, Isopropyl -D-1-thiogalactopyranoside). A–F represent transcriptional repressors to be chosen later from a parts library.
Figure 2.
An amorphous medium is a manifold where every point is a universal computational device that knows its neighbors' recent past state.
Figure 3.
Our genetic regulatory network designs are based on promoter-gene-terminator functional units such as the example shown above.
The regulatory gene is regulated by upstream transcriptional activator
and transcriptional repressor
, and produces proteins for downstream regulation. The parameters are defined in Section.
Figure 4.
Transfer function experiments and requirements.
Model and parameters are based on sigmoidal behaviors documented in the experimental literature, as in the graph from [30] shown in (a), showing sigmoidal responses of green and red fluorescence proteins upon Doxycycline (Dox) induction. In this network implemented in AINV15 cells, Dox binds rtTA and activates expression from the TRE promoter of an Enhanced Green Fluorescence Protein and mammalian-optimized LacI repressor. In turn, LacI represses production of DsRed2 from a Hef1a promoter engineered with lac operators. (b) Every sigmoidal curve has an input concentration window that results in large output variations. The curve shown is for transcriptional activation. Repression is represented by an analogous inverse sigmoidal curve.
Figure 5.
Mathematical representation of the functional unit in Figure 3, via (a) ordinary differential equation that describes the kinetics of the transcription factor . (b) The 3D profile of protein
as a function of inputs
and
. (c,d) Typical input-output relations of the functional unit when modulating only one of the inputs.
Figure 6.
Diagrammatic representation of representative variants for repressors and activators along parameters ,
, and
characterizing the behavior of the sigmoidal curve.
Curves in different insets correspond to their specific position in this space.
Figure 7.
Example of BioCompiler motif declarations.
(a) Logical not operator, (b) Green fluorescence actuator, (c) IPTG sensor and (d) A non-branching logical and operator. Terminators are not shown in the gene network diagrams for simplicity.
Figure 8.
A Proto dataflow computation is compiled to an abstract genetic regulatory network in two stages.
First, each operator is mapped to a motif and each dataflow edge is mapped to a regulatory protein (blue dotted lines). These elements are then linked together using the structure of the dataflow graph to form an abstract genetic regulatory network (red dotted lines).
Figure 9.
Example of optimization, applied to the compiled genetic regulatory network from Figure 8.
Copy propagation changes GFP to be repressed by rather than activated by
, then dead code elimination removes first
and then the regulatory region where
was formerly produced.
Figure 10.
Proto code for a two-bit adder, showing operators in color.
Inputs are purple, logic operators are red, functions are blue-green, and outputs are in their corresponding color.
Table 1.
Input/output logic table for single-not system.
Table 2.
Input/output logic table for three gate system.
Table 3.
Input/output logic table for quad-not system.
Table 4.
Input/output logic table for 2-bit adder system.
Figure 11.
Large-scale example of Proto motif-based compilation: (a) a two-bit adder program, interpreted into a Proto computation and (b) transformed into an optimized genetic regulatory network (GRN) which is approximately half the size of the original network.
The image is color coded to distinguish crossing edges; small-molecule binding reactions are elided. Note that although in this case the initial gene network has a one-to-one mapping between Proto operations and regulatory proteins, the final implementation logic is largely but not entirely inverted.
Figure 12.
Simulation of automatically generated genetic regulatory networks executing for single-not, three-gate, and quad-not programs.
The upper graphs for each network show small-molecule input concentrations and the bottom graphs show output GFP concentrations for the optimized (solid blue) and unoptimized (dashed black) networks.
Figure 13.
Simulation of automatically generated genetic regulatory networks for the two-bit adder.
The upper graphs show small-molecule input concentrations and the lower three graphs show output CFP, RFP, and GFP concentrations for the optimized (solid blue) and unoptimized (dashed black) networks.
Table 5.
Optimization results for the four test systems.