Parts & pools: a framework for modular design of synthetic gene circuits

Abstract

Published in 2008, Parts & Pools represents one of the first attempts to conceptualize the modular design of bacterial synthetic gene circuits with Standard Biological Parts (DNA segments) and Pools of molecules referred to as common signal carriers (e.g., RNA polymerases and ribosomes). The original framework for modeling bacterial components and designing prokaryotic circuits evolved over the last years and brought, first, to the development of an algorithm for the automatic design of Boolean gene circuits. This is a remarkable achievement since gene digital circuits have a broad range of applications that goes from biosensors for health and environment care to computational devices. More recently, Parts & Pools was enabled to give a proper formal description of eukaryotic biological circuit components. This was possible by employing a rule-based modeling approach, a technique that permits a faithful calculation of all the species and reactions involved in complex systems such as eukaryotic cells and compartments. In this way, Parts & Pools is currently suitable for the visual and modular design of synthetic gene circuits in yeast and mammalian cells too.

Keywords: Boolean gates; Parts; Pools; gene circuits; modeling; synthetic biology.

Figure 1

Bacterial repressilator. One of the first synthetic gene circuits realized in E. coli is the so called repressilator (Elowitz and Leibler, 2000). Its core scheme is organized in three transcription units (T_i, i = 1, …, 3) wired together via the exchange of as many different repressor proteins (R_i, i = 1, …, 3). The original circuit design and mathematical model (as re-proposed in this figure) neglect the transcription unit structure in DNA Parts and any specific interactions between, on one hand, RNA polymerases and the DNA and, on the other hand, ribosomes and the mRNA. Furthermore, the action of the repressors on their target promoters is lumped into Hill functions. The overall mathematical model requires six ODEs, two for each unit. Here, α_0i represents the leakage rate constants, α_i the transcription rate constants, β_i the translation rate constants; δ_i and Δ_i are the mRNA and protein decay rate constants, respectively; $K_{H_j}$ are the Hill constants and n_j the Hill (cooperativity) coefficients.

Figure 2

Symbols. In the original paper presenting Parts & Pools, Standard Biological Parts were represented by icons taken from the MIT registry. Here, the currently adopted Synthetic Biology Open Language (SBOL) (Galdzicki et al., 2014) symbols are shown. Pools’ icons did not change with respect to our first publication (Marchisio and Stelling, 2008).

Figure 3

Design and modeling in Parts & Pools framework. (A) I1 FFL (incoherent 1 feed forward loop). The three transcription units (T₁, T₂, and T₃) that form this network motif (Alon, 2007) are enclosed into boxes. T₁ produces an activator protein that, upon binding the signal s, activates transcription along T₂ and T₃. T₂ encodes for small RNAs that bind T₃ mRNA at the RBS and repress the translation of the circuit readout. Parts are interested only by PoPS and RiPS fluxes, as shown inside transcription unit T₃. Pools, in contrast, exchange with the connected transcription units (or Pools) both fluxes and molecules’ concentrations. (B) Model for transcription unit T₁. RNA polymerase Pool is connected to T₁ promoter and terminator, ribosome Pool is linked to T₁ RBS and coding region. All the fluxes are shown as dashed arrows. PoPS^b and RiPS^b are bidirectional fluxes (the superscript b stands for balance) and arise from the binding/unbinding interactions between RNA polymerases (pol^free) and the promoter (P) or between ribosomes (r^free) and the mRNA (b) transcribed into the RBS. All the other fluxes flow in a unique direction. PoPS generated by the promoter is equal to k₂[Ppol] and goes entirely into the species [PolB] belonging to the RBS Part. [PolB] represents a complex between RNA polymerases and the RBS DNA sequence. Similarly, PoPS flows from the RBS into the complex [PolA] inside the coding region (A refers to the ATG codon) and from [PolA] into a new complex [PolT] inside the terminator. Here, RNA polymerases leave the DNA and flow back (as PoPS) to their Pool. mRNA is modeled with four species: b and [rb] into the RBS, [ra] and [ru] inside the coding region. b is the mRNA free of ribosomes, [rb] represents ribosomes bound to the mRNA during the initiation phase. A RiPS flux [equal to k_2r[rb]] is generated into the RBS and sent to the coding region where it joins the complex [ra] (a comes from the AUG triplet). From [ra], RiPS flows into a new complex [ru] (u represents the first nucleotide of a STOP codon) from which ribosomes leave the mRNA (returning, as RiPS, into their Pool) and release the activator proteins. The latter flow, as FaPS, into their transcription factor Pool where they become free molecules (f^free) and can then interact with both T₂ and T₃ promoters.

Figure 4

XOR gates designed by our algorithm (Marchisio and Stelling, 2011). The schemes here shown have the lowest S both in POS (A) and SOP (B) configuration. Our algorithm is based on rather strict assumptions: POS solutions accept, as inputs, only corepressor chemicals able to switch off aptamers or activate repressor proteins; SOP solutions demand inducer chemicals that activate either aptamers or activator proteins. The input layer contains, both in POS and SOP, either YES or NOT gates. (A) The two corepressor inputs a and b act directly on riboswitches/ribozymes whereas their negated signals are a unique active repressor (R^a). (B) The two inputs are inducers that activate their riboswitch/rybozyme target and their negated signals are an active activator (A^a) for a and a key (k, an sRNA that induces translation) for b. Here, moreover, the two NOT gates are made of two genes. The internal layer of POS solutions is made of NOR gates (whenever a gate takes a single input, it becomes a NOT gate); AND gates (YES for a single input) are present in SOP schemes instead. NOR gates require transcription and/or translation repression; AND gates transcription/translation activation. Both circuits in figure belong to what we called single-gate class of solutions since their final layer is made of only one gate: NOR in POS, OR in SOP. Single-gate configurations are, generally, the least complex ones but not necessarily the most efficient. Every gate is here represented by its Parts (the terminator is always omitted) together with its electronic symbol.

Figure 5

XOR gates based on simplified designs (Marchisio and Stelling, 2014). The latest version of the algorithm for the automatic design of bacterial gene digital circuit allows using inducers and corepressors as inputs for both POS and SOP circuits. Furthermore, two new interactions are taken into account: inducers binding repressors and corepressors binding activators. In both cases, the chemical inactivates its target protein. The circuits here shown take as inputs the inducer a, which activates a riboswitch/ribozyme, and the corepressor b, which inhibits an activator (A^a). NOT(a) is an active repressor (R^a); NOT(b) a small RNA (l, which means lock since, by annealing to the mRNA, prevents ribosome binding and translation initiation). (A) POS solution is still organized in three layers of gates and Pools. The corresponding Boolean formula has been rearranged as: $NOT\left(\left(\overline{a}\wedge \overline{b}\right)\vee \left(a\wedge b\right)\right).$ (B) SOP solution is designed according to the distributed output architecture. This implies a reduction in the complexity score with respect to the corresponding POS configuration.

Figure 6

Modular, rule-based modeling with Parts & Pools. A text file is converted into an MDL file containing a eukaryotic module description via the interaction of Parts & Pools and BioNetGen. MDL files are loaded into ProMoT where gene circuits are designed and exported, for instance, into SBML format for simulations and analysis.

Figure 7

Eukaryotic repressilator. The repressilator scheme is drawn with eukaryotic Parts & Pools. Green straight lines represent transcription, blue ones, translation. mRNA maturation is modeled into each coding region where pre-mature mRNA interacts with the spliceosome. This requires a link between each transcription unit and the spliceosome Pool. Mature mRNA is exported into a Pool in the cytoplasm where translation takes place. Once synthesized, repressors are brought to their Pools in the nucleus from where they can flow to their target promoters and inhibit transcription.