Fig 1.
The software environment is composed of 5 tools: a BB-SPICE netlist parser, a SPICE netlist generator, a SBML-to-SPICE translator, a SBML model generator and a SPICE simulator, i.e. NGSPICE.
Fig 2.
Electrical equivalent circuit for the self-inhibited enzymatic reaction.
The sub-circuit (A) corresponds to the model of the constant production of the substrate. The sub-circuit (B) is the model of the enzymatic reaction. It is composed of a biological transistor modeling the synthesis of the product and which depends on the concentration of substrate and product according to Eq (3) and another biological transistor modeling the consumption of the substrate which also depends on the concentration of the substrate and the product. (C) corresponds to the complete electrical equivalent circuit obtained by putting together sub-circuits (A) and (B) and adding degradation resistors and capacitors.
Fig 3.
Electrical equivalent circuit for the toggle switch.
(A) is the biological representation of the system as regulated genes. (B) is the interaction network representation of the toggle switch and (C) is the electronic equivalent circuit. Nodes X1 and X2 as well as associated devices are not represented in the schematic for simplicity sake.
Table 1.
Types of reactions implemented in the current version of BB-SPICE.
Table 2.
List of the simulation directives implemented in the current version of BB-SPICE.
Fig 4.
Comparison of simulation results obtained with a model written in BB-SPICE and, on the one hand, translated and simulated with NGSPICE and, on the other hand, translated in SBML and simulated with COPASI.
The system modeled are a band detector (A), a kinase/phosphatase cascade (B) and a genetic half-adder (C).
Table 3.
Benchmark of the biological systems used for the comparison between NGSPICE and COPASI.
Table 4.
Benchmark of the SBML models picked up from the Biomodels database, used for the validation of the SBML to NGSPICE translator.
Fig 5.
Comparison of computation time obtained with NGSPICE, COPASI and SPECTRE® for two different benchmarks of biological models.
(A) is the transient simulation of gene regulator networks composed of variable number of genes. For SPECTRE® and COPASI, compilation time and simulation time are distinguished. (B) is the steady state simulation of linear metabolic pathways with a variable number of involved species. For COPASI, the range of tested value is reduced due to two limitations. First, the resolution of the CPU time measurement is the second. Thus, at least 50 reactions are required to obtain a significant value. Second, above 1000 reactions, the model is too huge to compilation failed due to memory errors. Finally, (C) is the steady state of metabolic pathways with 20 species and a variable number of reactions. Again, computation time measurement is not significant with COPASI under 50 reactions.
Fig 6.
Results on the penicillin sensor.
(A) is the overview of the building blocks of the model. Green blocks have been described in BB-SPICE whereas blue ones have been described directly in NGSPICE and integrated in the BB-SPICE netlist preceded by the ∃ character. (B) is a drain-source current vs reference electrode voltage characteristics of the ISFET alone. (C) and (D) are the simulation results for the biological part of the model alone. (C) is the variation of pH in the solution as a function of concentration of penicillin for two different phosphate buffer concentrations. (D) is the transient evolution of the pH on the gate of both ISFETs for a penicillin concentration of 0.05 mol/l. Finally, (E) is a transient simulation for the whole model (biological part, ISFETs, biasing and processing electronics). The evolution of the output voltage is given for different initial penicillin concentrations.