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The goal of this page is to explain the way the VHDL and VHDL-AMS model are built. Although the development of the model was not directly an objective of the project, we had to understand how the models work in order to generate it. A first version of the model used in the following have already be published by our advisors [1]. However, to make them easy to be generated, their structures have been reviewed by our team.

In the 80's, the digital circuits designers attempted to standardize the way to describe digital circuit. Until now, this was done with electronic schematics (with different symbols from one country to another), state diagram, sequential function chart … This universal description method they choose is a language, namely “hardware description language” (HDL). The first version, standardized by the IEEE in 1987, is the Very High Speed Integrated Circuit HDL. Today, only the ‘V’ of VHSIC remains. Quickly, VHDL was adopted by EDA tools (both for simulation and for synthesis).

In 1999, the dedicated IEEE standardization committee decided in 1999 to create an extension of VHDL to describe analog circuits and multi-domain (electro-thermal, for example) system. The VHDL-AMS language (AMS for Analog and Mixed Signal) was born. It aims at mid- term to replace the famous Spice simulator allowing the user to easily describe more complex behaviors.

Today, these two languages, as well as their brother in Verilog and Verilog-AMS are the keystones of the design flow.

Up to now, we still do not really track how the language provided to describe electronic circuits could be used to describe biological systems. A first indication comes from [2]. It shows that the behavior of biological system may be modeled by an electronic circuit composed essentially with logic gates. Thus, a digital abstraction could be extracted for each BioBrick. This leads to the so-called behavioral model.

Another approach is to say that a BioBrick is a "transfer function" transforming biological signals to other biological signals. In this approach, each BioBrick is seen as a black box with input and outputs and differential equations to link output quantities to input quantities. The biological system is a diagram of such black boxes. At each simulation step, the quantities are computed step by step and the amount of species present in each cell is updated. This approach is called signal flow model.

The third approach lead to conservative model. This means that, potentially, each BioBrick may have an influence on each species present in the cell. This set of potential interaction can define, for each species, an interaction network leading to one differential equation by species. In practice, the differential equations of each species are coupled, giving a set of coupled equations to be solved at each simulation step.

Behavioral models are the easiest to describe. It is based on VHDL language. In the cell, each protein can have only two states: “present” or “absent”. The chemical reactions or genetic processes that occur within the cell are modeled by logical functions:

• The mechanism of synthesis involving an activator A and repressor R and synthesizing the protein X can be modeled by the Boolean equation X = A AND NOT (R). This is the abstraction of Hill’s equation for which the Hill coefficients are infinite and the strength of the repressor is much larger than for the activator.

• The mechanism of complex reaction can be modeled by a Boolean AND function: the presence of the complex in the cell requires the presence of both reactants. It is an abstraction of a standard chemical differential equation for which kon is much larger than koff.

• If, in such a reaction, focus in put on a reactants (eg. A), another biological function (the inhibition) has to be defined. A "virtual protein" A’ is created at the output of this function giving the actual presence of reactant at the end of the reaction. The Boolean equation is A’ = A AND NOT (B), where B is the second reactant.

• In the case of two proteins A and B play an equivalent role for a given process, we introduce an OR gate and a virtual protein X = A OR B to connect to the targeted process.

In VHDL, the description of the digital blocks is quite simple. Below is the example for the complexation process.

Signal flow or conservative?