The topic of project section C is the development of an infrastructure including calculation procedures to design genetic circuits at the computer and predict their behavior.

Therefore circuits and circuit components are transferred to models of different granularity. Models do not have to be necessarily mathematical equations; they may also appear as raw calculation regulations like computer programs. While kinetic population models are needed to calculate the behavior of the whole circuit on a physiologic time scale, molecular dynamic models grant information about the structural properties of single circuit components. On the other side computer programs offer many possibilities for the model description and are nowadays easily analyzed by formal methods of informatics like mathematical models.

In CompuGene the generation of models is concentrated to display the context dependency of the experimental circuits correctly. Using the data of project sections A and B in CompuGene inference algorithms are applied and upgraded to design the models predicatively. Subsequently calibrated and context dependent models are examined for their robustness. In this case especially the identification of these context variables are highly important, which affect the circuit behavior most of all.

The knowledge of this opens new ways for CompuGene to optimize circuits in regard to their robustness at the computer. Additionally, CompuGene tries new approaches and develops methods to combine previous characterized circuit components to totally new circuits. Thereby concepts of formal synthesis of programs and digital switches are applied. This attempt displays a promising alternative against the current trial-and-error layout process.

### Molecular-biophysical modeling of context dependences

### Project head: Kay Hamacher

The molecular functionality and the construction of gates and circuits out of single components depend on a biophysical basis. Therefore, molecular models have to be generated and the time scale of sub-molecular components in the range of nucleotide up to intracellular systems has to be simulated in silico to estimate and control modularization, robustness and combinability of circuits. Because of basic (resources) as well as pragmatic reasons (engineering as target) so called coarse-graining approaches are utilized, which granted in the last few decades a variety of qualitative insights of the molecular, structural and cellular biology.

The coarse-grained models of proteins and nucleotides of project C-1 are used to connect to the length scale of the following project C-2 and lead to the molecular area of circuit modeling. In further steps these models are upgraded by the atomistic effects (based on the experiences of AG Hamacher in the section of knowledge-based potential and the ab initio parameterization). This addition enables the in silico combination of aptamers in project A-1 as well as the detailed molecular analysis of synergy effects and known but unwanted cross talk of the circuit composition. The concrete research questions are:

(1) How can sub-molecular ligands of aptamers (especially tetracycline and neomycin) be parameterized to apply the elastic network models of RNA mechanics?

(2) How can the model of the RNA-folding be upgraded by the parameters of the aptamer conditions (context dependency) to investigate the thermodynamic of the RNA-switch?

(3) How can these detailed insights be applied to the modeling of population models?

## Project C-2:

### Inference algorithms for circuit models and their context dependence

### Project head: Heinz Köppl

Model parameters, model structure as well as context dependences have to be extracted out of the data of project sections A and B to create models of components and circuits, which are produced quantitatively according to the data. Models without parameterization are not well suited for the other projects of section C, because the circuit behavior and robustness change heavily with the chosen parameters. Especially, the composition of circuit components (C-3 and C-4) leads to a propagation of uncertainty. Without any model inference no conclusion about the total behavior can be made. Despite the fact that the measurement technique of section B offers a promising data collection, the numerical process has to be designed accordingly and kept updated.

This project aims on new scalable methods with a faster and more robust inference of stochastic and deterministic population models. The focus is on the measurement of single cells (B-2) and cell-free implementations (B-1). Parameters, context dependency and partly the model structure will be learned. This results in the following concrete research topics:

(1) How can the context dependency be reconstructed from data?

(2) How are hybrid models learned efficiently, which combine stochastic and deterministic dynamics?

(3) How can the protocols of sections A and B be optimized to maximize the informative data for the inference model?

## Project C-3:

### Analysis of robustness and context dependence of circuit models

### Project head: Barbara Drossel

In every case the performance of the components or of a whole circuit depends on external conditions. Once components are added to a circuit the condition for all contained components are changed. Especially, in vivo experiments include several cellular factors, which influence the circuits [9] like the availability of ribosomes, competitive and unspecific bindings of protein to DNA- and RNA-sequences, lacking nucleotides or ATP-availability. Therefore, circuits that act robust among changes of conditions or are adapted to the actual condition, are essential. This is important for both in vitro- and in vivo-experiments.

In project C-3 the robustness and context dependence of the developed and calibrated models of C-2 are analyzed and if necessary the models are upgraded. The following questions are processed in particular:

(1) What is the robustness of single compounds under change of important input- and output parameters?

(2) How does the assembly of components to circuits change the dynamic performance of the components?

(3) Which part plays the stochastic influence?

(4) What is the reaction of circuits to different condition factors in the cellular context, which is important according to the experiments?

## Project C-4

### Verification and synthesis of circuits

### Project head: Reiner Hähnle

In this partial project methods for the formal specifications of software are used to model, analyze and synthesize genetic circuits. Contrary to the other partial projects of project section C for this purpose discrete, symbolic, logic based characterization-formalisms are applied, which were developed for the modeling of concurrent programs. This leads to a precise modeling of complex internal conditions of circuits and their cellular environment. Additionally, for the first time concepts of modeling initially developed to describe software formally are utilized to model genetic circuits. Formal models of software include the benefit of feasibility. That means they can be directly simulated and visualized. Also they can be analyzed computer based and enable – analogous to the generation of test cases the automatic generation of directed experiments, which are performed subsequently in the project sections A and B. The superior topic of this project is the synthesis of formal models of optimized genetic circuits.