Computational design of signalling networks by in silico evolution

Song Feng1, Julien F Ollivier2, and Orkun S Soyer1,3

1. School of Life Sciences, University of Warwick, United Kingdom. E- mail: O.Soyer@warwick.ac.uk

2. Centre for Nonlinear Dynamics, Department of Physiology, McGill

University, Montreal, Canada

3. Warwick Centre for Integrative Synthetic Biology, University of Warwick, Coventry, United Kingdom

ABSTRACT

Synthetic biologists aim to utilise the power of engineering principles to construct de novo biological circuits. One of these principles is the automation of the design process towards the creation of systems with desired properties. The
current design approaches in synthetic biology focus on gene regulatory circuits and are mostly concerned with ensuring the best implementation routes for known designs (e.g. tools for codon and plasmid optimisation) rather than discovering de novo designs from given biological components. Here, we present
a design approach that focuses on discovering a range of possible signalling circuits with a given response dynamics. This approach uses in silico evolution of rule-based models of signalling proteins and their interactions. The evolving models are developed from first principles of protein interactions and include allosteric regulation and presence of multiple phosphorylation and catalytic sites
on proteins. We demonstrate the application of this approach by designing signalling circuits with different response dynamics. In particular, we evolve ultrasensitive and bistable signalling circuits that display both known and hereto unknown design features. For example, we find designs with ultrasensitive
response dynamics that implement a phosphorylation-desphosphorylation cycle (i.e. a kinase-phosphatase pair acting on the same substrate). In addition, we find designs that exploit allosteric kinases and phosphatases, and that allow for bistable dynamics with as few as three interacting components. These circuits
provide novel design examples for bistable signalling circuits that can be incorporated in synthetic biology and exploited for achieving memory and logic functions in cells. More broadly, our approach can be extended to other types of circuits and response dynamics and allows for an evolutionary design paradigm
for synthetic biology.
Key words: in silico evolution, computational design, signalling networks, ultrasensitive response, bistability

INTRODUCTION AND BRIEF SUMMARY OF RESULTS

Computational design has been widely used in many engineering areas. It is also crucial in systematic design and constructing of novel biological systems, one of the ultimate goals in synthetic biology 1-3. Most of the current efforts for
computational design of biological systems in synthetic biology focus implementation rather than de novo design. In metabolic systems, for example, many studies aim to design alteration of fluxes in an existing metabolic circuit 4. Similarly, most of the existing design tools for synthetic gene regulatory circuits
focus on predicting the quantitative behavior of known designs through simulation (e.g. see 5,6) or optimizing the implementation of known designs through automation of identification of suitable components for circuit implementation 7-9 . Designing fully novel systems de novo is a more difficult problem that is only addressed in few studies. In the case of metabolic system design, approaches based on graph theory and modeling of chemical conversions were developed to identify metabolic paths between given compounds 10-13 . In the context of gene regulatory and RNA networks, evolutionary algorithms were combined with first-principles based models of gene expression and protein interaction to discover novel circuit designs 14-17 .
The extension of the in silico evolution approach to signaling circuits has been limited and was considered only with simplistic toy models 18-21. While informative, the findings of these studies do not directly lend themselves to applications in synthetic biology, where one needs relatively realistic models of signaling proteins and their interactions in order to be able to convert in silico discovered designs into reality. One reason that de novo design approaches to signaling circuits remains challenging is the lack of scalability in protein-protein interaction models 22-25 . In particular, signaling proteins exhibit multiple domains and complex conformational regulations, which consequently result in a combinatorial explosion for possible designs. It is currently not possible to explore and mine this design space for circuits implementing a desired function or response dynamics. As a result, current synthetic engineering of signaling circuits rely mostly only purely experimental approaches. For example, random shuffling of protein domains and scaffolding interactions is used to
experimentally discover functional systems 26-33. Other experimental studies take a rational approach that focuses solely on engineering of interaction specificity rather than response dynamics 34-37. While these experimental approaches have
been highly productive, their power can be extended through application of computational design tools that could allow in silico exploration of the design space in signaling systems.
Here, we present a design approach based on a novel combination of in silico evolution with a specific rule-based modeling of signaling proteins called Allosteric Network Compiler (ANC) 38. The use of rule-based models allows us to define biochemical features of signaling proteins in detail, while overcoming the combinatorial explosion in model structure that arises from evolving protein interactions. At its core, the rule sets in the ANC model define two-state allosteric proteins, whose state (active or inactive) depends on their interaction with other proteins or ligands through their different catalytic, binding, or phosphorylation domains 38. Thus, the rule sets in the ANC framework allows us to define any number of signaling proteins, each with a number of domains, and their interactions, i.e. a complete signaling circuit. Combining the ANC with an in silico evolutionary algorithm, we are able to evolve such signaling circuit models according to a user-defined fitness function 39. We applied this approach to explore signaling circuit design exhibiting switch-like (i.e. ultrasensitive) and bistable response dynamics. These types of response dynamics are particularly important in information processing and decision-making in cells 40-43 .
After defining an appropriate selection function for ultrasensitive response dynamics, we simulated evolution of signaling circuits from three different initial
â??seedâ?? systems. For each initial seed circuit, we run 20 independent evolutionary
simulations, 10 for each different settings of output protein concentration. In total, 21 signaling circuits with ultrasensitive response dynamics emerged from these evolutionary simulations. A well-known mechanism for ultrasensitivity in signaling networks is the zero-order sensitivity 40,42, where a protein with a single phosphorylation site is acted upon by a kinase and a phosphatase that operate in saturation 44. To see how well the evolved circuits confer with this known mechanism, we characterized the saturation level of the kinases and phosphatases in each model. We found that approximate half of 21 evolved ultrasensitive networks displayed distinctive zero-order sensitivity.
Interestingly, the remaining circuits displayed bistability, which was not described before in the context of zero-order sensitivity and phosphorylation- desphophosphorylation cascades. The only suggested cases for bistability in phosphorylation based signaling networks were based on multiple phosphorylation sites and obvious feedback loops where phosphorylated proteins acted upon their own, upstream kinases 41,45-48. The evolved bistable circuits we find displayed neither of these features, but instead contained allosteric regulation of kinases and phosphatases. To better understand the role of allosteric regulation, we analyzed the simplest found circuit with bistability and further reduced its complexity by removing reactions from it. This led to the identification of a design for bistability, in which a protein with a single phosphorylation site is phosphorylated by an allosteric kinase. To our knowledge, this is a minimal design for bistability in a signaling circuit. We show that it could be implemented in synthetic biology through the usage of common signaling proteins, such as those found in mitogen-activated protein kinase (MAPK) cascades 43,49,50, or engineered novel functioning signaling proteins 51.
This analysis demonstrates the power of an in silico evolution approach in designing signaling networks as well as the potentials for discovering design principles of ultrasensitive and decision making in cells.

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