Modularity or complexity: plasticity in response dynamics

As discussed above, both retroactivity and cross-talks are prevalent in biological systems, while they act as nuisance in conventional engineering principles. Such contradictions suggest that the evolutionary designed biological systems can poten- tially provide new perspectives and principles for engineering such perspectives and principles may be applicable to other engineering areas. For biological systems, the contradictions indicate the gaps between modular biology and “systems” biology. Again, it encourages us to study the biological systems under the light of evolution. As the biological systems are results from evolution in fluctuating environments, their regulation systems were never selected by a single function rather by multiple objectives. Evolution under such multiple objectives inevitably brings retroactivity and cross-talks between modules. The hypothetical solutions provided by evolution is probably the plasticity in cellular networks that networks can perform multi- ple functions through minimal regulations and costs [35, 167, 206, 246, 307–311]. Validation and formalisation of such hypothesis requires further research inputs.

Appendix A

Manual of BioJazz

A.1

Introduction

Biological systems employ sophisticated mechanisms to sense and process informa- tion then achieve proper phenotypic behaviours so that it enables their survival in environments. The essential part of the regulation involves large-scale biochem- ical reaction networks that accurately compute the input signal into output re- sponse, though the computational capabilities results from interactions between proteins with merely two types of reactions: non-covalent binding reaction and post-translational modification. Observations from experiments reveal evolutionary innovations from complex signalling networks, such as allosteric regulation, cross- talk, regulatory motifs, facilitating computability of the cell [Rowland:2014bk, 88, 122, 193, 312, 313].

To fully understand the complexity of signalling network and its evolution, one need to utilize computational models rather than intuitively trying to capture its dynamics. Besides, it is necessary to study the evolution of complex signalling networks in order to uncover principles of nature design as well as to reverse engi- neer it or design novel functions beyond nature. Many researches have been carried out about evolutionary simulation of metabolic networks, or gene regulatory net-

works [121, 123]. Here, we introduce a tool for evolutionary simulating dynamic biochemical networks, aiming to explore the design principles of signalling network in cells.

BioJazz is a tool for evolving and designing biochemical reaction networks using genetic algorithm (GA). Typically, a BioJazz user wishes to evolve or design a small network or motif that accomplishes a specific function, such as a switch or an oscillator module. The network comprises a set of proteins whose attributes are encoded in a network’s “genome”. The “genome” is a binary string which contains all the information necessary to determine how many proteins are present in the network, their structure, which proteins interact and the biochemical parameters of their interaction.

BioJazz implements a genetic algorithm through a process of replication, mu- tation, and selection, attempts to incrementally improve how well those ”genomes” perform a user-specified function. By encoding the network in a fashion that mimics the way nature does, BioJazz can use a larger variety of mutational operators than do traditional GAs (which use point mutations and crossover), such as gene duplica- tions, gene deletions, and domain shuffling. Thus, BioJazz has the ability to change and evolve networks with respect to both topology and biochemical parameters, by starting from a designed network “de novo”, or a partially or completely functional seed network. While the genetic algorithm itself is not very tasking, scoring each individual of a population of genomes may require a lot of processing power. There- fore, BioJazz has an integrated capability to use workstation clusters to speed the computation.

Much of BioJazz’s ability to design realistic networks comes from the accom- panying Allosteric Network Compiler (ANC) [156]. ANC is a stand-alone, rule-based compiler which has the ability to turn a high-level description of allosteric proteins into the corresponding set of biochemical equations. The proteins can exhibit many of the behaviours observed in nature, such as co-localization, allosteric transitions,

binding and catalytic reactions. The rule-based approach implemented in ANC fits in with allosteric biochemical networks. It utilizes thermodynamically grounded methodology to abstract protein structures and allosteric regulation.

Rule-based model not only solve the combinatorial explosion occurred in modelling signaling networks, but more importantly, it also makes network restruc- turing possible due to clustering reaction patterns by interaction rules and parame- terisation of allosteric regulation with two key parameters, “Γ” and “Φ” [156], based on thermodynamic changes of protein conformation when under binding and post- translational modifications. BioJazz is likely the first tool to couple a rule-based compiler with an evolutionary algorithm.

To evolve the protein-protein interaction networks, one need to store and mutate the network of which protein structures, reaction rules and corresponding parameters are the most important. BioJazz encodes all information with binary string, that can be ”transcribed” into interaction networks without losing any infor- mation. Moreover, in order to study the evolution of complex interaction networks, we need to embed the mutations of networks, both structure and kinetic parame- ters, into a realistic matter rather than choosing arbitrarily alter network structure and kinetic parameters. Therefore, binary string encoding provides an advantage on storing and mutating biochemical networks as an analogue of the real biological systems.

BioJazz is also highly configurable. For example, the user can specify evolu- tionary parameters such as mutation rates. Also, the user may restrict BioJazz to changing a subset of the network’s attributes. This is useful to ”freeze” the network topology, with the effect that only the network’s biochemical parameters and not its structure are allowed to evolve.

The main features of BioJazz are:

• designs a network “de novo”, or starting from user-specified seed network

• uses workstation clusters to speed up the design

• produces a human-readable model of network

• highly configurable