Determinism and boundedness of self-assembling structures

2019

Preprint

The self-assembly of proteins into protein quaternary structures is of fundamental importance to many biological processes, and protein misassembly is responsible for a wide range of proteopathic diseases. In recent years, abstract lattice models of protein self-assembly have been used to simulate the evolution and assembly of protein quaternary structure, and to provide a tractable way to study the genotype-phenotype map of such systems. Here we generalize these models by representing the interfaces as mutable binary strings. This simple change enables us to model the evolution of interface strengths, interface symmetry, and deterministic assembly pathways. Using the generalized model we are able to reproduce two important results established for real protein complexes: The first is that protein assembly pathways are under evolutionary selection to minimize misassembly. The second is that the assembly pathway of a complex mirrors its evolutionary history, and that both can be derived from the relative strengths of interfaces. These results demonstrate that the generalized lattice model offers a powerful new framework for the study of protein self-assembly processes and their evolution.Protein complexes assemble by joining individual proteins together through interacting binding sites. Because of the long time scales of biological evolution, it can be difficult to reconstruct how these interactions change over time. We use simplified representations of proteins to simulate the evolution of these complexes on a computer. In some cases the order in which the complex assembles is crucial. We show that biological evolution increases the strength of interactions that must occur earlier, and decreases the strength of later interactions. Similar knowledge of interactions being preferred to be stronger or weaker can also help to predict the evolutionary ancestry of a complex. While these simulations are not realistic enough to make exact predictions, this general link between ordered pathways in assembly and evolution matches well-established observations that have been made in real protein complexes. This means that our model provides a powerful framework for the study of protein complex assembly and evolution. Introduction 1 Many proteins self-assemble into protein quaternary structures, which fulfill a multitude 2 of functions across a wide range of biological processes [1]. Abstract models trade off 3 the complexity arising from conformations, buried surfaces, cooperative binding, etc., 4 but still retain qualitative realism. A general class of polyomino tile self-assembly 5 models have strong analytic potential while maintaining semblance to protein quatenary 6 structure. 7 The polyomino self-assembly model [2] combines lattice tile self-assembly with a 8 quantification of biological complexity, examining the relationship between genetic 9 description length and phenotypic complexity. The same model was developed and 10 expanded with evolutionary dynamics by Johnston et al. [3], and used to probe general 11 properti...

Section: Genotypes and Phenotypesmentioning

confidence: 99%

mentioning

confidence: 99%

Evolution of interface binding strengths in simplified model of protein quaternary structure

2019

Preprint

“…Reasonably bound and deterministic assembly graphs can only support a limited number of interactions relative to the number of subunits Tesoro et al (2018) . This limit can be recast in terms of the maximum “complexity” an assembly graph can support, as more interactions require more information to encode.…”

Section: Introductionmentioning

confidence: 99%

Duplication accelerates the evolution of structural complexity in protein quaternary structure

2020

Preprint

9Gene duplication, from single genes to whole genomes, has been observed in organisms across all 10 taxa. Despite its prevalence, the evolutionary benefits of this mechanism are the subject of ongoing 11 debate. Gene duplication can significantly alter the self-assembly of protein quaternary structures, 12 impacting the dosage or interaction proclivity. Here we use a lattice model of self-assembly as a 13 coarse-grained representation of protein complex assembly, and show that it can be used to 14 examine potential evolutionary advantages of duplication. Duplication provides a unique 15 mechanism for increasing the evolvability of protein complexes by enabling the transformation of 16 symmetric homomeric interactions into heteromeric ones. This transformation is extensively 17 observed in in silico evolutionary simulations of the lattice model, with duplication events 18 significantly accelerating the rate at which structural complexity increases. These coarse-grained 19 simulation results are corroborated with a large-scale analysis of complexes from the Protein Data 20 Bank. 21 22 37ing. Importantly, both symmetric homomeric and heteromeric interactions are possible, as well 38 as combinations thereof, allowing for more general assembly dynamics than previously permitted 39 in polyomino models. We additionally allow variable genetic length, with genotypes growing and 40 1 of 16 Manuscript submitted to eLife shrinking dynamically through duplication and deletion respectively. 41 The importance of duplication in the structural evolution of proteins was unknown when first 42 encountered in the 1970s, but was quickly realised to be ubiquitous McLachlan (1979). Whether 43 duplication is predominantly a driver of innovationMagadum et al. (2013), distributor of subfunc-44 tionsGibson and Goldberg (2009), safeguard against extinctionCrow and Wagner (2005), or merely a 45 passive passengerKimura (1991) remains more an open question. However, evolutionary histories 46 are rife with duplication events, from single genes to whole genomes, and there is some consensus 47 109 site changes the interaction strength by two increments, affecting both the location of the point 110 mutation and the counter-aligned bit. This property of symmetric homomeric interactions is not 111 unique to polyomino models, with greater variance in interaction energetics preferring symmetric 112 homomeric formation extremely generallyLukatsky et al. (2007); Lukatsky and Shakhnovich (2008). 113 The simplicity of binary string binding sites allows the formation rates of both symmetric 114 homomeric and heteromeric interactions to be calculated analytically. The formation of interactions 115 is modelled by an absorbing Markov chain of interaction strengths, randomly walking below the 116 strength threshold. Point mutations correspond to stepping to adjacent strength states. Symmetric 117 homomeric interactions, which can only increment by two states, can be mapped to an equivalent 118 3 of 16 497 Greenbury S, Johnston I, Louis A, Ahnert S. A trac...

“…Any self-assembling system requires two ingredients: assembly subunits with binding sites, and a method for determining the strength of an interaction between two such sites. The arrangement of the sites and their interactions can be described in the form of an assembly graph [13]. From these simple components, structures can be formed through the following stochastic assembly process:…”

Section: Introductionmentioning

confidence: 99%

“…There are many sources of nondeterminism, ranging from unbound aggregations of subunits to branching pathways in the course of the assembly process. A more general insight into nondeterminism in polyomino self-assembly is given by Tesoro, Ahnert, and Leonard [13].…”

Section: Introductionmentioning

confidence: 99%

Evolution of interface binding strengths in simplified model of protein quaternary structure

2019

PLoS Comput Biol