A Dynamic Model for the Evolution of Protein Structure

Abstract

Protein domains are three-dimensional arrangements of atomic structure that are recurrent in the proteomes of organisms. Since the three-dimensional structure of a protein determines its function, it is the fold, much more than the underlying protein sequence and underlying chemistry, that is evolutionarily conserved. We are interested in probing the history of life with these domain structures and glimpsing qualitative changes over time by studying a dynamic model of protein evolution. Using standard phylogenetic methods and a census of protein domain structure in hundreds of genomes, we have reconstructed phylogenetic trees of protein domains, defined using the Structural Classification of Proteins (SCOP), where the nodes are folds or fold superfamilies (FSFs), the character vector for each node is a list of abundances of said fold or FSF across a range of species that spans all three superkingdoms of life, and the character states are linearly polarized by abundance; higher abundance within and among species equates to older structures and determines tree structure.Here we explore at what rate fold or FSF variants and new folds or FSFs appear in evolution. We also explore what collective model of proteome evolution explains such rates. Briefly, what are the dynamics of change? A set of birth-death differential equations was selected to capture the change of interest, with one set for folds and another for FSFs. The models assume that at any given moment there are a certain number of different folds or FSFs, with various abundances, and as each fold or FSF diversifies there are slight changes in the folds or FSFs, producing fold or FSF variants. Eventually as the variants continue to diversify and change as well, a new fold or FSF is born. Thus, there are two rate parameters in each model: the growth rate of fold or FSF variants and the rate of appearance of new folds or FSFs. The model governs the rate change of the average total abundance of a fold or FSF with time. It is fit to the tree so only those fold or FSF transitions ii actually present in the tree are assumed possible in the equations. It assumes a global perspective: the total abundance of a fold or FSF is that of the fold or FSF across all species, not within one organism. This perspective is used to properly discount terms of horizontal transfer in a birth-death model since such a transfer contributes no new folds or FSFs to the net abundance across all organisms.Our model determines 1) that there is a tight connection between the history of folds and FSFs, 2) that the corresponding transition probabilities to new variants of a fold experienced a sharp increase just as the transition probabilities to new folds experienced a steep decline and 3) that this simultaneous sharp increase and decline is explainable by and consistent with the combinatorial explosion of structural domains, referring to the period of high combination and rearrangement of domains and distribution of these new combinations in novel lineages, and the rise of organisma...

Phylogenetic Tracings of Proteome Size Support the Gradual Accretion of Protein Structural Domains and the Early Origin of Viruses from Primordial Cells

“…We fitted the models to data from ToDs assuming that only transitions present in the trees were possible between fold structures and that branches emerged directly from a trunk. We found that parameters of growth of domains within FSFs (FSF reuse) and diversification of FSFs (FSF use) showed emergent biphasic patterns with opposing trends, i.e., increases in FSF innovation were always counterbalanced by decreases in growth of FSF abundance, and vice versa, with the growth of the many more recent FSFs offsetting the growth of the older FSFs (Tal et al, 2016). Since the model is global and independent of the existence of proteomes, simulations suggest a frustrated and complex interplay of growth and diversification of domain structures in the protein world that emerges from organismal diversification but is not a consequence of proteome size.…”

“…While there are a number of Heaps-like scaling relationships in the vocabulary of genomes that appear universal, some reflecting the scaling of number of genes in different functional categories as a function of genome size (Molina and van Nimwegen, 2009), the link between dynamic and static properties of the models must always be confirmed with phylogenetic methods. We recently built global dynamic models for the evolution of structural domains that used birth-death differential equations with global abundances of domains as state variables without the need to capture the distribution of domains in proteomes (Tal et al, 2016). We fitted the models to data from ToDs assuming that only transitions present in the trees were possible between fold structures and that branches emerged directly from a trunk.…”

From chemical metabolism to life: the origin of the genetic coding process

“…These escape routes allowed cells to begin to evolve toward miniaturisation, further evolving the process that had led to the formation of chromosomes, now grouping together genes with common functional associations and co-transcribing them together as operons [81]. These processes would be reflected in a stepwise evolution of the structure of proteins, as indeed observed by Caetano-Anollés and co-workers [82]. …”

Testing Empirical Support for Evolutionary Models that Root the Tree of Life

“…While the first appearance of these innovations are rare events, their retention and loss in trees of these highly conserved features is a durable and relatively common phenomenon. We have made the distinction between innovation and innovation spread explicit in a dynamic model of proteome evolution, which we found explains the phylogenomics of the CA 2 characters (Tal et al 2016 ). The model uses global birth–death differential equations and domain abundances as state values and is governed by two parameter classes, λ j or the rate (birth minus death) of generating new variants of a same domain structure j , and a ij or the rate of ‘forward’ transition from structure j to structure i .…”

“…It could be argued, however, that stepmatrix models could be tested and improved by a mathematical approximation to more realistic statistical models, using, for example, fitted model and time parameters inferred from an evolutionary model of proteome evolution (e.g. a dynamic birth–death model; Tal et al 2016 ) or probabilities informed by stepmatrices obtained from CSR. Indeed, the HK model has been parametrized for Bayesian reconstruction from binary characters of FSF occurrence (Harish and Kurland 2017b ) using the nonstationary model developed by Klopfstein et al ( 2015 ).…”