Escape from Adaptive Conflict follows from weak functional trade-offs and mutational robustness

Abstract

A fundamental question in molecular evolution is how proteins can adapt to new functions while being conserved for an existing function at the same time. Several theoretical models have been put forward to explain this apparent paradox. The most popular models include neofunctionalization, subfunctionalization (SUBF) by degenerative mutations, and dosage models. All of these models focus on adaptation after gene duplication. A newly proposed model named "Escape from Adaptive Conflict" (EAC) includes adaptive processes before and after gene duplication that lead to multifunctional proteins, and divergence (SUBF). Support for the importance of multifunctionality for the evolution of new protein functions comes from two experimental observations. First, many enzymes have highly evolvable promiscuous side activities. Second, different structural states of the same protein can be associated with different functions. How these observations may be related to the EAC model, under which conditions EAC is possible, and how the different models relate to each other is still unclear. Here, we present a theoretical framework that uses biophysical principles to infer the roles of functional promiscuity, gene dosage, gene duplication, point mutations, and selection pressures in the evolution of proteins. We find that selection pressures can determine whether neofunctionalization or SUBF is the more likely evolutionary process. Multifunctional proteins, arising during EAC evolution, allow rapid adaptation independent of gene duplication. This becomes a crucial advantage when gene duplications are rare. Finally, we propose that an increase in mutational robustness, not necessarily functional optimization, can be the sole driving force behind SUBF.

Fig. 1.

A biophysical model of neutral network topology and fitness. (A) The extent of the inter-connected neutral networks A and B (for the depicted structures X_A and X_B) are indicated, respectively, by lightly colored regions of blue and pink. Their region of overlap is in light magenta. Symbols (nodes) represent model protein sequences (genes) with either X_A or X_B (diamonds for prototypes, circles otherwise), or both (magenta squares), in their native states. Sequences that differ by one point mutation are connected by edges. Symbols for sequences with single and multiple native conformations are shown, respectively, in lighter and darker colors. Nonprototype sequences encoding for more stable native states are denoted by larger symbols. (B) Fitness before and after duplication of a multifunctional gene (square). A genotype is either a single gene or a pair of genes that originates from duplication. Fitness of a genotype is the sum of fitness contributions W_A and W_B, which are functions of C_A and C_B respectively. As illustrated by the examples shown, W_A and W_B increase linearly, respectively, with C_A and C_B below a threshold concentration θ (dotted vertical line) and is a constant above θ.

Fig. 2.

NEOF and SUBF occur under different degrees of fitness trade-offs. (A, B) Examples of fitness landscapes are shown for the network in Fig. 1A under high (A) and low (B) selection pressures. Single-gene fitness W_i is plotted along a vertical axis orthogonal to a planar representation of sequence space used in Fig. 1A. Note that gene-pair fitness W_ij = W_i + W_j is not plotted in these landscapes. A key to the symbols used to describe major evolutionary processes on these landscapes are provided in the Insets in A and in C . C, D Evolutionary dynamics simulated using the master equation formulation in SI Text for the fitness landscapes in A and B, respectively. Genotype frequency P (left vertical scale) provides the relative population of the sum of P_i(q)’s (for single genes) or of P_ij(q)’s (for gene pairs) that belong to a given genotype category as a function of time (q, in logarithmic scale). The corresponding evolution of average population fitness is plotted in orange (right vertical scale). Evolution in the two scenarios of dosage effect after gene duplication (d = 0 or 1) are also compared. (E, F) Schematics of evolutionary steps during NEOF (E) and SUBF (F) with dosage effects (d = 1). Genotype fitness is given as W_i (single genes) or W_ij (gene pairs) that depends on protein concentrations C_A and C_B (cf. Fig. 1B).

Fig. 3.

Strong tendency towards mutationally robust genotypes during SUBF. Steady-state populations were obtained from the SUBF simulations in Fig. 2D (θ = 0.5 and d = 1). The scatter plot shows ln(P_ij)_st versus the number of genotypes that are within two point mutations from (i,j) in the network. Data points for the 24 bridge pairs and 1,728 subfunctionalized pairs are plotted, respectively, by filled magenta squares and black diamonds. The plot thus contains all 1,752 genotypes with maximum fitness at steady state (among all 34,410 genotypes—single genes and gene pairs—for X_A and X_B in Fig. 1A). The corresponding scatter plot for a randomized network topology is shown in the Inset. Results from a control simulation that artificially eliminated the epistatic barriers are shown by the open symbols. Magenta squares, orange triangles, and gray diamonds represent data points for bridge, mixed, and SUBF pairs, respectively. The inclusion of mixed pairs with ad hoc optimal fitness leads to increased numbers of neutral genotypes adjacent to the bridge pairs and thus abolishes the separation between bridge and SUBF pairs observed in the original model. Nevertheless, a tight correlation between ln(P_ij)_st and genotype entropy is maintained and SUBF pairs remain the most populated steady-state genotypes.