Evolution of weak cooperative interactions for biological specificity

Abstract

A hallmark of biological systems is that particular functions and outcomes are realized in specific contexts, such as when particular signals are received. One mechanism for mediating specificity is described by Fisher's "lock and key" metaphor, exemplified by enzymes that bind selectively to a particular substrate via specific finely tuned interactions. Another mechanism, more prevalent in multicellular organisms, relies on multivalent weak cooperative interactions. Its importance has recently been illustrated by the recognition that liquid-liquid phase transitions underlie the formation of membraneless condensates that perform specific cellular functions. Based on computer simulations of an evolutionary model, we report that the latter mechanism likely became evolutionarily prominent when a large number of tasks had to be performed specifically for organisms to function properly. We find that the emergence of weak cooperative interactions for mediating specificity results in organisms that can evolve to accomplish new tasks with fewer, and likely less lethal, mutations. We argue that this makes the system more capable of undergoing evolutionary changes robustly, and thus this mechanism has been repeatedly positively selected in increasingly complex organisms. Specificity mediated by weak cooperative interactions results in some useful cross-reactivity for related tasks, but at the same time increases susceptibility to misregulation that might lead to pathologies.

Keywords: evolvability; gene regulation; phase separation; specificity; weak cooperative interactions.

Fig. 1.

Representation of the evolutionary model. (A) A schematic depiction of the space that represents the gene products of organisms and the tasks that they need to perform to function properly. Each axis describes a particular characteristic of a task or matching characteristic in a gene product that determines their interactions (see Model Development and Methods). Tasks are shown as stars and gene products as red dots. When a task and a gene product are within a distance equal to ε₁, the gene product performs the corresponding task with high specificity. When a task and a gene product are within a distance equal to ε₂, the gene product performs the corresponding task incompletely. When two gene products have closely matched interaction characteristics, they can act cooperatively (indicated with a line connecting them above), to perform tasks together (see Model Development and Methods). (B) The free energy of interaction between a task and a gene product is defined to be a function of the distance between a task and a single gene product as shown in the graph. The interaction free energy is parabolic when the task-gene distance is less than ε₂ and becomes 0 when the distance is larger than ε₂. As defined in Model Development and Methods, for cooperating gene products, their free energies with a given task are added up. (C) Schematic depiction of the processes of gene mutation, loss, and duplication included in the evolutionary model. For example, in this schematic the orange gene has mutated to black, the yellow gene is lost, and the purple gene is duplicated. (D) Depiction of the model for evolutionary dynamics (only one generation of evolution is depicted).

Fig. 2.

WCI evolve as organisms become more complex. This figure shows the variation of the average number of genes in organisms and the number of tasks specifically done via WCI between gene products as the number of tasks required for an organism to function properly increases (or organisms become more complex). The number of tasks performed by single gene products is also shown. When the number of tasks equals 10, 33% of tasks are done via WCI, and when the number of tasks equals 40, this proportion is 56%. Three characteristics describe the interaction characteristics of tasks and gene products.

Fig. 3.

Limited cross-reactivity accompanies the evolution of WCI. (A) Variation of the extent of cross-reactivity with the evolution of WCI. The x axis shows the number of tasks done by the same cluster of gene products, and the y axis is the percentage of such clusters that are preforming two, three, four, and five tasks in this cross-reactive fashion. (B) Snapshot of simulation results when new tasks are introduced such that they are either closely related to tasks from an earlier era or not. Two modules of such related tasks are depicted in characteristics space. Large spheres with radius ε₂ are drawn around each task. Brown spheres show tasks being performed by single-gene products, blue spheres show closely related tasks being performed by clusters of cooperating gene products. Small spheres correspond to gene products. (C) The percentage of two tasks completed by the same gene products is high only for related tasks. Three characteristics describe the interaction characteristics of tasks and gene products.

Fig. 4.

The evolution of WCI for biological specificity makes organisms more evolvable. (A) The response time for the organisms to evolve to function properly after a new task is introduced is shown as a function of the number of tasks (or complexity). Results are shown for both the full model and one wherein cooperative interactions between gene products is not allowed. (B) The number of mutations (which includes gene mutation, duplication, and loss) that the average organism needs to acquire to function properly after a new task is introduced is shown as a function of the number of tasks (or complexity). Results are shown for both the full model and one wherein cooperative interactions between gene products is not allowed.