Stochastic innovation as a mechanism by which catalysts might self-assemble into chemical reaction networks

Abstract

We develop a computer model for how two different chemical catalysts in solution, A and B, could be driven to form AB complexes, based on the concentration gradients of a substrate or product that they share in common. If A's product is B's substrate, B will be attracted to A, mediated by a common resource that is not otherwise plentiful in the environment. By this simple physicochemical mechanism, chemical reactions could spontaneously associate to become chained together in solution. According to the model, such catalyst self-association processes may resemble other processes of "stochastic innovation," such as Darwinian evolution in biology, that involve a search among options, a selection among those options, and then a lock-in of that selection. Like Darwinian processes, this simple chemical process exhibits cooperation, competition, innovation, and a preference for consistency. This model may be useful for understanding organizational processes in prebiotic chemistry and for developing new kinds of self-organization in chemically reacting systems.

Fig. 1.

Agents (lettered circles) and resources (numbered squares). (a) Agent of type A converts substrate 1 to product 2. (b) Agent of type B converts substrate 2 to product 3. (c) When agents A and B are complexed together, two reactions are chained together, converting substrate 1s to product 3s.

Fig. 2.

Attraction and shielding. (a) Attraction. Bs are attracted to 2s, which are produced by As, hence Bs are attracted to As. (b) Shielding. When 2s are plentiful in the environment, Bs are attracted to them in all directions, hence have no special net tendency to associate with As.

Fig. 3.

Attraction on the lattice. (a) Agent A leaves the bulk and binds to the surface lattice in a region where resource 1s are concentrated. (b) Agent A converts 1s to 2s. (c) Agent B leaves the bulk and binds to the surface lattice where 2s are concentrated, which tends to be near the As that produced them. (d) Agent B produces 3s. (e and f) Agent B associates with A (e), forming a complex, which is now (f) a machine that converts 1s to 3s.

Fig. 4.

Processes in the lattice model. (a) Molecules exchange between the bulk solution and bound to a random lattice site. (b) Agents have an additional binding rate at lattice regions with their input resource. (c) Bound molecules move about the surface. (d) Agents convert input resources to output resources at their site. (e) Two agents at a site can form an agent complex.

Fig. 5.

Numbers of AB complexes formed vs. time. Dark line: under attraction conditions, no environmental supply of resource 2 (E₁ = 10⁴, E₂ = 0). Light line: under shielding conditions, with resource 2 provided by the environment (E₁ = 10⁴, E₂ = 10³). Dashed line: control experiment; no 2s are available because the environment has none, and As are unproductive because of the absence of 1s (E₁ = 0, E₂ = 0). (Time is in units of 1,000 simulation units for this and following plots.)

Fig. 6.

Competition. (a) Agent B can associate with either agent A or agent A*, a superior producer of resource 2. (b) Complex formation increases as the productivity of As increase. (c) Agent A competes with a superagent A* (for A*, k_x-y = 0.1 and for A, k_x-y = 0.001). Competition enhances the difference between A*B and AB complex formation.

Fig. 7.

Formation of multiagent complexes. (a) Eight agents assemble sequentially to form a catalytic chain, using only the input resource for agent A. (b) When there is no environmental shielding, the full chain assembles rapidly, with no stable intermediates. (c) The presence of environment resources (E₅ = 100) shields the step between agents D and E, resulting in longer-lived minor intermediates. (d) A 10-fold stronger environmental supply (E₅ = 1,000) results in the stable dominance of the A-D intermediate chain over the complete chain. (e) The presence of environment resources (E₃ = 100) at an earlier stage, between B-C, leads to an initially stronger, but ultimately minor, intermediate chain.