Self-assembly, modularity, and physical complexity
- The amount of information required for evolved, or nanoengineered, structures to self-assemble is important in evolutionary biology and nanotechnology: we provide a consistent mathematical formalism to describe the physical complexity of structures motivated by self-assembly processes
Many structures in biology self-assemble -- that is, they are made up from individual subunits which stick to each other when mixed, so that the structure forms with no external "guiding hand". The process is like shaking a bag full of magnets and them sticking to each other -- though often a lot more subtle, with pairs of subunits interacting in specific ways and in specific arrangements.
Self-assembling is interesting both because it produces important machinery in biology -- like the proteins in our cells -- and because it could be an efficient way of producing structures in nanotechnology. If we can figure out a set of subunits and interactions that allows a desired product to self-assemble "automatically", we don't need to precisely manipulate tiny objects on the nanoscale to build nanotech.
But how difficult is it to design such a set of subunits and interactions? This question is important in both the biological and nanotech pictures -- nanotech because it represents the design effort required to produce a structure, and bio because how evolution has "learned" to produce complex structures through self-assembly is underexplored (though not, as intelligent design advocates would claim, an argument against evolution).
Self-assembling is interesting both because it produces important machinery in biology -- like the proteins in our cells -- and because it could be an efficient way of producing structures in nanotechnology. If we can figure out a set of subunits and interactions that allows a desired product to self-assemble "automatically", we don't need to precisely manipulate tiny objects on the nanoscale to build nanotech.
But how difficult is it to design such a set of subunits and interactions? This question is important in both the biological and nanotech pictures -- nanotech because it represents the design effort required to produce a structure, and bio because how evolution has "learned" to produce complex structures through self-assembly is underexplored (though not, as intelligent design advocates would claim, an argument against evolution).
The process of describing a structure in terms of a self-assembling ruleset. 1. The structure (here a protein) is broken into its subunits. 2. The interactions between subunits are identified. 3+4. Subunits with different patterns of interactions are labelled different (red, blue, yellow); subunits with the same pattern of interactions are labelled the same (two yellows). 5. The subunit types and their interactions are recorded in a "genome".
In a paper in Physical Review E here (free here), we suggest a mathematical description of a structure that reports how much information is required for that structure to be self-assembled from interacting subunits. We give an algorithm to compute this for any structure, and link it to the concept of "algorithmic complexity" from computer science. In so doing, we link the process of self-assembling a structure to the progress of an algorithm producing a given output. This picture accounts for symmetry and modularity in structures, which reduce complexity because they involve existing information being repeated (for example, the same pattern appearing on different sides of a shape). This complexity measure describes the amount of information required to build a given self-assembling structure -- but can also be used more generally, to describe the complexity of structures in a self-consistent way. We use it to explore patterns of complexity in protein structures, highlighting the highly symmetric and modular structures often found in biology (an efficient way of minimising the required genetic information for a structure). Iain
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