Self-assembly from colloids to biology

The term "self-assembly" refers to the situation where many building blocks spontaneously form well-defined aggregates. Building blocks can be molecules, macromolecules (such as proteins, DNA), or colloids. In these notes I make use of statistical thermodynamics to address self-assembly in relatively complex situations. These situations are allostery, transcription regulation, virus capsid assembly, and the formation of charged, finite-size colloidal clusters. The first two situations can be reduced to a problem of adsorption onto substrates or templates. In the case of allostery, the state of the substrate couples to the binding affinity, leading to potentially strong "collective" effects. In transcription regulation, the adsorption of transcription factors (proteins) onto the promoter regions on DNA is proportional to the level of transcription of a gene. There, the main complication is that there are other substrates on which transcription factors may adsorb, a competition effect that may dramatically influence the level of transcription. The last two paragraphs are about virus capsid stability and finite-size, charged colloidal aggregates, respectively. In theses situations, finite-size aggregates occur without the presence of templates. In the case of virus capsids, finite size is presumed, and the question is addressed under what conditions (temperature, ionic strength) capsids are stable relative to the non-assembled state. For colloidal cluster, on the other hand, the building blocks are assumed to interact by short-range attraction and long-range repulsion, the magnitude of the latter being determined self-consistently from properties of the colloids and the solvent.