Successive Eras in Molecular and Biophysical Aggregation

University Of California-Berkeley, Berkeley CA

Investigators

Abstract

The research will analyze three related aggregation processes, ranging from the creation of large molecular aggregates from a supersaturated solution by adding one molecule at a time, to the formation and subsequent evolution of pores in the cell's membrane caused by an electric shock, to the pattern formation in myxobacteria facilitated by `contact chemical signaling' when opposite-moving bacteria collide. Although these aggregation processes arise from diverse physical and biological contexts, their analysis reveals an underlying connection: They all proceed by distinct succession of eras. Large molecular aggregates start with the initial formation of tiny clusters of monomers, their subsequent growth to macroscopic size, and finally the assimilation of smaller aggregates by the larger. The eras are 'matched' in the sense that the end of the previous era sets the conditions for the beginning of the next one. The successive eras of electroporation, `initial charging,' `pore creation,' and `coarsening' closely resemble their counterparts in molecular aggregation. Finally, pattern formation in myxobacteria starts with time-oscillatory waves of bacterial concentration, proceeds to the formations of more permanent concentrations called 'fruiting bodies,' and then there is a growth of the larger fruiting bodies at the expense of smaller. This research will focus on the asymptotic and numerical analysis of the selected eras in each problem and on establishing their connection to the subsequent eras by matched asymptotic expansions, and will involve collaborators from Biomedical Engineering and Molecular and Cell Biology. The three aggregation processes investigated here have important theoretical and practical applications. The work on the creation of large molecular aggregates will address the main gap in the existing literature that prevents a global understanding of the whole process, from non-aggregated monomer units to late-stage coarsening. In addition, it informs new and fundamental problems in semiconductor fabrication. Electroporation has great promise as a means to transfer genes and/or drugs to specific organs or cancer tumors, without poisoning the rest of the body. However, a computationally efficient model of pore nucleation is needed for modeling of transport of drugs and genes through the electropores and for using the modeling results in the design of pulsing protocols used in experiments and in therapies. The benefits of the myxobacteria problem lie in its long-range contribution to understanding how the multicellular life organizes itself. This problem features the very original mechanism of pattern formation based on direct contact chemical signaling, which is radically different from the traditional mechanisms based on the long-range diffusion of morphogens but more relevant to morphogenesis in higher organisms, including humans.