Please excuse any typographical issues as this is going up right after lunch. I’ll proofread and remove this message later.

The morning session was mostly computational/simulation studies. Ibáňez talked about threshold networks and how they can be used to simulate complex reactions and biological regulation.

Hajiaghayi and Doty talked about stochastic and differential equation based simulators. The limitations of using a formal language to describe reactions and reaction networks are that it makes assumptions about concentrations and that it is limited to rather small numbers of molecules. The advantage is that the reaction (number of molecules of each chemical species) can be highly precisely defined in time. I have always taken an ODE approach; the stochastic nature of this approach makes me nervous. Both approaches are reasonable and highlight a fundamental, interesting distinction that all nano-scientists need to make: deal with such large numbers of molecules that you can treat them as a fungible quantity, or deal with small numbers of molecules on a discrete basis.

For example: if you take the volume of a bacterium (1 µm³ or 1×10^-18 l) and a fairly normal pH of 6 you get a H⁺ concentration of 1×10^-6 Mol/l of H⁺. Divide in Avagadro’s number and you get something like .6 atoms of H⁺. That should seem weird. It really just means that there is an H⁺ in the cell 60% of the time and the H+ is gone 40% of the time. But, still, it is something that a differential equation approach doesn’t capture. An accurate simulator would fluctuate between 0 and 1 at that point; a standard differential equation solver just hovers at .6. They might give similar answers, but not always.

Finally, there were two presentations on tile assembly. Andrew Winslow talked about translating between different methods of describing “tiles” in order to determine their assembled structure efficiently. Then Dandan Mo talked about a hexagonal tile method. I’m proud to say I influenced this material a little bit. The idea is that assembly can occur with strong and weak linkages; the intermediate assemblies can have their weak links melted and leave only the strong links. Thus the assembly process can be “guided” through discrete steps using weak links and thermal cycling. This seems complex, but it allows for a new method of controlling the process and preventing unwanted assembly patterns.

Tile assembly (and algorithmic self-assembly) are big interests of mine. The key is that these don’t just make periodic/crystalline materials. The little entities that are gathering together use a small amount of internal computation to assemble into a complex structure based on a distributed program. This is more like biological development: cells make autonomous decisions based on interactions with their neighboring cells and their internal state and from that distributed network of interactions emerges a finished organism. I don’t know of any system but DNA computation that approaches a programmable version of this distributed computation/self-assembly.

For a look at self assembling tiles, I recommend this open access article: