Saturday, October 13, 2012

49. Kauffman's Work on Genetic Regulatory Networks

A genetic regulatory network (GRN) in a cell is a set of DNA segments that interact with one another and govern the rates at which the genes in the network are transcribed into mRNA. As discussed in Part 48, GRNs in single-celled organisms like E. coli respond to external stimuli to do what is good for the organism. In multicellular organisms the GRNs play other roles also, like cell differentiation (there are some 285 different types of cells in the human body).

A variety of models have been developed for understanding the GRNs. I shall focus on a model based on random Boolean networks (RBNs), on which pioneering work was done by Stuart Kauffman.

In Kauffman's RBN model a gene (represented as a node of the network) was modelled as a binary device (like an electric bulb which is either 'on' or 'off'), the whole network having N such nodes. Each gene or node was modelled as receiving K inputs (KN) from randomly chosen ‘controlling’ genes or nodes, and also receiving one random ‘update’ function for its K inputs. The update function prescribed the state of the gene in the next time step, given its state in the current time step, and was chosen according to some probability-distribution function. By varying N and K for these RBNs, the behaviour of a variety of such finite sequential switching 'automata' could be investigated. At any time step, each gene or node had a value 1 or 0, and the network was a collection of these 1s and 0s, representing the ‘state’ of the network. This pattern of 1s and 0s served as the input, determining the pattern for the next time step of the gene.

The RBN has 2N possible states; i.e. it has a finite number of states. This finiteness, coupled with the fact that the modelled dynamics is deterministic, implies that, as the RBN proceeds through a sequence of states, it must eventually return to a pattern it had at some earlier time step, and from then on it must repeat the same pattern-sequence periodically. That is, it must be trapped in a re-entrant cycle of states, or an attractor in phase space. Each such state cycle or attractor represents a distinct temporal mode of behaviour of the net, and was equated by Kauffman with a distinct cell type (kidney, liver, etc.). Cell types differ only in the pattern of gene activity; they all carry the same genome.

Kauffman focussed his attention on ‘critical’ RBNs. These lie at the edge of chaos, i.e. at the boundary between frozen networks and chaotic networks. Frozen networks have very short attractors or cycle lengths. And chaotic networks have large-sized attractors that may include a substantial portion of the phase space. To quote Kauffman:

Let’s talk about networks as a model of the genetic regulatory system. My claim is that sparsely connected networks in the ordered regime, but not too far from the edge (of chaos) do a pretty good job of fitting lots of features about real embryonic development, and real cell types, and real cell differentiation. And insofar as that’s true, then it is a good guess that a billion years of evolution has in fact tuned real cell types to be near the edge of chaos. So that’s very powerful evidence that there must be something good about the edge of chaos. So let’s say the phase transition is the place to be for complex computation. Then the second assertion is something like ‘Mutation and selection will get you there.’
Thus Jacob & Monod’s cell types, distinguished from one another by the distinct and stable network patterns of gene activity, were interpreted by Kauffman as represented by different attractors in phase space. For K = 1 and for K = N the length of the attractor cycles is very large. But for K = 2, i.e. when there are two inputs per gene, the lengths of the cycles are very small, roughly scaling as ~√N for critical networks. For example, for N = 1000, i.e. for 21000 possible states of the network, the modelled genome was found to cycle typically among just 30 time steps, a remarkable result indeed.

Kauffman's work demonstrated that highly ordered dynamical behaviour is typical even for randomly constructed genetic networks getting just a few inputs per component. This implied that homeostasis in living complex systems is a direct consequence of the high molecular specificity among the macromolecules involved. Similarly, cell differentiation reflects the capacity of complex adaptive systems to behave in several distinct, highly localized ways.

Kauffman’s work established that complex genetic networks could come into being by spontaneous self-organization, without the need for slow evolution by trial and error. After all, the whole thing had to be there together, and not partially, to function at all.

Kauffman also tackled the question of how extremely large molecules like RNA and DNA came into existence in the first place. In any case, even DNA requires the availability of certain protein molecules for its genetic role. Therefore, there must have been a mechanism which resulted in the spontaneous creation of protein molecules without the intervention of DNA or RNA.In other words, there must have been a non-random origin of life. There must have been another way, independent of the need to involve DNA molecules, for self-reproducing molecular systems to have got started. Kauffman carried Melvin Calvin’s (1969) idea of autocatalytic reactions much further to explain how this could happen. In Kauffman’s model, life originated before the advent of RNA or DNA. And his network model could incorporate features like reproduction, as also competition and cooperation for survival and evolution (including 'coevolution').

More on this in future posts.