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24R.Wallace/BioSystems103 (2011) 18–26

sequence,but also by the interacting partner.Essentially,they are without a hydrophobic core.

Serdyuk(2007),in fact,proposes four basic protein forms:

In addition to the axiomatic native state–a rigid tertiary structure–it is proposed to consider three more states: molten globule,completely disordered chain,and the structure comprising domains connected with long enough linkers and containing,as a rule,rather long disordered regions at the ends.

These four states cover all conformations that are now known based on the physical understanding of protein structure.

Thus the spectrum of Fig.1becomes an expansion,via sub-groupoids,of a single class within this larger taxonomy,having the magic number four,implying a larger,embedding,‘spherical’error code topology,in Tlusty’s sense.

It is possible,using the previous section,to say something about IDP rates of binding to their targets that,according to Huang and Liu(2009),are greater than for ordered proteins,via a highlyflexi-ble‘fly-casting’mechanism,in contrast with ordered proteins that must dock to their targets.IDPs have,then,greater effective cap-ture radius and can weakly bind to targets from a larger distance, and then‘reel themselves in’to thefinal configuration.Huang and Liu conclude that both fractions of the native interchain contacts and the distance between mass centers,quantities widely used in protein binding problems,only partially describe the features of the binding process,so that better coordinates will be required.

Taking the perspective of Section6above,we assume that IDPs are transferred hand-to-hand,to avoid cellular clean-up processes. Thus,for a given IDP,symbolized by I,there is an initial partner,i, and afinal partner f,defining larger-scale structures.Then we are interested in the number of possible paths,N(n),having n steps leading from an initial partnership S i*1to afinal partnership S f*1. This instantiates a larger version of the metanetwork of‘languages’discussed above.

Collapsing the argument via Eqs.(7)and(10),the‘fly-casting’mechanism might better be described as a snake slithering down a rocky hillside.That is,an IDP‘falling’down a noisy folding funnel undergoes a self-lubricating catalysis that decreases 2in some-thing like Fig.6,increasing the rate of reaction above what would be expected from a rigid molecule havingfixed tertiary struc-tures.Indeed,the child’s toy slinky-spring walking down a staircase comes to mind,and is probably not a bad model.

8.Discussion

Tlusty(2007,2010a,Table1)constructs a relatively smooth error network-symmetry based taxonomy for the evolution of the genetic code,and suggests that future evolutionary process could well expand that code’s expression from20to as many as25amino acids.The globular/amyloid disjunction explored here,in conjunc-tion with the spectrum of possible geometries identified in the horizontal dispersion of Fig.1–the nested protein folding groupoid –suggests a markedly different evolutionary trajectory for the‘pro-tein folding code’,such as it is.If amyloid proteins were indeed the primitive form,as Wang et al.(2008)conjecture,then a remarkable evolutionary change occurred,reducing the topological complex-ity of the code from a double toroid to a sphere with a few small attachment handles.This suggests a very highly punctuated equi-librium transition,in the sense of Eldredge and Gould(1972),a shift from one to three-dimensional protein structures in which the‘protein folding code’became topologically simplified while the overall protein topology became more complex.This is a strikingly different evolutionary pathway from that inferred by Tlusty for the genetic code.More likely,amyloidfibrils in particular,and perhaps most of the other geometric forms across Fig.1,have largely been evolutionary dead ends since prebiotic times,and cellular or other mechanisms against their production have been with us a very long time.

Maury’s‘amyloid world’hypothesis is one possible explanation, i.e.,that amyloid frangibility was,itself,thefirst reproductive code, characterized by the quasi-species effects consequent on segment length variation and combinatorial effects,and ultimately leading to the later RNA/DNA worlds in which prion diseases remain as fossilized remnants of that earlier time.

Cellular regulatory machinery assisting protein folding–chap-erone processes associated with the endoplasmic reticulum–must inevitably be cognitive in the sense Atlan and Cohen(1998) attribute to the immune system.It should thus be possible to develop a‘cognitive paradigm’for active protein folding regulation, in the sense of Wallace and Wallace(2008,2009,in press),and begin to incorporate the catalytic effects of epigenetic factors,including patterns of culture and psychosocial stress,into the etiology of pro-tein folding disorders.Such catalytic effects emerge directly from the necessary association of a basic information source with a broad class of cognitive processes,and from the role of an information source as a kind of free energy.Thus patterned external signals from an information source can serve to catalyze cognitive regula-tory phenomena via a form of canalization.In the case of human protein folding disorders,this effect seems to emerge as a kind of premature aging of the cellular regulatory apparatus by a life course trajectory of psychosocial,cultural,and and other environmental stressors.

Thus Serdyuk’s fourfold classification,the set of equivalence classes across Fig.1,and the nested sets within the valleys of the native state,amyloidfibrils,and possible other structures such as the spherulites of Krebs et al.(2009),imply a complex nested groupoid structure for protein folding geometry.This shows there can be …… 此处隐藏：5702字，全部文档内容请下载后查看。喜欢就下载吧 ……