Gad Yagil

Dept. of Cell Biology, The Weizmann Institute, Rehovot, Israel 76100.

A major issue concerning pattern formation in living entities is whether biological structures are formed solely by spontaneous, self-assembling processes or whether additional, genome encoded signals are required for the specification of biostructures. In a classical demonstration of a self-assembling process, Fraenkel-Conrat (1963) dissociated the small RNA virus TMV (Tobacco Mosaic Virus) into its two components, RNA and coat protein, and showed that when these two components are remixed, fully infective virus particles are regained.

A different picture emerges when more complicated viruses such as the double stranded DNA bacteriophages are examined. Bacteriophage T4, for example, is composed of two principal parts, a head and a tail part. The tail structure is made of a sheath, a baseplate and 6 fibers attached to the base plate (see Figure), arranged in a close to perfect hexagonal symmetry. Bacteriophage T4 has a genome of about 166000 nucleotides (168699 nt in the t4 phage database as of 6/1994), compared with 6394 nt for TMV virus, and codes for at least 130 genes (Mosig and Eiserling, 1988). The correct expression of at least 49 of these genes is required for the assembly of the intact virion structure. Most of these genes code for the proteins composing the structure, but at least four genes are not found in the final structure: gene 57 codes for an enzymatic activity required for tail fiber assembly; gene 51, although essential, does not code for an identified protein and its role, is so far obscure; the product of gene 63 ("gp63") is responsible for chaperoning the correct joining of long tail fibers to the tail part (Wood and Crowther, 1983); gene 38 directs the correct assembly of tail fiber components (see Table 1 and Casjens and Hendrix, 1988). Gp29 and/or gp48 are proposed to serve as a tape or jig determining the correct length of the tail tube (Berget and King, 1983; Casjens and Hendrix, 1988). Other gene products have a role in directing the correct assembly of the head structure: gene 21 codes for a protease needed to cleave some of the head proteins before they can be properly assembled. Gp22 appears in the prohead to serve as a scaffold for the assembly of a correct head shell; only its degradation products appear in the final head structure (Black and Showe, 1983). It is clear that a simplistic principle of self-assembly is not applicable to bacteriophage T4. Rather, specific genomic instructions, some via yet unknown molecular pathways, have to be implemented before an infective virion particle can be produced in the infected cell. Direction by Such genomic signals may be dominating in higher organisms.

In this paper we shall apply a previously formulated theory of biocomplexity (Yagil, 1985; 1993a,b) to compare the structural complexity of the two virions - the self-assembling TMV virion with the instruction-directed T4 phage. It will be shown that a great difference in the numerical complexities of the two structures exists, leading to the proposition that self-organization can work well mainly for structures of low complexity, while template generated instructions are required for the generation of the more highly complex structures.

Structural biocomplexity has been defined as the length of the shortest list of numerical and symbolic specifications necessary to describe a given structure (Yagil, 1985). This definition can be regarded as a form of the Kolmogorov algorithmic complexity (cf. Li and Vitanji, 1991) adapted to real, physical structures. The length of the list of specifications describing a physical system is determined by the number of regularities (i.e. identical numerical specifications) in a system - the more regularities that can be identified in the elements of the system (e.g. in the phage particles), the shorter is the specification list required. In quantitative form (Yagil, 1985):

where C designs the structural complexity of the system; c(k) the number of point coordinates sharing a k fold regularity and c' the 5-6 coordinates necessary to place a rigid structure in the external world. We have previously shown how complexity C is evaluated for small molecules such as methane, ethane and adenine (1985), for proteins (1993a) and for hydrocarbon isomers (1993b). Here we shall apply the procedure to evaluate, the structural complexities of the virion structure of TMV and of the bacteriophage T4 tail structure.

The first step in the analysis is to decide upon the hierarchical level of interest, e.g. whether virion complexity is to be evaluated in terms of its structural proteins, in terms of their composing amino acids, or possibly in terms of the atoms constituting each amino acid. The decision is an arbitrary one and depends on the kind of information needed. When coding capacity of a genome is of interest, complexity in terms of gene products, i.e proteins, is called for. A simple level rule (Yagil, in preparation) connects the complexities of the different hierarchical levels.

In the fourth step it should be determined whether each of the listed coordinates is a random or an ordered one. An ordered coordinate is one for which a fixed numerical value applies to all members of an ensemble (e.g. for all phage particles in a test tube), while a disordered,or random coordinate is one which takes a different value in each member of the ensemble. For instance, each tail fiber of T4 has two subparts the length of which is constant ("ordered coordinates") but have variable angles, depending on the extent each fiber is drawn in or extended (see Figure). These angles are "disordered coordinates", because they take a different value in every phage in an ensemble of phage particles and are assigned values of "Any" in Table 1. The angles of free rotating amino acids chains are other examples of random coordinates, while neighboring carbon - carbon distances are ordered features of these molecules. A coordinate is ordered only when it takes up the same value in each particle in ensemble. The distinction between disordered (random) and ordered coordinates is important, because only ordered coordinates, which can be assigned defined numerical values, contribute to the complexity of the system. For disordered coordinates it can not be stated whether they are complex or simply arranged; they have therefore to be excluded from the analysis. This is a major feature of the approach presented here.

C = 102 - 6 = 96

       Specifications:      1         1            1            1

A more detailed discussion of the assumptions made in this analysis can be found in the three previous publications cited. These publications discuss also the relation between complexity as used here and common thermodynamic and information-theoretic quantities. In brief, biocomplexity can be regarded as an zero point entropy, which exists already at 0o Kelvin, and does not contribute, by the 3rd law, to the thermodynamically measured entropy of the system. The DNA and RNA of the viruses, really the heaviest contributors to the complexity of the two viruses (166000 nt and 6892 nt), have not been included in the present analysis; this has been done in order to highlight the structural contribution to biocomplexity. The contribution of nucleotide base sequence is nevertheless decisive in determining both shape and function of the viruses. This is a major point, as the increase in structural and functional complexity during evolution can hardly be imagined without the parallel increase in template complexity (certain aspects of brain function may be an exception). It is the emergence of templates capable of specifying organizing instructions which confers to living entities their high complexities, with all their manifestations. The complexities reached by the genetic templates remain unmatched in the inanimate world.

The difference between the two simple semi-organisms thus highlights the limitation of self-organization in producing complex biological structures. The requirement for template-specified directions should by no means be regarded as a conceptual hurdle - all highly evolved organisms have a vast repertoire of DNA with ample space for yet unaccounted functions (Hood, 1993). A search for novel organizational signals encoded in DNA, via small ORFs or otherwise, could be rewarding. The main object of this presentation is to illustrate, by way of an example, the relation between biocomplexity and morphogenetic elements and to point at the potential of complexity analysis to shed light on the emergence of the intricate patterns of life.