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A theory of evolutionary construction of viruses
700 A THEORY
OF EVOLUTIONARY
CONSTRUCTION
OF VIRUSES
R. KILKSON Department
of Molecular Department
Biology
of Medical
and Biophysics, Yale Physics, Karolinska Received
October,
University, Institutet,
New Haven, Stockholm,
Conn., Sweden
U.S.A.
and
10, 1964
IN an attempt to define and apply a physical basis for biomolecular arrangements, the author proposed in a previous publication the theory of discrete states of biological structures [3]. The theory limits the possible variety of macromolecular arrangements in biological structures. In this communication the theory is applied to highly ordered viruses that have well defined symmetries. The theoretical limitations on these structures are combined with necessary biological properties in order to be able to predict the possible variety of sfructure states [3]. On the basis of established virus biology, it will be assumed that outside its host cell a virus must have at least the following minimum biological properties: it must contain its own genetic information (nucleic acid), it must protect the nucleic acid, and it must be able to transmit this genetic information into the host cell. The last requirement implies attachment of the virus to the host cell, and a subsequent injection of the virus nucleic acid (and possible other virus parts) into the cell. Viruses and their component parts are constructed preferentially of small identical subunits (principle II of the generalized theory 131). Consequently the possible virus structure states can be derived by starting with one molecule of single-stranded nucleic acid (ssna) with its linear functional symmetry [3]. To this are added other molecules of subunits pi (i is a running sequential index for operationally different subunits. The operational subunit may not be identical with the chemically extracted subunit.) To conform with the general theory the following requirements must be met: (a) the equivalence of the identical subunits in the structure, or their respective structural parts (a single type of identical interaction and environment); (b) a sequential incorporation of different operational subunits and a preferential use of a single type of subunit for each kind of structural part. For the actual assembly this does not rule out cooperative processes like crystallization. Simultaneous cocrystallization of many virus parts would require too high a coincidence to be probable; (c) a common complementary functional symmetry subgroup of structurally connected virus parts (principle III [3]). The restrictions listed above are combined with the minimum biological properties as stated. Therefore, upon the addition of a new and different pi the single-stranded nucleic acid molecule, or a nucleoprotein structure derivable from it, may undergo one of the following processes: (1) a flexible, linear or helical assembly may condense randomly and be surrounded by a protein coat (or coats for multiple sequential biological action); (2) a stiff nucleoprotein conformation may be surrounded by an external protein coat. The nucleoprotein acts as a surface constraint [3]; (3) a consecutive helical coiling; Experimental
Cell Reseurch
36
Virus structure evolution
701
(3’) formation of multiple coaxial layers of helical toilings is valid separately for each layer); (4) crystallization of two or more identical (linear or helical) blies. The present report proceeds only up to the treatment nucleic acid (dsna, a helical two-crystal of two ssna);
(equivalence
of parts
nucleoprotein assemof double-stranded
Fig. I.-The resulting graphic representation of the derivation of virus structures, derivation tree: ssna, single-stranded nucleic acid (RNA or DNA); dsna, double-stranded nucleic acid (RNA or DNA); 1, . . . . 5”, refer to wrapping processes defined in text; same + . . ., same structure as at left (along d-lines) + added parts); pi, the i ” kind of subunits; at!., attachment apparatus; inj., turnip yellow mosaic virus injection apparatus, coaxial to the attachment apparatus; TYMV, (11; TMV, tobacco mosaic virus [5]; VSV, vesicular stomatitis virus [2]; Bm, silk worm virus (81; T-2, T-2 bacteriophage [4]; K, Kilham’s mouse pneumonitis virus 161; Mumps, mumps virus [I]; ---, possible extension of the derivation process; r.c., random coil.
(5) attachment of other, different parts. Due to the minimum biological needs two types of such parts will be considered; (5’) a special apparatus for the attachment of the virus to the cell. This should be necessary only for viruses of high structural polarity, as for example is produced by process 3’. The position of the attachment apparatus is defined by the symmetry of the nucleoprotein arrangement; (5”) a special apparatus for the injection of virus nucleic acid into the cell. This is necessary after step 5’. The rigidity of the nucleoprotein assembly further restricts which of the processes l-5” may be possible. The dimensions of the nucleic acid functional symmetry subunit limit the dimensions of pi that may be connected to the nucleic acids. The possible groupings of structure states can be derived following the procedures as outlined above. These groupings can be ordered into a derivation tree. Fig. 1. The root of the derivation tree is ssna. (The concepts tree and root come from graph theory [7]). Each derivation line in the derivation tree corresponds to a process that is generated by the addition of at least one new pi (the numbers on the derivation lines indicate the process numbers). Each block represents a grouping of structure Experimental
Cell
Research
36
702
R. Kilkson
states that are generated from the structure block at their left. In the blocks are included short descriptions of the structures, and an example virus whenever there are reasonable experimental foundations available. The structures that belong to the same block are generated by similar processes, but the pi and the orders of the symmetry operators need not be identical. A block may represent a grouping of viable structure states only if all the biological properties are satisfied. The complexity of the structures (in terms of principle II [3]) increases as one moves from left to right in the derivation tree. The treatment here points out some further biological consequences of the structure theory. A radical change in the inner zones of the structure diagram, described earlier in [3], disrupts the structure state, with a consecutive loss of the outer zones and their respective biological functions. Therefore, the evolution should be primarily restricted to the outermost zones of the structure diagram. Evolution should follow the derivation tree from left to right. (For a complete analysis the possible alternatives in respect to the host cell have to be included.) Due to limitations on size (principle II [3]), it should not be necessary to follow the derivation tree more than a few steps. Larger structures should be compounded from smaller units corresponding to the beginning of the derivation tree. Flexible bondings introduce a broadening and an increase in the multiplicity of the structure states under the general restrictions of imposed physical constraints. This theory and the corresponding derivation tree have been extended to cover viruses of less rigid symmetries and some ordered cellular structures. A comprehensive account of this work is published separately, that includes detailed discussion of possible virus structure states, their general appearances, symmetries, nucleoprotein arrangements, some specialized biological properties and a number of experimentally observable parameters. This research has been supported by U.S. Public Health Service grant (AI-0339904 BBC) and a special fellowship (l-F3-GM-23, 949-01) for a year (64/65) of research at the Dept. of Medical Physics, Karolinska Institutet. REFERENCES 1. 2. 3. 4. 5. 6. 7. 8.
HORNE,
R. W. and
P., Aduan. Virus Res. 10, 101 (1963) G. F., Virolow 16, 466 (1962). KILKSON, R., Proc. Nat1 Acad. Sci. U.S. 51, 543(1964). KILKSON, R. and MAESTRE, M. F., Nature 195, 494 (1962). KLUG, A. and CASPAR, D. L. D., Aduan. Virus Res. 7, 225 (1960). MATTERN. C. IT. T.. ALLISON, A. C. and ROWE, W. P., Virolow 20, 413 (1963). ORE, O., ‘Graphs c&d their .uses. Random Hcmse, New Yo$ 1963. SMITH, K. M., Aduan. Virus Res. 9, 195 (1962).
HOWATSON,
Experimental
A.
F.
WILDY,
and WHITMORE,
Cell Research
36
OF EVOLUTIONARY
CONSTRUCTION
OF VIRUSES
R. KILKSON Department
of Molecular Department
Biology
of Medical
and Biophysics, Yale Physics, Karolinska Received
October,
University, Institutet,
New Haven, Stockholm,
Conn., Sweden
U.S.A.
and
10, 1964
IN an attempt to define and apply a physical basis for biomolecular arrangements, the author proposed in a previous publication the theory of discrete states of biological structures [3]. The theory limits the possible variety of macromolecular arrangements in biological structures. In this communication the theory is applied to highly ordered viruses that have well defined symmetries. The theoretical limitations on these structures are combined with necessary biological properties in order to be able to predict the possible variety of sfructure states [3]. On the basis of established virus biology, it will be assumed that outside its host cell a virus must have at least the following minimum biological properties: it must contain its own genetic information (nucleic acid), it must protect the nucleic acid, and it must be able to transmit this genetic information into the host cell. The last requirement implies attachment of the virus to the host cell, and a subsequent injection of the virus nucleic acid (and possible other virus parts) into the cell. Viruses and their component parts are constructed preferentially of small identical subunits (principle II of the generalized theory 131). Consequently the possible virus structure states can be derived by starting with one molecule of single-stranded nucleic acid (ssna) with its linear functional symmetry [3]. To this are added other molecules of subunits pi (i is a running sequential index for operationally different subunits. The operational subunit may not be identical with the chemically extracted subunit.) To conform with the general theory the following requirements must be met: (a) the equivalence of the identical subunits in the structure, or their respective structural parts (a single type of identical interaction and environment); (b) a sequential incorporation of different operational subunits and a preferential use of a single type of subunit for each kind of structural part. For the actual assembly this does not rule out cooperative processes like crystallization. Simultaneous cocrystallization of many virus parts would require too high a coincidence to be probable; (c) a common complementary functional symmetry subgroup of structurally connected virus parts (principle III [3]). The restrictions listed above are combined with the minimum biological properties as stated. Therefore, upon the addition of a new and different pi the single-stranded nucleic acid molecule, or a nucleoprotein structure derivable from it, may undergo one of the following processes: (1) a flexible, linear or helical assembly may condense randomly and be surrounded by a protein coat (or coats for multiple sequential biological action); (2) a stiff nucleoprotein conformation may be surrounded by an external protein coat. The nucleoprotein acts as a surface constraint [3]; (3) a consecutive helical coiling; Experimental
Cell Reseurch
36
Virus structure evolution
701
(3’) formation of multiple coaxial layers of helical toilings is valid separately for each layer); (4) crystallization of two or more identical (linear or helical) blies. The present report proceeds only up to the treatment nucleic acid (dsna, a helical two-crystal of two ssna);
(equivalence
of parts
nucleoprotein assemof double-stranded
Fig. I.-The resulting graphic representation of the derivation of virus structures, derivation tree: ssna, single-stranded nucleic acid (RNA or DNA); dsna, double-stranded nucleic acid (RNA or DNA); 1, . . . . 5”, refer to wrapping processes defined in text; same + . . ., same structure as at left (along d-lines) + added parts); pi, the i ” kind of subunits; at!., attachment apparatus; inj., turnip yellow mosaic virus injection apparatus, coaxial to the attachment apparatus; TYMV, (11; TMV, tobacco mosaic virus [5]; VSV, vesicular stomatitis virus [2]; Bm, silk worm virus (81; T-2, T-2 bacteriophage [4]; K, Kilham’s mouse pneumonitis virus 161; Mumps, mumps virus [I]; ---, possible extension of the derivation process; r.c., random coil.
(5) attachment of other, different parts. Due to the minimum biological needs two types of such parts will be considered; (5’) a special apparatus for the attachment of the virus to the cell. This should be necessary only for viruses of high structural polarity, as for example is produced by process 3’. The position of the attachment apparatus is defined by the symmetry of the nucleoprotein arrangement; (5”) a special apparatus for the injection of virus nucleic acid into the cell. This is necessary after step 5’. The rigidity of the nucleoprotein assembly further restricts which of the processes l-5” may be possible. The dimensions of the nucleic acid functional symmetry subunit limit the dimensions of pi that may be connected to the nucleic acids. The possible groupings of structure states can be derived following the procedures as outlined above. These groupings can be ordered into a derivation tree. Fig. 1. The root of the derivation tree is ssna. (The concepts tree and root come from graph theory [7]). Each derivation line in the derivation tree corresponds to a process that is generated by the addition of at least one new pi (the numbers on the derivation lines indicate the process numbers). Each block represents a grouping of structure Experimental
Cell
Research
36
702
R. Kilkson
states that are generated from the structure block at their left. In the blocks are included short descriptions of the structures, and an example virus whenever there are reasonable experimental foundations available. The structures that belong to the same block are generated by similar processes, but the pi and the orders of the symmetry operators need not be identical. A block may represent a grouping of viable structure states only if all the biological properties are satisfied. The complexity of the structures (in terms of principle II [3]) increases as one moves from left to right in the derivation tree. The treatment here points out some further biological consequences of the structure theory. A radical change in the inner zones of the structure diagram, described earlier in [3], disrupts the structure state, with a consecutive loss of the outer zones and their respective biological functions. Therefore, the evolution should be primarily restricted to the outermost zones of the structure diagram. Evolution should follow the derivation tree from left to right. (For a complete analysis the possible alternatives in respect to the host cell have to be included.) Due to limitations on size (principle II [3]), it should not be necessary to follow the derivation tree more than a few steps. Larger structures should be compounded from smaller units corresponding to the beginning of the derivation tree. Flexible bondings introduce a broadening and an increase in the multiplicity of the structure states under the general restrictions of imposed physical constraints. This theory and the corresponding derivation tree have been extended to cover viruses of less rigid symmetries and some ordered cellular structures. A comprehensive account of this work is published separately, that includes detailed discussion of possible virus structure states, their general appearances, symmetries, nucleoprotein arrangements, some specialized biological properties and a number of experimentally observable parameters. This research has been supported by U.S. Public Health Service grant (AI-0339904 BBC) and a special fellowship (l-F3-GM-23, 949-01) for a year (64/65) of research at the Dept. of Medical Physics, Karolinska Institutet. REFERENCES 1. 2. 3. 4. 5. 6. 7. 8.
HORNE,
R. W. and
P., Aduan. Virus Res. 10, 101 (1963) G. F., Virolow 16, 466 (1962). KILKSON, R., Proc. Nat1 Acad. Sci. U.S. 51, 543(1964). KILKSON, R. and MAESTRE, M. F., Nature 195, 494 (1962). KLUG, A. and CASPAR, D. L. D., Aduan. Virus Res. 7, 225 (1960). MATTERN. C. IT. T.. ALLISON, A. C. and ROWE, W. P., Virolow 20, 413 (1963). ORE, O., ‘Graphs c&d their .uses. Random Hcmse, New Yo$ 1963. SMITH, K. M., Aduan. Virus Res. 9, 195 (1962).
HOWATSON,
Experimental
A.
F.
WILDY,
and WHITMORE,
Cell Research
36