The “Wow! signal” of the terrestrial genetic code
Vladimir I. shCherbaka and Maxim A. Makukovb*aDepartment of Mathematics, al-Farabi Kazakh National University, Almaty, Republic of Kazakhstan
e-mail: Vladimir.shCherbak@kaznu.kz
bFesenkov Astrophysical Institute, Almaty, Republic of Kazakhstan
e-mail: makukov@gmail.com, makukov@aphi.kz

ARTICLE INFOABSTR ACTThis is the authors’ version of themanuscript published in Icarus.
Changes resulting from the publishing process may not be reflected in this document. Changes
may have been made to this work
since it was submitted for publication. For the journal version see

It has been repeatedly proposed to expand the scope for SETI, and one of the suggested alternatives to radio is the biological media. Genomic DNA is already used on Earth to store nonbiological information. Though smaller in capacity, but stronger in noise immunity is the genetic
code. The code is a flexible mapping between codons and amino acids, and this flexibility allows
modifying the code artificially. But once fixed, the code might stay unchanged over cosmologicaltimescales; in fact, it is the most durable construct known. Therefore it represents an exceptionally reliable storage for an intelligent signature, if that conforms to biological and thermodynamic
requirements. As the actual scenario for the origin of terrestrial life is far from being settled, theproposal that it might have been seeded intentionally cannot be ruled out. A statistically strong
intelligent-like “signal” in the genetic code is then a testable consequence of such scenario. Here
we show that the terrestrial code displays a thorough precision-type orderliness matching thecriteria to be considered an informational signal. Simple arrangements of the code reveal an ensemble of arithmetical and ideographical patterns of the same symbolic language. Accurate andsystematic, these underlying patterns appear as a product of precision logic and nontrivial computing rather than of stochastic processes (the null hypothesis that they are due to chance coupledwith presumable evolutionary pathways is rejected with P-value < 10–13). The patterns are profound to the extent that the code mapping itself is uniquely deduced from their algebraic representation. The signal displays readily recognizable hallmarks of artificiality, among which are thesymbol of zero, the privileged decimal syntax and semantical symmetries. Besides, extraction of
the signal involves logically straightforward but abstract operations, making the patterns essentially irreducible to any natural origin. Plausible way of embedding the signal into the code andpossible interpretation of its content are discussed. Overall, while the code is nearly optimized
biologically, its limited capacity is used extremely efficiently to store non-biological information.

http://dx.doi.org/10.1016/j.icarus.2013.02.017_________________________
Article history:
Submitted 26 June 2012
Revised 3 October 2012
Revised 31 January 2013
Accepted 12 February 2013____________________
Keywords:
astrobiology
genetic code
directed panspermia
SETI____________________* Corresponding author
For additional information see:https://bioseti.info

putative recipients. Being energy-efficient (Rose & Wright,
2004) and self-replicating, the biological channel is also freefrom problems peculiar to radio signals: there is no need to relyon time of arrival, frequency and direction. Thus, due to theserestrictions the origin of the famous “Wow!” signal received in1977 remains uncertain (Ehman, 2011). The biological channel
has been given serious considerations for its merits in SETI,
though with the focus on genomes (Yokoo & Oshima, 1979;
Freitas, 1983; Nakamura, 1986; Davies, 2010; Davies, 2012).
Meanwhile, it has been proposed to secure terrestrial life byseeding exoplanets with living cells (Mautner, 2000; Tepfer,2008), and that seems to be a matter of time. The biologicalchannel suggests itself in this enterprise. To avoid anthropocentric bias, it might be admitted that terrestrial life is not thestarting point in the series of cosmic colonization (Crick &Orgel, 1973; Crick, 1981). If so, it is natural to expect a statistically strong intelligent-like “signal” in the terrestrial genetic
code (Marx, 1979). Such possibility is incited further by thefact that how the code came to be apparently non-random andnearly optimized still remains disputable and highly speculative (for reviews on traditional models of the code evolution
see Knight et al., 1999; Gusev & Schulze-Makuch, 2004;
Di Giulio, 2005; Koonin & Novozhilov, 2009).
The only way to extract a signal, if any, from the code is toarrange its elements – codons, amino acids and syntactic signs –by their parameters using some straightforward logic. Thesearrangements are then analyzed for patterns or grammar-like

Introduction
Recent biotech achievements make it possible to employ
genomic DNA as data storage more durable than any media
currently used (Bancroft et al., 2001; Yachie et al., 2008;
Ailenberg & Rotstein, 2009). Perhaps the most direct application for that was proposed even before the advent of synthetic
biology. Considering alternative informational channels for SETI,
Marx (1979) noted that genomes of living cells may provide agood instance for that. He also noted that even more durable is
the genetic code. Exposed to strong negative selection, the code
stays unchanged for billions of years, except for rare cases ofminor variations (Knight et al., 2001) and context-dependent
expansions (Yuan et al., 2010). And yet, the mapping between
codons and amino acids is malleable, as they interact via modifiable molecules of tRNAs and aminoacyl-tRNA synthetases(Giegé et al., 1998; Ibba & Söll, 2000; see also Appendix A).
This ability to reassign codons, thought to underlie the evolution of the code to multilevel optimization (Bollenbach et al.,2007), also allows to modify the code artificially (McClain &Foss, 1988; Budisa, 2006; Chin, 2012). It is possible, at least in
principle, to arrange a mapping that both conforms to functional
requirements and harbors a small message or a signature, allowed by 384 bits of informational capacity of the code. Once
genome is appropriately rewritten (Gibson et al., 2010), the newcode with a signature will stay frozen in the cell and its progeny, which might then be delivered through space and time to1

structures of some sort. The choice of arrangements and parameters should exclude arbitrariness. For example, only those parameters should be considered which do not depend on systemsof physical units. However, even in this case a priori it is unknown exactly what kind of patterns one might expect. So there
is a risk of false positives, as with a data set like the genetic code
it is easy to find various patterns of one kind or another.
Nonetheless, the task might be somewhat alleviated. First, it
is possible to predict some general aspects of a putative signal
and its “language”, especially if one takes advantage of active
SETI experience. For example, it is generally accepted that numerical language of arithmetic is the same for the entire universe(Freudenthal, 1960; Minsky, 1985). Besides, symbols andgrammar of this language, such as positional numeral systems
with zero conception, are hallmarks of intelligence. Thus, interstellar messages sent from the Earth usually began with naturalsequence of numbers in binary or decimal notation. To reinforce
the artificiality, a symbol of zero was placed in the abstract position preceding the sequence. Those messages also included symbols of arithmetical operations, Egyptian triangle, DNA and other notions of human consciousness (Sagan et al., 1972; The Staff
at the NAIC, 1975; Sagan et al., 1978; Dumas & Dutil, 2004).
Second, to minimize the risk of false positives one can impose requirements as restrictive as possible on a putative signal.
For example, it is reasonable to expect that a genuinely intelligent message would represent not just a collection of patterns ofvarious sorts, but patterns of the same “linguistic style”. In thiscase, if a potential pattern is noticed, further search might benarrowed down to the same sort of patterns. Another stringent
requirement might be that patterns should involve each elementof the code in each arrangement, whereas the entire signal
should occupy most, if not all, of the code’s informational capacity. By and large, given the nature of the task, specifics of thestrategy are defined en route.
Following these lines, we show that the terrestrial code harbors an ensemble of precision-type patterns matching the requirements mentioned above. Simple systematization of the code
reveals a strong informational signal comprising arithmetical andideographical components. Remarkably, independent patterns of
the signal are all expressed in a common symbolic language. We
show that the signal is statistically significant, employs informational capacity of the code entirely, and is untraceable to natural
origin. The models of emergence of primordial life with original
signal-free genetic code are beyond the scope of this paper;
whatever it was, the earlier state of the code is erased by palimpsest of the signal.

Fig. 1. The genetic code. (a) Traditional representation of the standard, or universal, code. Codons coding the same amino acid form sy nonymic series denoted with opening braces. Number of codons in aseries defines its redundancy (degeneracy). Whole codon families
consist of one series of redundancy IV. Other families are split. Most
split families are halved into two series of redundancy II each, one
ending with pyrimidines {T, C} and another with purines {A, G}.
Three codons in the standard code are not mapped to any amino acidand are used as Stop in translation. The Start is usually signified by
ATG which codes Met. Closing brace shows the only difference between the euplotid and the standard code. (b) Contracted representation of the euplotid version. Synonymous full-size codons are replaced
by a single contracted series with combined third base. FASTA desi gnations are used: R and Y stand for purines and pyrimidines, respe ctively, N stands for all four bases and H stands for {T, C, A}. Series
are placed vertically for further convenience. The pictogram on the left
helps in figures below. Filled elements denote whole families here.

of bases, and these families generally consist of either one or two
equal series of codons mapped to one amino acid or to Stop
(Fig. 1a). In effect, the standard code is nearly symmetric in redundancy. There are only two families split unequally: those
beginning with TG and AT. The minimum action to restore thesymmetry is to match TG-family against AT-family by reassigning TGA from Stop to cysteine. Incidentally, this symmetrized version is not just a theoretical guess but is also found innature as the nuclear code of euplotid ciliates (Meyer et al.,1991). While the standard code stores the arithmetical component of the signal, the symmetrical euplotid version keeps theideographical one (the interrelation between these two code
versions is discussed later). Regular redundancy leads also to
the block structure of the genetic code. This makes it possible todepict the code in a contracted form, where each amino acidcorresponds to a single block, or a contracted series (Fig. 1b).
The three exceptions are Arg, Leu and Ser, which have one IVseries and one II-series each.
Apart from regular redundancy, a wealth of other features
were reported afterwards, among which are robustness to errors(Alff-Steinberger, 1969), correlation between thermostability
and redundancy of codon families (Lagerkvist, 1978), nonrandom distribution of amino acids among codons if judged bytheir polarity and bulkiness (Jungck, 1978), biosynthetic pathways(Taylor & Coates, 1989), reactivity (Siemion & Stefanowicz,
1992), and even taste (Zhuravlev, 2002). The code was also shown
to be effective at handling additional information in DNA(Baisnée et al., 2001; Itzkovitz & Alon, 2007). Apparently, thesefeatures are related, if anything, to the direct biological functionof the code. There are also a number of abstract approaches tothe code, such as those based on topology (Karasev & Stefanov,2001), information science (Alvager et al., 1989), and number
theory (Dragovich, 2012). However, the main focus of theseapproaches is in constructing theoretical model descriptions ofknown features in the code, rather than dealing with new ones.

BackgroundShould there be a signal in the code, it would likely have manifested itself someway during the half-century history of traditional
analysis of the code organization. So it is of use to summarize
briefly what has been learned about that up to date. Also, for thesake of simplicity in data presentation, we will mention in advancesome a posteriori information concerning the signal to be described, with fuller discussion in due course. We suggest to areader unfamiliar with molecular mechanisms behind the genetic
code first to refer to Appendix A, where it is also explained why
the code is amenable to intentional “modulation” (to use the language of radio-oriented SETI) and, at the same time, is highly
protected from casual “modulation” (has strong noise immunity).
The code at a glance. As soon as the genetic code was biochemically cracked (Nirenberg et al., 1965), its non-random structure
became evident (Woese, 1965; Crick, 1968). The most obvious
pattern that emerged in the code was its regular redundancy. The
code comprises 16 codon families beginning with the same pair2All in all, only two intrinsic regularities, observed early on in
the study of the code, might suggest possible relation to a putative signal due to their conspicuous and unambiguous character.
They also suggest two dimensionless integer parameters for signal extraction. These are quantity of codons in a series mapped
to one amino acid (redundancy) and quantity of nucleons in amino acid molecules. These parameters might be called “ostensive
numerals” by analogy with the quantity of radio beeps in Lingua
Cosmica (Freudenthal, 1960).

below, this anticorrelation is a derivative of the signal. Moreover, exactly this observation suggests simple systematization forboth “ostensive numerals”: monotonous arraying of nucleon andredundancy numbers in opposite directions.
On the whole, Hasegawa and Miyata dealt with amino acids
whereas Rumer dealt with codons. Combined, these approaches
yield assignments between codons and amino acid nucleon numbers convenient for systematization. Stop-codons code for no
amino acid; therefore, to include them into the systematization,
they are assigned a zero nucleon number.

Rumer’s bisection. Rumer (1966) bisected the code by redundancy – the first “ostensive numeral”. There are 8 whole families
and 8 split families in the code (Fig. 2a). Rumer found that codons in these families are mapped to each other in a one-to-one
fashion with a simple relation TG, CA, now known as Rumer’s transformation. There are two more transformations ofsuch type: TC, AG and TA, CG. They also appear in
Rumer’s bisection and each makes half of what Rumer’s transformation makes alone.
Arbitrary bisection of the code has small chances to produce
a transformation, and still less – their ordered set (see Appendix
B). Rumer’s finding was rediscovered by Danckwerts & Neubert(1975), who also noted that this set might be described with astructure known in mathematics as the Klein-4 group. That triggered a series of yet other models involving group theory to describe the code (Bertman & Jungck, 1979; Hornos & Hornos,
1993; Bashford et al., 1998), which, admittedly, did not gain
decisive insights. Meanwhile, in traditional theories of the code
evolution this feature was ignored altogether, though it was repeatedly rediscovered again (e.g., see Wilhelm & Nikolajewa,
2004). Noteworthy, this regularity – which turns out to be asmall portion of the signal – was first noticed immediately aftercodon assignments were elucidated. Together with the fact ofrediscoveries, this speaks for the anticryptographic nature of thesignal inside the code.

The activation key. All arithmetical patterns considered further
appear with the differentiation between blocks and chains in all
20 amino acids and with the subsequent transfer of one nucleon
from side chain to block in proline (Fig. 2b). Proline is the only
exception from the general structure of amino acids: it holds its
side chain with two bonds and has one hydrogen less in its
block. The mentioned transfer in proline “standardizes” itsblock nucleon number to 73 + 1 and reduces its chain nucleons
to 42 – 1. In itself, the distinction between blocks and chains ispurely formal: there is no stage in protein synthesis where amino acid side chains are detached from standard blocks. Therefore, there is no any natural reason for nucleon transfer in proline; it can be simulated only in the mind of a recipient toachieve the array of amino acids with uniform structure. Suchnucleon transfer thus appears artificial. However, exactly thisseems to be its destination: it protects the patterns from any
natural explanation. Minimizing the chances for appealing tonatural origin is a distinct concern in messaging of such kind,and this problem seems to be solved perfectly for the signal in
the genetic code. Applied systematically without exceptions,the artificial transfer in proline enables holistic and arithmetically precise order in the code. Thus, it acts as an “activationkey”. While nature deals with the actual proline which does notproduce the signal in the code, an intelligent recipient easily
finds the key and reads messages in arithmetical language (seealso Discussion).

Amino acid nucleons. Hasegawa & Miyata (1980) arranged
amino acids in order of increasing nucleon number – the second“ostensive numeral” which, unlike other amino acid properties,
does not rely on arbitrarily chosen system of units. Such arrangement reveals a rough anticorrelation: the greater the redundancy the smaller the nucleon number (Fig. 2b). This promoted
speculations that prevailing small amino acids occupied the series of higher redundancy during the code evolution. As shown

Decimalism. The arithmetical patterns to be described holdtrue in any numeral system. However, as it turned out, expressed in positional decimal system, they all acquire conspicuously distinctive notation. Therefore, here we briefly provide
some relevant information.

Fig. 2. Preceding observations. (a) Rumer’s bisection. Whole families are opposed to split ones, thereby bisecting the code. Codons in opposedfamilies are mapped to each other with the ordered set of Rumer’s transformation and two half -transformations. Transformation of third bases istrivial as they are the same in any family; therefore contracted representation is adequate to show this regularity. The regularity is valid both forthe standard and the euplotid (shown here) version. (b) Categorization of amino acids by nucleon numbers. Free molecules unmodified by cyt oplasmic environment are shown. Each of them is formed of the standard block and a side c hain. Blocks are identical in all amino acids except
proline. Chains are unique for each amino acid. Numbers of nucleons, i.e. protons and neutrons, are shown for both blocks and chains. To avoid
ambiguity, it is judicious to consider only most common and stable isotopes: 1H, 12C, 14N, 16O, 32S. The bar at the bottom shows the redundancy ofamino acids in the code. Cross-cut bonds symbolize the distinction between standard blocks and unique side chains of amino acids. The arrow inproline denotes hereafter the “activation key” (see text).

3

no unique order in presenting them. We will begin with arithmetical component and then move on to ideography.
The arithmetical component
Full-size standard code. One logically plain arrangement of thecode was proposed by George Gamow in his attempt to guessthe coding assignments theoretically before the code wascracked in vitro (see Hayes, 1998). One of his models, though it
did not predict the actual mapping correctly, coincided remarkably with one of the signal components. Gamow arranged codons
according to their composition, since 20 combinations of fourbases taken three at a time could account for 20 amino acids(Gamow & Yčas, 1955). Bringing nucleon numbers, activation
key and few “freezing” conditions into this arrangement reveals
total nucleon balancing ornate with decimal syntax.
Codons with identical and unique bases comprise two smaller sets (Fig. 5a). Halved, both sets show the balance of side
chains with 703 = 037×019 nucleons in each half as well as thebalance of whole molecules with 1665 = 666 + 999×1 nucleons.
Importantly, the halving is not arbitrary. Codons are opposed by
Rumer’s transformation along with the half-transformation
TC, AG in the first set and TA, CG in the second set.

Fig. 3. Digital symmetry of decimals divisible by 037. Leading zeroemphasizes its equal participation in the symmetry. All three-digit
decimals with identical digits 111, …, 999 are divisible by 037. The
sum of three identical digits gives the quotient of the number divided
by 037. Analogous sum for numbers with unique digits gives the central quotient in the column. Digits in these numbers are interconnectedwith cyclic permutations that are mirror symmetrical in neighb or columns. Addition instead of division provides an efficient way to perform checksums (see Appendix C). The scheme extends to decimals
with more than three digits, if they are represented as a + 999×n,
where n is the quotient of the number divided by 999 and a is theremainder, to which the same symmetry then applies (for three-digit
decimals n = 0). Numbers divisible by 037 and larger than 999 will beshown in this way.

Nature is indifferent to numerical languages contrived by intelligence to represent quantities, including zero. A privileged
numeral system is therefore a reliable sign of artificiality. Intentionally embedded in an object, a privileged system mightthen demonstrate itself through distinctive notation to any
recipient dealing with enumerable elements of that object. For
example, digital symmetries of numbers divisible by prime
037 exist only in the positional decimal system with zero conception (Fig. 3). Thus, distinctive decimals 111, 222 and 333
look ordinarily 157, 336 and 515 in the octal system. This
notational feature was marked by Pacioli (1508) soon after thedecimal system came to Europe. Analogous three-digit featureexists in some other systems, including the quaternary one(see Appendix C).

Results
The overall structure of the signal is shown in Fig. 4, whichmight be used as guidance in further description. The signal iscomposed of arithmetical and ideographical patterns, wherearithmetical units are represented by amino acid nucleons,
whereas codon bases serve as ideographical entities. The patterns of the signal are displayed in distinct logical arrangements of the code, thereby increasing both the informational
content of the signal and its statistical significance. Remarkably, all of the patterns bare the same general style reflected inFig. 4 with identical symbols in each signal component (represented by boxes). Namely, distinct logical arrangements of thecode and activation key produce exact equalities of nucleon
sums, which furthermore display decimalism and are accompanied by Rumer’s and/or half-transformations. One of thesearrangements furthermore leads to ideography and semanticalsymmetries. All elements of the code – 64 codons, 20 aminoacids, Start and Stop syntactic signs – are involved in eacharrangement.
Unlike radio signals which unfold in time and thus have sequential structure, the signal in the genetic code has no entry
point, similar to the pictorial message of Pioneer plaques(Sagan et al., 1972). However, instead of providing pictograms
the signal in the genetic code provides patterns that do not depend on visual symbols chosen to represent them (be it symbols for nucleotide bases or for the notation of “ostensive numerals”). These patterns make up the organic whole, so there isFig. 4. The structure of the signal. All details are discussed sequentially in the text. The image of scales represents precise nucleon equalities.
DEC stands for distinctive decimal notation of nucleon sums. The dotted box denotes the cytoplasmic balance (see Appendix D), the only
pattern maintained by actual proline and cellular milieu. All other patterns are enabled by the “activation key” and are valid for free aminoacids. K stands for {T, G}, M stands for {A, C}. Though all three typesof transformations act in the patterns, only Rumer’s transformation isindicated for simplicity.

4tical bases type. Though not balanced, these halves again show
distinctive decimal syntax with 888 and 1110 = 111 + 999×1
nucleons. Decimalism of one of these sums is algebraically dependent, as from the previous case (Fig. 5b) the sum of thewhole set is known to be divisible by 037; if a part of this set isdecimally distinctive, the other one will be such automatically.
Notably, an independent pattern nonetheless stands out here.
Namely, a part of the previous threefold balance has an equivalent in one half here, where the same amino acids are represented
by synonymous codons (Fig. 5b and c). Whole molecules of thisequivalent – 333 side chain and 444 standard block nucleons –are balanced with 777 chain nucleons in the rest of the subset.
Note that all those distinctive notations of nucleon sums
appear only in positional decimal system. Positional notation isso customary in our culture that most of its users hardly remember a fairly complex rule behind it that encodes numbers
as an–1×qn–1 + … + a1×q1 + a0×q0, where q = 10 in case of thedecimal system, n is the quantity of digits in notation, and ai –digits 0-9 that are left in the final notation.
Decomposed standard code. Another arrangement of the code isbrought about by decomposition of its 64 full-size codons. This
yields 192 separate bases and reveals a pattern of the same type
as in full-size format. Identical bases make up four sets of 48
bases in each. Each base retains the amino acid or Stop of its
original codon (Fig. 6a). Thus, the four sets get their individual
chain and block nucleon sums.
In total, there are 222 + 999×10 side chain nucleons in thedecomposed code – obviously, thrice as much as the total sum inthe previous full-size case (with the activation key still applied).
Only one combination of the four sets displays distinctive decimalism of side chain nucleon sums. These are 666 + 999×2 nucleons in the T-set and 555 + 999×7 nucleons in the joint CGAset (Fig. 6b). Meanwhile, there are exactly 222 + 999×10 block
nucleons in the CGA-set (note that the sets have unequal blocksums due to different accumulation of Stops). Thus, while chain
nucleons are outnumbered by block nucleons overall the code,
they are neatly balanced with their CGA-part.
Fig. 5. Gamow’s sorting of codons according to their nucleotide basecomposition. Base combinations (shown on triangular frames) produce three sets: 4 codons with three identical bases, 24 codons withunique bases and 36 codons with two identical bases. (a) The first
and the second sets halved by vertical axis with Rumer’s and halftransformations along with Spin  Antispin transformation denotedwith circular arrows. Applied to triangular frames, these arrows define the sequence of bases in codons. Note that while any block sum(with the activation key applied) is divisible by 037 as each block has
74 = 2×037 nucleons, chain sums are not restricted in this way.
(b) The third set halved according to whether identical bases are
purines or pyrimidines. (c) The third set halved with horizontal axis
according to whether unique bases are purines or pyrimidines.

Contracted code and the systematization rule. In a sense, contraction of codon series (see Fig. 1b) is an operation logically
opposite to decomposition. Besides displaying new arithmetical
patterns, contracted code also reveals ideographical component

The Spin  Antispin transformation does not affect the first set
but finally freezes elements of the second one. There is only one
degree of freedom left since there are no reversible transformations that might connect both sets, so one of them is free toswap around the axis. The balance appears in one of the twoalternative states.
The third set includes codons with two identical bases. When
halved according to whether they are purines or pyrimidines,
regardless of the unique base type, this set shows the balance
999 = 999 of side chains (Fig. 5b). Besides, such halving keeps
Rumer’s and one of the half-transformations again in place. In
its turn, the right half of the set is threefold balanced. Codons
with adenine side by side, guanine side by side and palindromiccodons make up three equal parts with 333 nucleons each.
In Fig. 5c the same set is halved according to whether uniquebases are purines or pyrimidines, this time regardless of the iden-

Fig. 6. The decomposed standard code. (a) Decomposition shown for one
family of codons. Three T-bases contribute three Cys molecules into Tset; one A-base contributes one Stop to A-set and so on for the entire
code. (b) Identical bases are sorted into four sets regardless of their position in codons. The sets are shown twice for convenience.

5

Fig. 7. The contracted euplotid code with the systematiza tion rule applied (compare with Fig. 2). (a) The resulting arrangement of contracted
codon series forming the ideogram. Side-by-side alignment of vertical series produces three horizontal strings of peer -positioned bases. Gln andLys have the same nucleon number; ambiguity in their positioning is eliminated by the symmetries considered further. ( b) The arithmeticalbackground of the ideogram (valid for the standard version as well, as it contributes another zero to the III, II, I set). For  and  side chain
levels see Discussion.

of the signal. The systematization rule leading to the ideography
combines findings of Rumer (1966) and of Hasegawa & Miyata(1980) and is symmetric in its nature (shCherbak, 1993). Contracted series are sorted into four sets according to their redundancy; within those sets they are aligned side-by-side in order ofmonotonously changing (e.g., increasing) nucleon number. The
sets themselves are then arranged in antisymmetrical fashion(e.g., in order of decreasing redundancy number). Stop-series isplaced at the beginning of its set representing zero in its special
position. Finally, Rumer’s bisection opposes the IV-set to III, II,
I sets. The resulting arrangement is shown in Fig. 7 for the euplotid code, with ideography of codon bases (see next section) in
Fig. 7a and arithmetical patterns of amino acids (shared by bothcode versions) in Fig. 7b.
A new balance is found in the joint III, II, I set. Side chain
nucleons of all its amino acids are equalized with their standard
blocks: 111 + 999×1 = 111 + 999×1 (Fig. 7b). This pattern manifests as the anticorrelation mentioned by Hasegawa & Miyata(1980). Chain nucleon sum of all series in the code is less than
the sum of all blocks. Only a subset of series coding mainly bigger amino acids may equalize its own blocks. Exactly this happens in the joint III, II, I set. As a consequence, smaller aminoacids are left in the set of redundancy IV.
Meanwhile, there are 333 chain and 592 block nucleons and333 + 592 = 925 nucleons of whole molecules in the IV-set.
With 037 cancelled out, this leads to 32 + 42 = 52 – numericalrepresentation of the Egyptian triangle, possibly as a symbol of
two-dimensional space. Incidentally, codon series in the ideogram (Fig. 7a) are arranged in the plane rather than linearly in agenomic fashion.
Rumer’s bisection is based on redundancy and thus makes useof third positions in codon series. Divisions of the contracted code
based on first and center positions also reveal similar patterns(Fig. 8). Another arithmetical phenomenon presumably related tothe signal – the cytoplasmic balance – is described in Appendix D.
Thus, the standard code reveals same-style and yet algebraically independent patterns simultaneously in decomposed, fullsize, and contracted representations (see Fig. 4). It is a highly
nontrivial algebraic task to find the solution that maps aminoacids and syntactic signs to codons in a similar fashion. Normally this would require considerable computational power.

Fig. 8. Additional arithmetical patterns of the contracted code(shared by both code versions). (a) The code is divided according
to whether first bases are purines or pyrimidines. This gives two
sets with equal numbers of series. The halve with pyrimidines infirst positions reveals a new balance of chains and blocks anal ogous to that in Fig. 7b. Another halve is algebraically dependent
except the decimal sum of its β, δ, ζ levels, see Discussion.
(b) The code is divided according to whether first bases are K or
M (left) or whether central bases are K or M (center). Both divisions produce halves with identical chain nucleon sums. As alg ebraic consequence of these divisions, series with K in first andcentral positions and series with M in first and central positions
are chain-balanced (right). Each of the three divisions is accomp anied by half-transformations and, remarkably, also produces equal
numbers of series in each half. This pattern is the only one thatshows no divisibility by 037. However, all three numbers – 654,
789 and 369 – are again specific in decimal notation where digits
in each of them appear as arithmetic progressions.

6

frame displays the semantical mirror symmetry of antonyms
with homogeneous AAA-codon in the center.
The codons of this reading frame are purely abstract symbols, given that they are read across contracted series. However, they are regularly crossed with the same codons in the ideogram, thereby reinforcing the semantical symmetry and making the current frame unique (Fig 10c). Besides, direction ofreading now becomes distinguished since such “crossword”
disappears if read in opposite way, though the palindrome
itself remains the same.
Remarkably, the triplet string in Fig. 10c is written with thecode symbols within the code itself. This implies that the signalharboring mapping had to be projected preliminarily (see Discussion). Besides, translation of this string with the code itself
reveals the balance 222 = 222 of chains and blocks (Fig. 10d).
Additional palindrome in the frame shifted by one position(Fig. 10e) reproduces the chain sum of 222, confirming that theideogram is properly “tuned in” to the euplotid version: TGA
stands for Cys here, not for Stop of the standard code.

Discussion
Artificiality. To be considered unambiguously as an intelligent
signal, any patterns in the code must satisfy the following two
criteria: (1) they must be highly significant statistically and (2) not
only must they possess intelligent-like features (Elliott, 2010), butthey should be inconsistent in principle with any natural process,be it Darwinian (Freeland, 2002) or Lamarckian (Vetsigian
et al., 2006) evolution, driven by amino acid biosynthesis(Wong, 2005), genomic changes (Sella & Ardell, 2006), affinities between (anti)codons and amino acids (Yarus et al.,2009), selection for the increased diversity of proteins (Higgs,

Fig. 9. Patterns of the short (a) and the long (b) upper strings. The
strings are arranged with the same set of symmetries: mirror symmetry(denoted with the central vertical axis), translation symmetry (denotedwith italicized letters and skewed frames) and purine  pyrimidine
inversion (denoted with color gradient, where black and white stand for
pyrimidines and purines, respectively). The image of DNA at the top
illustrates possible interpretation of the short string (see Discussion).

The ideographical component
Upper strings. We refer to the product of systematization in
Fig. 7a as the ideogram. The ideogram of the genetic code isbased on symmetries of its strings (shCherbak, 1988). The
strings are read across contracted series.
The upper short string demonstrates mirror, translation andinversion symmetries (Fig. 9a). Its bases are invariant under
combined operation of the mirror symmetry and inversion of thetype base  complementary base. A minimum pattern of thetranslation symmetry is represented by RRYY quadruplet.
The same three symmetries arrange the long upper string(Fig. 9b). The pair of flanking TATAT sequences is mirror
symmetrical. The pair of central AGC codons forms a minimum
pattern of the translation symmetry. First and third bases in theset of redundancy II are interconnected in an axisymmetric manner with purine  pyrimidine inversion and its opposite operation – the unit transformation producing no exchange.
Center strings. Placed coaxially, the short and the long center
strings appear interconnected with purine  pyrimidine inversion (Fig. 10a). Both strings exhibit purine-pyrimidine mirror
symmetry. The long string keeps the mirror symmetry even forordinary bases.
Codons of the short string CCC and TCT break the mirror
symmetry of ordinary bases, but they share a palindromic feature, i.e. direction of reading invariance. This feature restores themirror symmetry, this time of the semantical type (Fig. 10b). As
in the previous case, two center strings are expected to share thesame set of symmetries. Therefore, the semantical symmetry of
palindromic codons flanked by G-bases may indicate a similarfeature in the long string. Indeed, semantical symmetry is foundthere in the triplet reading frame starting after flanking G-base(Fig. 10c). This reading frame is remarkable with the regulararrangement of all syntactic signs of the euplotid code – both
Stop-codons and the Start-codon repeated twice. The reading

Fig. 10. Patterns of the short (a, b) and the long (a, c, d, e) center
strings. Both strings are arranged with purine-pyrimidine mirror symmetry, purine  pyrimidine inversion and semantical symmetry. The
first two are denoted in the same way as in Fig. 9,  denotes palindrome.

72009), energetics of codon-anticodon interactions (Klump,
2006; Travers, 2006), or various pre-translational mechanisms(Wolf & Koonin, 2007; Rodin et al., 2011).
The statistical test for the first criterion is outlined in Appendix B, showing that the described patterns are highly significant.
The second criterion might seem unverifiable, as the patterns
may result from a natural process currently unknown. But thiscriterion is equivalent to asking if it is possible at all to embed
informational patterns into the code so that they could be unequivocally interpreted as an intelligent signature. The answer
seems to be yes, and one way to do so is to make patterns virtual,
not actual. Exactly that is observed in the genetic code. Strictbalances and their decimal syntax appear only with the application of the “activation key”. Physically, there are no strict balances in the code (e.g., in Fig. 5b one would have 1002 ≠ 999
instead of 999 = 999). Artificial transfer of a nucleon in proline
turns the arithmetical patterns on and thereby makes them virtual. This is also the reason why we interpret distinctive notation
as an indication of decimalism, rather than as a physical requirement (yet unknown) for nucleon sums to be multiples of037: in general, physically there is no such multiplicity in thecode. In its turn, notationally preferred numeral system is byitself a strong sign of artificiality. It is also worth noting that all
three-digit decimals – 111, 222, 333, 444, 555, 666, 777, 888,
999 (as well as zero, see below) – are represented at least once inthe signal, which also looks like an intentional feature.
However, it might be hypothesized that amino acid mass isdriven by selection (or any other natural process) to be distributed in the code in a particular way leading to approximate massequalities and thus making strict nucleon balances just a likely
epiphenomenon. But it is hardly imaginable how a natural process can drive mass distribution in abstract representations of thecode where codons are decomposed into bases or contracted byredundancy. Besides, nucleon equalities hold true for free aminoacids, and yet in these free molecules side chains and standard
blocks had to be treated by that process separately. Furthermore,no natural process can drive mass distribution to produce thebalance in Fig. 10d: amino acids and syntactic signs that makeup this balance are entirely abstract since they are produced bytranslation of a string read across codons.
Another way to make patterns irreducible to natural events is
to involve semantics, since no natural process is capable of interpreting abstract symbols. It should be noted that notions ofsymbols and meanings are used sometimes in a natural sense(Eigen & Winkler, 1983), especially in the context of biosemiotics (Barbieri, 2008) and molecular codes (Tlusty, 2010). The
genetic code itself is regarded there as a “natural convention”
that relates symbols (codons) to their meanings (amino acids).
However, these approaches make distinction between organic
semantics of molecular codes and interpretive or linguistic semantics peculiar to intelligence (Barbieri, 2008). Exactly thelatter type of semantics is revealed in the signal of the genetic
code. It is displayed there not only in the symmetry of antonymous syntactic signs (Fig. 10c), but also in the symbol of zero.
For genetic molecular machinery there is no zero, there are nucleotide triplets recognized sterically by release factors at theribosome. Zero – the supreme abstraction of arithmetic – is theinterpretive meaning assigned to Stop-codons, and its correctness
is confirmed by the fact that, being placed in its proper front
position, zero maintains all ideogram symmetries. Thus, a trivial
summand in balances, zero, however, appears as an ordinal
number in the ideogram. In other words, besides being an integral part of the decimal system, zero acts also as an individual
symbol in the code.
In total, not only the signal itself reveals intelligent-like features – strict nucleon equalities, their distinctive decimal nota-

tion, logical transformations accompanying the equalities, thesymbol of zero and semantical symmetries, but the very methodof its extraction involves abstract operations – consideration ofidealized (free and unmodified) molecules, distinction between
their blocks and chains, the activation key, contraction and decomposition of codons. We find that taken together all these
aspects point at artificial nature of the patterns.
Though the decimal system in the signal might seem a serendipitous coincidence, there are few possible explanations,from 10-digit anatomy as an evolutionary near-optimum forbilateral beings (Dennett, 1996) to the fact that there are conveniently 74 = 2×037 nucleons in the standard blocks of αamino acids. Besides, the decimal system shares the triplet digital symmetry with the quaternary one (see Appendix C), establishing a link to the “native” language of DNA. After all, someof the messages sent from the Earth included the decimal system as well (Sagan et al., 1978; Dumas & Dutil, 2004), though
they were not supposed to be received necessarily by 10-digit
extraterrestrials. Whatever the actual reason behind the decimal
system in the code, it appears that it was invented outside theSolar System already several billions years ago.
Two versions of the code. The nearly symmetric code version
with arithmetical patterns acts as the universal standard code.
With this code at hand it is intuitively easy to infer the symmetric version with its ideography. Vice versa, if the symmetricversion were the universal one, it would be hardly possible toinfer the nearly symmetric code with all its arithmetical patterns.
Therefore, with the standard version alone it is possible to “receive” both arithmetical and ideographical components of thesignal, even if the symmetric version was not found in nature.
There are two possible reasons why it is actually found in euplotid ciliates: either originally when Earth was seeded there
were both versions of the code with one of them remaining currently in euplotid ciliates, or originally there was only the standard version, and later casual modification in euplotid lineage
coincided with the symmetric version.
What concerns other known rare versions of the code, they
seem neither to have profound pattern ensembles, nor to be easily
inferable from the standard code. As commonly accepted, they
represent later casual deviations of the standard code caused by
ambiguous intermediates or codon captures (Moura et al., 2010).
Embedding the signal. To obtain a code with a signature one
might search through all variant mappings and select the “mostinteresting” one. However, this method is unpractical (at least
with the present-day terrestrial computing facilities), given theastronomically huge number of variant codes. In a more realistic
alternative, the pattern ensemble of the signal is projected preliminarily as a system of algebraic expressions which is thensolved relatively easily to deduce the mapping of the code. Thus,
all described patterns might be represented post factum as a system of Diophantine expressions (i.e. equations and inequalities
allowing only integer solutions), and analysis of this systemshows that it uniquely determines the mapping between codon
series and nucleon numbers, including zeros for Stop-codons(see Appendix E). Though some amino acids have equal nucleon
numbers, as the case for Leu and Ile, or Lys and Gln, even they
are not interchangeable, as suggested by distinctive notation of
nucleon sums in ,  and other positional levels of side chains in
the contracted code (Figs. 7b and 8a). The activation key applies
here as well (note that - and -carbons in proline are positionally equivalent). The standard chemical nomenclature of carbon
atoms is extended here to denote positions of other nodal atoms.
Decimalism in different combinations of levels circumvents
algebraic dependence and employs chemical structure of aminoacids more efficiently.

8

These patterns within side chains go even deeper into chemical structure. Some of the canonical amino acids – His, Arg and
Trp – might exist in alternative neutral tautomeric forms differing in the position of one hydrogen atom in their side chains(Taniguchi & Hino, 1981; Rak et al., 2001; Li & Hong, 2011).
Though some of these tautomers occur very rarely at cytoplasmic pH (as the case for indolenine tautomer of Trp shown in Fig.
7b), all neutral tautomers are legitimate if idealized free molecules are considered, and taking only one of them would introduce arbitrariness. Notably, however, that while one Trp tautomer maintains the patterns in Fig. 7b, another one does the job in
Fig. 8a, whereas any neutral tautomer of His and Arg might betaken in both cases without affecting the patterns at all (which iseasily checked; to this end, both Arg tautomers are shown in Fig.
8a and both His tautomers are shown in Figs. 7b and 8a).
Importantly, preliminary projecting of a signal admits imposition of functional requirements as extra formal conditions. The
terrestrial code is known to be conservative with respect to polar
requirement (Freeland & Hurst, 1998), but not to molecular size
(Haig & Hurst, 1991). The signal in the code does not involve
polar requirement as such, so it might be used in a parallel formal condition to reduce effect of misreadings. However, thesignal does involve nucleon numbers which correlate with molecular volume. That interferes with an attempt to make the code
conservative with respect to size of amino acids as well.

becomes the symbol of duplex DNA located between genes.
Should this particular numbering have relation to the genomic
message, if any, is a matter of further research.
It is worth mentioning that all genomes, despite their huge
size and diversity, do possess a feature as universal as the genetic code itself. It is known as the second Chargaff’s rule. In almost all genomes – from viral to human – the quantities of complementary nucleotides, dinucleotides and higher oligonucleotides up to the length of ~9 are balanced to a good precision
within a single DNA strand (Okamura et al., 2007). Unlike thefirst Chargaff’s rule which quickly found its physicochemicalbasis, the second rule with its total orderliness still has no obvious explanation.
___________________________________________
Appendix A. Molecular implementation of the genetic code
Here we outline molecular workings behind the genetic code
which explain why it stays unchanged for billions of years and,at the same time, might be readily modified artificially, e.g., forembedding a signal. For simplicity, we skip the details such as U
instead of T in RNA, ATP energetics, wobble pairing, etc., that
do not affect understanding of the main point (for details see,e.g., Alberts et al., 2008).
The first type of molecules behind the genetic code is transfer RNAs (tRNAs). They deliver amino acids into ribosomes,
where protein synthesis takes place. tRNAs are transcribed as
final products from tRNA genes in genomes by RNA polymerase (Fig. A1a; for definiteness, the mechanism is shown for amino acid Ser and its TCC codon). With the length varying around80 nucleotides, tRNA transcripts fold in a specific spatial configuration due to base-pairing between different sections of thesame RNA strand, similar to as it occurs between two strands of
DNA helix (Fig. A1b). At its opposite sides the folded tRNA
molecule has an unpaired anticodon and the acceptor end towhich amino acid is to be bound. tRNAs with differing anticodons specifying the same amino acid (remember the code is redundant) are identical in their overall configuration. tRNAs specifying distinct amino acids differ from each other in anticodons aswell as other spots, so they have slightly different overall configurations. However, acceptor ends are identical in all tRNAs, so
for tRNA itself it makes no difference which amino acid is boundto it, no matter which anticodon it has at the opposite side. The
process of binding amino acids to tRNAs is performed by protein
enzymes called aminoacyl-tRNA synthetases (aaRSs, Fig A1b,bottom). Normally, there are 20 types of aaRSs, one for eachamino acid, and they themselves are translated from appropriate
genes in genome. Each of these enzymes recognizes with great
specificity both its cognate amino acid and all tRNAs specifyingthat amino acid; tRNAs are recognized primarily by their overall
configuration, not exclusively by their anticodons (Fig. A1c).
After binding and additional checking, aaRS releases tRNAcharged with amino acid to be delivered to ribosome (Fig. A1d).
In its turn, the ribosome does not care if tRNA carries an aminoacid specified by its anticodon; it only checks if the anticodon oftRNA matches complementarily the current codon in messenger
RNA (mRNA; Fig. A1e). If so, the amino acid is transferredfrom tRNA to the growing peptide chain and tRNA is released tobe recycled. If codon and anticodon do not match, tRNA with its
amino acid is dislodged from the ribosome to be used later until
it matches codon on mRNA (even with this overshoot the bacterial ribosome manages to add ~20 amino acids per second to a
peptide chain). The described mechanism results in relationships
between mRNA codons and amino acids (Fig. A1f) which, collected together in any convenient form (one possibility is shownin Fig. 1a), constitute the genetic code.

Possible interpretation. Besides having the function of an intelligent signature as such, the signal in the genetic code might also
admit sensible interpretations of its content. Without claim to becorrect, here we propose our own version. It is now tempting tothink that the main body of the message might reside in genomes(Marx, 1979; see also Hoch & Losick, 1997). Though the idea ofgenomic SETI (Davies, 2010) might seem naïve in view of random mutations, things are not so obvious. For example, a locus
with a message might be exposed to purifying selection throughcoupling to essential genes, and there is even possible evidence
for that (ibid.). Whatever the case, the ideogram does seem toprovide a reference to genomes. Thus, complementary mirrorsymmetrical bases of the short upper string (Fig. 9a) resemble
Watson-Crick pairs; the four central bases TC|GA and the central axis therefore possibly represent the symbol of the genomic
DNA itself. Flanking TATAT bases (Fig. 9b) might symbolize
consensus sequence found in promoters of most genes. Coding
sequences of genes are located between Start- and Stop-codons.
Vice versa, nontranslated regions are found between Stop- andStart-codons of neighbor genes. Therefore the triplet string in
Fig. 10c might symbolize intergenic regions, and may be interpreted as the address of the genomic message.
The privileged numeral system in the code might also be interpreted as an indication of a similar feature in genomes. It is
often said that genomes store hereditary information in quaternary digital format. There are 24 possible numberings of DNA
nucleotides with digits 0, 1, 2, 3. The ideogram seems to suggest
the proper one: T  0, C  1, G  2, A  3. In this case the
TCGA quadruplet (Fig. 9a), read in the distinguished direction,
represents the natural sequence preceded by zero. Palindromiccodons CCC and TCT (Fig. 10b) become a symbol of the quaternary digital symmetry 1114 and the radix of the corresponding
system 0104 = 4, respectively. Translationally related AGC, or
3214, codons (Fig. 9b) possibly indicate positions in quaternary
place-value notation, with higher orders coming first. The sumof digital triplets in the string TAG + TAA + AAA + ATG +ATG (Fig. 10c) equals to the number of nucleotides in the code
30004 = 192. Besides, T as zero is opposed to the other three“digits” in the decomposed code (Fig. 6). Finally, each complementary base pair in DNA sums to 3, so the double helix looks
numerically as 333…4, and the central AAA codon in Fig. 10c9Fig. A1. Molecular mechanisms of the genetic code (shown for the case of amino acid serine) and a simple example of its artificial modification. The
contour arrows indicate directionality of DNA and RNA strands as defined by orientation of their subunits (designated in biochemistry as 5′→3′ orientation; replication, transcription and translation occur only in that direction). (a) tRNASer gene (the gene of tRNA that specifies Ser in the standardcode) is transcribed by RNA polymerase from genomic DNA. (b) The folded tRNASer molecule (top), serine molecule (middle) and seryl-tRNA synthetase (SARS, an aaRS cognate for amino acid serine; bottom). (c) SARS recognizes both serine and tRNASer and binds them together. (d) SertRNASer released from SARS and ready to be delivered to ribosome. (e) The process of peptide synthesis at the ribosome (as an example, the mRNA
with the gene fragment of the SARS itself is shown). (f) The resulting fragment of the genetic code (also shown is Ala group, which will be used in
an example below). (g)-(k). A simple way of genetic code modification. The shaded sequence in (j) corresponds to the region shown in (e).

The key point in terms of changeability of the genetic code isthat there is no direct chemical interaction between mRNA codons and amino acids at any stage. They interact via moleculesof tRNA and aaRS both of which might be modified so that acodon is reassigned to another amino acid. As an example, Figures A1g-k show a simple way of changing the code where twoamino acids – Ser and Ala – interchange two of their codons. It
is known that in most organisms tRNA anticodons are not involved in recognition by aaRSs cognate for these amino acids(Giegé et al., 1998; the fact reflected in Fig. A1c with SARS not
touching the anticodon). Therefore, the three nucleotides intRNASer gene corresponding to anticodon might be replaced(Fig. A1g), in particular, to get GGC anticodon corresponding
to GCC codon in mRNA, which normally codes Ala. (To get
anticodon for a codon, or vice versa, one has to apply complementarity rule and reverse the resulting triplet, since complementary DNA/RNA strands have opposite directionalities).
After that, SARS will still bind Ser to tRNASer, even though it
now has new GGC anticodon (Fig. A1h). If analogous procedure is performed with tRNAAla genes to produce tRNAAla with
GGA anticodon, the genetic code would be modified: Ser and
Ala would have interchanged some of their codons (actually,
two codons, due to wobble pairing). However, the cell will notsurvive such surgery, since all coding genes in genome remain“written” with the previous code and after translation with the
new code they all produce non- or at best semi-functional proteins, with Ala occasionally replaced by Ser and vice versa. To
fix the new code in a cell lineage, one also has to change coding
mRNAs appropriately to leave amino acid sequences of coded
proteins unaltered (Fig. A1i). That would be automatically fulfilled if all coding genes are rewritten all over the genome sothat TCC codons are replaced with GCC and vice versa (Fig.
A1j); such operation is possible when genomes are even rewritten from scratch (Gibson et al., 2010). Now, amino acid sequences of proteins stay unaltered and a cell proliferates with
the new genetic code (Fig. A1k).
It must be clear now why the genetic code is highly protectedfrom casual modifications. If a mutation occurs in tRNA or aaRS
leading to codon reassignment, all genes in genome remain written with the previous code, and a cell quickly goes off the scene
without progeny. The chances that such mutation in tRNA/aaRS
is accompanied by corresponding mutations in coding genes allover the genome resulting in unaltered proteins are vanishingly
small, given that there are dozens of such codons in thousands ofgenes in a genome. Thus, the machinery of the genetic code experiences exceptionally strong purifying selection that keeps it
unchanged over billions of years.
It should be reminded that in reality the process of intentional
modification of the code is more complicated. For example, details
of tRNA recognition by aaRSs vary depending on tRNA species
and organism, and in some cases anticodon is involved, partiallyor entirely, in that process. However, this is avoidable, in principle, with appropriate methods of molecular engineering. Anotherissue is that modifications in the code that leave proteins unalteredstill might affect the level of gene expression (Kudla et al., 2009).
Therefore, additional measures might have to be taken to restore
the expression pattern with the new genetic code. These are surmountable technical issues; the point is that there are no principal
restrictions for changing the code artificially in any desired way.
In effect, elaborate methods of modifying the overall tRNA configuration and/or aaRS recognition sites might allow not only interchanging two amino acids, but introducing new ones.

10

The random variable in question is the number of independent patterns of the same sort in a code. Obviously, the more such
patterns are observed in a code, the less likely such observation
is. Probably, a good approximation here would be a binomial
distribution since, for example, a nucleon balance might be regarded as a Bernoulli trial: in a given arrangement the balance iseither “on” or “off”, where probability for “on” is much smaller
than for “off”. However, probabilities for balances in distinct
arrangements might differ, especially under conditions imposed.
Situation is even more complex with ideogram symmetries:
symmetry is not just “on” or “off”, it is also characterized by thelength of a string and the number of nucleotide types involved.
Therefore, we do not apply any approximations but use bruteforce approach to find distributions for appropriately definedscores for the patterns. Proline was considered with one nucleon
transferred from its side chain to its block (note that since theactivation key is applied universally, the actual code and thecode with the key applied are equivalent statistically).

Appendix B. Statistical test
It is appropriate to ask if the presented patterns are merely an
artifact of data fishing. To assess that, one might compare information volumes of the data set itself (V0) and of the pattern ensemble within that set (Vp). The artifact of data fishing mightthen be defined as the case when Vp << V0. As shown in Appendix E, the presented ensemble of patterns might be describedwith a system of Diophantine equations, where nucleon numbersof amino acids serve as unknowns. Given the set of canonicalamino acids (the range of possible values for the unknowns), thissystem is completely defined: it has a single solution and thatturns out to be the actual mapping of the code (this also implies
that there are no more algebraically independent patterns of thesame sort in the code). Hence, Vp = V0, so the pattern ensemble
employs informational capacity of the code entirely, showingthat it represents a feature inherent to the code itself, rather thanan artifact of data fishing.
One might ask then how likely such pattern ensemble is toappear in the genetic code by chance. Since this question implies
that the current mapping of the code has been shaped by naturalprocesses, it is more appropriate to ask how likely such patternensemble is to appear by chance under certain conditions reflecting presumable evolutionary pathways. We tested both versionsof the null hypothesis (“the patterns are due to chance alone” and“the patterns are due to chance coupled with presumable evolutionary pathways”). The results are of the same order of magnitude; we describe only the version with presumable evolutionary
pathways. Three such pathways reflecting predominant speculations on the code evolution were imposed on computergenerated codes in this test:(1) Redundancy must be on average similar to that of the realcode. This is thought to be due to the specifics of interaction
between the ribosome, mRNA and tRNA (Novozhilov et al.,2007). Besides, we took into account possible dependence of theprobability for a codon family to stay whole or to be split on thetype of its first two bases. This follows from the difference inthermostability between codon-anticidon pairs enriched withstrong (G and C) bases and those enriched with weak (A and T)
bases (Lagerkvist, 1978). For that, the probability for a family offour codons with leading strong doublets to specify a single amino acid was adopted to be 0.9, for those with weak doublets –0.1, and for mixed doublets it was 0.5. Each of the 20 aminoacids and Stop is recruited at least once; therefore codes withless than 21 generated blocks are discarded. After that blocks
were populated randomly with amino acids and Stop.
(2) Reduced effect of mutations/mistranslations due to natural selection. The cost function for polar requirement was adopted from Freeland & Hurst (1998), taking into account transversion-transition and mistranslation biases (see also Novozhilov et al., 2007). Only those codes were passed further which
had cost function value smaller than φ0 + σ, where φ0 is the value
for the universal code, and σ is the standard deviation for all
random codes filtered through the previous condition.
(3) Small departure from the cytoplasmic balance (see Appendix D). As argued by Downes & Richardson (2002), thisbalance might reflect evolutionary pathways optimizing the distribution of mass in proteins. With C standing for all side chain
nucleons in the code and B for all nucleons in block residues, thevalue δ = (C – B)/(C + B) is distributed approximately normallywith μ = 0.043 and σ = 0.024 (under the first condition describedabove). Only those codes were considered which had δ in therange 0 ± σ, centered on the value of the standard code. As that
range corresponds to codes with smaller (“early”) amino acids
predominating, this condition also reflects presumable history of
the code expansion (Trifonov, 2000; Wong, 2005).

Nucleon balances. Arithmetical patterns in the standard code are
all of the same style: equality of nucleon sums + their distinctive
decimal notation + at least one of the three transformations (except the decomposed case). The search for a random code with afew patterns of this sort turned out to be time-consuming, so therequirements were greatly simplified. Only nucleon equalities
were considered, without requirement of distinctive notation in
any numeral system. Presence of transformations was required
only in Gamow’s arrangement for codons with identical andunique bases, since transformations act there in the first place,not as companions of another sorting logic. Also for simplicity,
only global patterns were considered; “local” features like thethreefold balance in Fig. 5b were not checked.
Alternative codes might have balances in arrangements andcombinations different from those in the real code. Contrary to
as it might seem, there are not so many ways of arranging thecode based on a straightforward logic with minimum arbitrariness. For example, along with Gamow’s sorting, several otherarrangements were proposed during early attempts to deducethe code theoretically (see Hayes, 1998). One of them is known
as the “code without commas” (Crick et al., 1957). However,unlike Gamow’s sorting, this and other proposed arrangements
do not allow “freezing” the code elements completely, leaving
a large degree of arbitrariness. Ultimately, the following arrangements were considered in the test:- divisions based on redundancy;- divisions based on positions in codons (alternating all combinations such as S or W in the first position, R or Y in thesecond position, etc.);- sortings based on nucleotide composition of codons (alternating
all combinations of “freezing” conditions and division logic);- arrangements based on decomposition of codons into bases(alternating all combinations of the four nucleotide sets).
Besides, the first two types might be arranged with full-size orcontracted codons. The only possible balance of the peptide representation (Appendix D) was also checked. In total, 160 potential balances (of both chain-chain and block-chain types) werechecked in all these arrangements. Precautions were made toignore arithmetical dependencies, as for certain code versions
some balances are trivially fulfilled if few others occur. A simple
scoring scheme was adopted: the score of a code is the numberof algebraically independent nucleon equalities it happens topossess in all arrangements. In this scheme the simplified version of arithmetical patterns in the standard code has the score 7.
Computer estimation shows that probability for a code to havethe score not less than 7 by chance under imposed conditions is
p1 = 1.5×10–8 (Fig. B1a).

11

single code under imposed conditions is p1p2p3 = 2.4×10–14.
Since the redundancy-symmetric code is not even needed to befound in nature to reveal the ideogram, the final P-value will notdiffer much from that value.
This result gives probabilities for the specific type of patterns –nucleon equalities, ideogram symmetries and transformations.
However, testing the hypothesis of an intelligent signal shouldtake into account patterns of other sorts as well, as long as theymeet the requirements outlined in Introduction. After analysis of
the literature on the genetic code our opinion is still that nucleon
and redundancy numbers are the best candidates for “ostensive
numerals”. We accept though that there could be other possibilities and that the obtained P-value should be regarded as a roughapproximation (keep in mind simplifications in the test as well).
But admittedly, there are just not enough candidates for “ostensive
numerals” and corresponding (algebraically defined) pattern ensembles to compensate for the small P-value obtained and to raise
it close to the significance level.

Fig. B1. Distribution of variant codes by their scores for (a) nucleon
equalities and (b) ideogram symmetries. The size of the sample in bothcases is one billion codes.

Ideogram symmetries. An ideogram might be built for each variant code in the same way as shown in Fig. 7 (however, no requirement is imposed for whole and split families to be linked
with any transformation). There are a few more conceivableways to build an ideogram using contracted codon series (ideograms based on full-size codons suffer with ambiguities). For
example, nucleon and redundancy numbers might be arrangedin the same direction, rather than antisymmetrically. Anotherway is to divide the code by positions in codons (e.g., R or Y in
the first position; though these ideograms are simpler as two of
their four upper strings are always binary, whereas in ideograms based on redundancy all strings are, in general, quaternary). In total, 9 ideogram versions were built for each codeand checked for symmetries. Namely, each of the four strings
was checked for M, M + I, T, T + I, where M and T stand for
mirror and translation symmetries and I denotes pair inversionsof all three types. For each symmetry a string of length L getsthe score L/2, if it contains only two types of bases (or if thesymmetry holds only in binary representation RY, SW or KM),
and L, if it contains three or all four types of bases. Only
whole-string symmetries were considered (in this case multiple
symmetries organizing different parts of a string such as inFig. 9b are not detected; the whole string in Fig. 9b, however,is mirror symmetrical in KM representation). For each ambiguous position (two neighboring series with equal nucleon numbers) the penalty L/3 was introduced. Semantical symmetries
and balances of translated amino acids were not checked. Finally, if at least one of the four strings has none of the symmetries, the score is divided by 2. The euplotid code has the score
35 in this scheme: 8 for M + I(TA, CG) and 4 for TRY in theupper short string, 4 for MRY in the center short string, 8 for
MKM in the upper long string, 16 for M in the center long string,
penalty -16/3 ≈ -5 for Lys and Gln (though in this case their interchange affects neither MKM in the upper string, nor M in thecenter one). Computer estimation shows that probability for acode to have the score not less than 35 by chance under imposed
conditions is p2 = 9.4×10–5 (Fig. B1b).
We also checked transformations in Rumer’s bisections ofgenerated codes, since these transformations served as theguiding principle for signal extraction in the real code. Under
the conditions imposed, probability for a random code to haveequal numbers of whole and split families which are furthermore linked with any of the three possible transformations wasfound to be 4.6×10–2. Given that one transformation takes
place, the other two might be distributed among codons in theratios 8:0 (p = 0.125), 4:4 (p = 0.375), or 2:6 (p = 0.5). For thereal code this ratio is 4:4 (see Fig. 2a), so finally p3 = 1.7×10–2.
As suggested by a separate computational study, mutual influence of the three types of patterns is negligible, so the total
probability for a (very simplified) signal to occur by chance in a

Appendix C. Digital symmetries of positional numeral systems
The digital symmetry described in the main text for thedecimal system is related to a divisibility criterion that might
be used to effectively perform checksums. Consider the number 27014319417 as an example. Triplet reading frame splits
this number into digital triplets 270, 143, 194, 170 (any of thethree reading frames might be chosen; zeros are added at flanks
to form complete triplets). The sum of these triplets equals to
777. Its distinctive notation indicates that the original number
is divisible by 037. In four-digit numbers that appear duringsummations thousand’s digits are transferred to unit’s digits. If
notation of the resulting sum is not distinctive, add or subtract
037 once. Subsequent distinctive notation will confirm thedivisibility of the original number by 037 while its absence will
disprove it. Thus, the other two frames for the exemplary number yield:
002 + 701 + 431 + 941 + 700 = 2775 → 002 + 775 = 777;
027 + 014 + 319 + 417 = 777.
This criterion applies to numbers of any length and requires aregister with only three positions. Moving along a linear notation, such register adds digital triplets together and transfers
thousand’s digits to unit’s digits.
The same triplet digital symmetry and related divisibility criterion exist in all numeral systems with radix q that meets therequirement (q – 1)/3 = Integer. The symmetry-related prime
number in those systems is found as 111q/3. Thus, the featureexists in the quaternary system (q = 4) with prime number 7(0134), septenary system (q = 7) with prime number 19 (0257),
decimal system (q = 10) with prime number 037, the system withq = 13 and prime number 61 (04913), and so on. The digitalsymmetry of the quaternary system is shown in Fig. C1.

Fig. C1. Similar to the decimal system, the quaternary system also displays symmetry of digital triplets, where 7 (0134) acts instead of 037.

12

Appendix D. The cytoplasmic balance
Fig. D1 represents the entire genetic code as a peptide. Eachamino acid is inserted into this peptide as many times as it appears in the standard code. Amino acid block residues make up
the peptide backbone. The resulting polymer is 61 amino acids
long. If its N- and C-termini are eliminated by closing the peptide into a ring, its backbone and side chains appear preciselybalanced. Notably, this feature is common to natural proteins:their mass is distributed approximately equally between peptide
backbone and side chains (Downes & Richardson, 2002). This
also automatically implies that frequencies of amino acids innatural proteins correlate with their abundance in the genetic
code (see data in Gilis et al., 2001).
Not only the activation key is discarded in this balance, butamino acid molecules are considered as they appear in cytoplasmic environment (where side chains of some of them areionized). For these reasons the balance shown in Fig. D1 is referred to as natural or cytoplasmic. Nevertheless, unusual peptide form (though circular peptides do occur rarely in nature, seeConlan et al., 2010) and distinction between amino acid blocks
and chains suggest that the cytoplasmic balance and the “virtual”
balances shown in the main text are likely to be related phenomena. Possibly, this balance is intended to validate the artificial
nature of the activation key, showing that only actual proline canmaintain patterns in natural environment. This balance wasfound by Downes & Richardson (2002) from biological aspect.
Simultaneously, Kashkarov et al. (2002) found it with a formalarithmetical approach.

Fig. D1. Amino acids of the standard genetic code in the form of a circular peptide (sequence order does not matter). The peptide is formed byaggregating standard blocks of amino acids into polymer backbone.
Formation of each peptide bond releases a water molecule reducing eachamino acid block to 56 nucleons (55 in proline). Asp and Glu lose one
proton each from their side chains at cytoplasmic pH, while Arg and Lys
gain one proton each (denoted with –1 and +1, respectively). Other amino acids are predominantly neutral in cytoplasmic environment (Alberts
et al., 2008). As a result, nucleon sum of the peptide backbone is exactly
equal to that of all its side chains.

Appendix E. Algebraic representation of the signal
Here we describe a possible way the signal-harboring mapping might have been obtained. As initial data, one has a set of
64 codons and another set of 20 canonical amino acids plus Stop.
Suppose, the mapping between those two sets is unknown and it
has to be deduced from the given pattern ensemble of the signal.
There are ~1083 possible mappings between the two sets, provided that each element from the second set is represented at least
once. Knowing the ideogram (without knowing nucleon numbers
mapped to individual codons) is equivalent to knowing the block
structure of the code. From this follows the first portion of equations ggt = ggc = gga = ggg = ggn, ttt = ttc = tty, etc., wherecodons are used to denote variables – unknown nucleon numbersof amino acid side chains. Thus, the number of elements in thefirst set is essentially reduced from 64 to 24. But there are still~1030 possible mappings left. Now one might write down the
nucleon sums from Figs. 5-8 and 10 (leaving out algebraicallydependent parts and standard block sums, as we are provided
with the set of canonical amino acids; in case of projecting thepatterns Stop might be preliminarily assigned to certain codons
to make things easier with the block sums):

2aay + aar + tar + car + gar = 333 (Fig. 5b);3ggn + tgg + cgn + agr = 333 (Fig. 5b);ath + acn + agr + gtn + gcn + gar = 333 (Fig. 5b);
tty + 2ctn + 2tcn + ccn + 2aay + tar + ath + car + acn + 2ggn
+ tgg + gtn + cgn + gcn = 888 (Fig. 5c);
5tty + 4ttr + 5ctn + 4ath + atg + 5gtn + 5tcn + ccn + acn + gcn+ 3tay + 2tar + cay + aay + gay + 3tgy + tga + tgg + cgn+ agy + ggn = 666 + 999×2 (Fig. 6b);2tar + aar + 2atg = 222 (Fig. 10d);
agy + 2aar + tgh = 222 (Fig. 10e).
The cytoplasmic balance is not accounted here as it has no algebraic connection to this system due to the activation key. There arealso additional inequalities provided by the ideogram (Fig. 7a):ggn ≤ gcn ≤ tcn ≤ ccn ≤ gtn ≤ acn ≤ ctn ≤ cgn;
tgh ≤ ath;tar ≤ agy ≤ ttr ≤ aay ≤ gay ≤ car ≤ aar ≤ gar ≤ cay ≤ tty ≤agr ≤ tay;atg ≤ tgg.

ggn + gcn + tcn + ccn + gtn + acn + ctn + cgn = 333 (Fig. 7b);
tgy + tga + ath + tar + agy + ttr + aay + gay + car + aar + gar+ cay + tty + agr + tay + atg + tgg = 111 + 999 (Fig. 7b);
tty + ttr + tcn + tay + tar + tgy + tga + tgg + ctn + ccn + cay+ car + cgn = 814 (Fig. 8a);tty + ttr + tcn + tay + tar + tgy + tga + tgg + gtn + gcn + gay+ gar + ggn = 654 (Fig. 8b);
tty + ttr + ctn + ath + atg + gtn + tgy + tga + tgg + cgn + agy+ agr + ggn = 789 (Fig. 8b);
tty + aar + ath + tcn + cay + 2gcn + ctn + tgy + tga + gay + atg+ car + agy = 703 (Fig. 5a);ggn + ccn + ctn + 2acn + tay + tcn + 2gtn + 2cgn + agy + tar+ gay = 703 (Fig. 5a);tty + 2ttr + 3ccn + 2ctn + ath + gtn + 2tcn + acn + gcn + tay+ tgy + cay + cgn = 999 (Fig. 5b);

Finally, tgh = tgy to account for two code versions. In total, there
are 26 unknowns, 16 equations and 20 inequalities. Generally,such systems of Diophantine equations and inequalities havemultiple solutions. Since we are interested here in obtaining the
mapping of the code given the patterns and the fixed set of canonical amino acids plus Stop, the solution is to be searched over the
fragmentary domain of integers and zero {0, 1, 15, 31, 41, 43, 45,
47, 57, 58, 59, 72, 73, 75, 81, 91, 100, 107, 130}. In this caseanalysis of the system with any computer algebra system capableof dealing with Diophantine expressions shows that this system
has a single solution coinciding with the actual mapping of nucleon numbers onto codons: tty = 91, ggn = 1, tga = 0, ath = 57,

13

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etc. That still leaves us with several mappings for amino acids
though, since two of the roots – 57 and 72 – represent two aminoacids each. This ambiguity is eliminated when the patterns withinside chains (Figs. 7b and 8a) are also taken into account. Afterthat the actual mapping of the code is deduced unambiguously
from the algebraic system of the patterns. In fact, analysis showsthat unambiguous solution is achieved even if the restriction offragmentary domain is applied only to some of the unknowns. In
another approach (shCherbak, 2003) unambiguous solution isachieved only with few assumptions about the amino acid set.
Acknowledgments
The study was partially financed by the Ministry of Education and Scienceof the Republic of Kazakhstan. The research was appreciably promoted byProfessor Bakytzhan T. Zhumagulov from the National Engineering Academy of the Republic of Kazakhstan. Part of the research was made during
V.I.S.’ stay at Max-Planck-Institut für biophysikalische Chemie (Göttingen,Germany) on kind invitation of Professor Manfred Eigen. V.I.S. expresses
special thanks to Ruthild Winkler-Oswatitsch for her valuable help andcare. M.A.M. acknowledges the support by the administration of Fesenkov
Astrophysical Institute. The authors are grateful to Professor Paul C.W.
Davies, Felix P. Filatov, Vladimir V. Kashkarov, Artem S. Novozhilov,
Denis V. Tulinov, Artem N. Yermilov and Denis V. Yurin for objective
criticism and fruitful discussions of the manuscript. We deeply appreciate
Icarus Editorial Staff for organizing the peer review and the three reviewers
for their comments which led to the improvement of the manuscript.

Authors’ contributions
V.I.S. conceived of and performed the research, developed graphic arts.
V.I.S. and M.A.M. analyzed data, introduced interpretation of the activation
key, outlined structure of the paper. M.A.M. performed statistical test andalgebraic analysis, wrote the manuscript.

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