The Extension of the Standard Genetic Code via Optimal Codon Blocks
Division
Kuba Nowak
1
, Paweł Bła
˙
zej
2
, Małgorzata Wnetrzak
2
, Dorota Mackiewicz
2
and Paweł Mackiewicz
2
1
Faculty of Mathematics and Computer Science, University of Wrocław, ul. Joliot-Curie 15, Wrocław, Poland
2
Department of Genomics, Faculty of Biotechnology, University of Wrocław, F. Joliot-Curie 14a, 50-383 Wrocław, Poland
Keywords:
Code Extension, Codon Reassignment, Genetic Code, Graph Theory, Mutation, Optimisation.
Abstract:
The standard genetic code (SGC) is a crucial biological system, which allows to transmit genetic information
from DNA sequences to the protein world. The idea of the optimal extension of the SGC with new information
appears especially interesting in the context of successful experimental achievements in reprogramming of this
code. The aim of this code engineering is incorporating non-canonical amino acids (ncAAs) into synthesised
artificial proteins with novel functions. Such molecules open new perspectives in medicine, chemistry and
biotechnology. Several methods extending the canonical coding system were proposed. Here, we would like
to investigate a problem of the optimal genetic code extension using graph theory methodology. We measured
the quality of considered coding systems applying the set conductance, which determines the robustness level
against point mutations of individual codon blocks encoding the same information. Thanks to that, we were
able to find several possible optimal extensions of the SGC based on utilization of the codons redundant in the
original code. We found codes that could encode up to 16 ncAAs and simultaneously code for 20 canonical
amino acids and one stop translation signal. One of these codes was the most balanced, i.e. it consisted of
the canonical set and the extended set that were characterized by the same level of robustness against point
mutations. The proposed codes could be helpful in experimental construction of artificial genetic codes, which
can encode new amino acid with new useful properties.
1 INTRODUCTION
The standard genetic code (SGC) is a template ac-
cording to which genetic information stored in DNA
sequences is decoded into the protein world. This
coding system is nearly universal in all domains of
life, with some rare exceptions (Santos et al., 2004;
Sengupta and Higgs, 2005; Bła
˙
zej et al., 2019a). The
SGC is redundant because its 64 codons are assigned
to 20 amino acids and stop translation signal. There-
fore, 18 amino acids as well the stop signal are coded
by more than one codon called synonymous. This
property poses a question about potential using of the
redundant codons in coding new information.
Recently, several methods for reducing the redun-
dancy of the SGC and using it in the genetic code
extension were proposed (Chin, 2014). Thanks to
them, new non-canonical amino acids (ncAAs) with
new desired functions can be introduced into the cod-
ing system. One of the most commonly used method
to extend the SGC is based on the stop-codon sup-
pression. In this approach, a rarely used stop codon,
for example amber UAG codon, is assigned to a new
amino acid (Noren et al., 1989; Chin, 2017; Italia
et al., 2017; Young and Schultz, 2018). However,
this method has a strong limitation, i.e. the number
of newly added ncAAs cannot be greater than two
because one of three stop codons must be left in the
code.
Other method is based on a programmed frame-
shift suppression. Here, four-base codons (quadru-
plets) are used to encode new genetic informa-
tion (Hohsaka et al., 1996; Anderson et al., 2004;
Neumann et al., 2010). Generally, these extended
codons are constructed by an addition of one base to
rare classical codons in a given coding system. Ad-
ditionally, modified tRNAs with four-base anticodons
recognising the corresponding quadruplets should be
constructed. However, the reading of such codons is
not always perfect, because tRNAs reading classical
codons can compete with those reading the quadru-
plets.
Another interesting approach uses synonymous
codons of the SGC to encode various ncAAs (Iwane
30
Nowak, K., Bła
˙
zej, P., Wnetrzak, M., Mackiewicz, D. and Mackiewicz, P.
The Extension of the Standard Genetic Code via Optimal Codon Blocks Division.
DOI: 10.5220/0010215500300037
In Proceedings of the 14th International Joint Conference on Biomedical Engineering Systems and Technologies (BIOSTEC 2021) - Volume 3: BIOINFORMATICS, pages 30-37
ISBN: 978-989-758-490-9
Copyright
c
 2021 by SCITEPRESS – Science and Technology Publications, Lda. All rights reserved

et al., 2016). This is obtained by depletion of their
corresponding tRNAs and addition of tRNAs pre-
charged with the desired ncAAs. Using this method-
ology, the authors expanded the repertoire of canon-
ical amino acids by three new ncAAs via division of
multiple codon boxes. Despite methodological diffi-
culties of these methods, there is no doubt that they
allow us to synthesis of new proteins with demanding
new properties, which can revolutionize drug discov-
ery and chemical biology in the future.
However, it should be noted that all the studies
that have been carried out so far do not investigate
the problem of potential effectiveness of newly cre-
ated coding systems. The optimality of extended SGC
seems to be desired feature in terms of the quality of
the preservation, storing and decoding of the genetic
information. Recently, Nowak and co-authors have
opened a discussion about the optimal extension of
the SGC (Nowak et al., 2020). Basing on methodol-
ogy borrowed from graph theory, the authors exam-
ined the minimum set of codons encoding the canon-
ical genetic information as well as the set of vacant
codons that potentially might encode ncAAs.
Here, we would like to continue the previous study
about the genetic code extension. However, in con-
trast to the previous work, we would like to investi-
gate in details the way of the SGC extension assum-
ing the specific codon blocks structure observed in the
SGC. These blocks consists of four codons which en-
code the same information and differ only in the third
codon positions. We propose that new ncAAs can
be encoded by codon groups fulfilling the same rule.
Following this approach, we can extend the canonical
coding system to encode up to 16 new ncAAs.
2 PRELIMINARIES
We used the methodology based on graph theory to
describe the properties of individual codon blocks as
well as the whole coding system represented by a
graph partition. This approach was applied success-
fully to studies on the structure of the SGC and its ro-
bustness against point mutations (Bła
˙
zej et al., 2018a;
Bła
˙
zej et al., 2019b; Aloqalaa et al., 2019). In addi-
tion, a possible extension of this coding system using
six-letter alphabet (Bła
˙
zej et al., 2020) was consid-
ered.
Following (Bła
˙
zej et al., 2018a; Bła
˙
zej et al.,
2019b; Aloqalaa et al., 2019; Bła
˙
zej et al., 2020), let
G(V, E) be a graph in which V is the set of vertices
representing all possible 64 codons, whereas E is the
set of edges between these vertices. We say that two
codons u, v ∈ V are connected by the edge e(u, v) ∈ E
if and only if the codon u differs from the codon v in
exactly one position. Set E defined in this way de-
scribe all possible point mutations, which may occur
between codons. So G is by definition unweighted
and regular. According to this representation, every
coding system, which uses 64 codons, is a partition P
of the graph G into a selected number l ≥ 21 of codon
sets S
i
. Therefore, we used the following definition:
P = {S
1
, S
2
, . . . , S
l
: S
i
∩S
j
=
/
0, S
1
∪S
2
∪. . .∪S
l
=V }.
As a consequence of that, the problem of study-
ing genetic code structure can be reformulated as a
question about properties of its respective graph parti-
tion P. Similarly to the previous studies (Bła
˙
zej et al.,
2018a; Bła
˙
zej et al., 2019b; Aloqalaa et al., 2019;
Bła
˙
zej et al., 2020), we used the set conductance mea-
sure in order to describe the level of robustness of a
given codon group against point mutations.
Definition 1. For a given graph G, let S be a subset
of V . Then the conductance of S is defined as:
φ(S) =
E(S,
¯
S)
vol(S)
,
where E(S,
¯
S) is the number of edges of G crossing
from S to its complement
¯
S and vol(S) is the sum of
all degrees (from full graph) of the vertices belonging
to S.
Clearly, φ describes the robustness of a given
codon group S against point mutations that may
change the encoded genetic information. Using the
definition of φ, it is also possible to define the k-size
conductance as a lower bound on the set conductance
for the sets of a given size k. A smaller value of φ
indicates that there are relatively few point mutations
that can change an amino acid or stop signal encoded
by a given codon group.
Definition 2. The k-size-conductance of the graph G,
for k ≥ 1, is defined as:
φ
k
(G) = min
S⊆V,|S|=k
φ(S) .
The definition 2 appears to be especially use-
ful in describing the most optimal codon structure.
Particularly, if we take into account that the graph
G has the representation as a Cartesian product of
graphs (Bła
˙
zej et al., 2018a), i.e.
G = K
4
× K
4
× K
4
,
where K
4
is a 4-clique with the set of vertices repre-
senting four bases {A,U, G,C}, then using the The-
orem 1 from (Bezrukov, 1999), we get that codon
set S composed of the first k codons according to
a selected lexicographic order fulfils the property
φ(S) = φ
|S|
(G). It should be noted that including all
The Extension of the Standard Genetic Code via Optimal Codon Blocks Division
31

possible linear orders on the set {A,U, G,C} and also
all possible orders on the three codon positions, there
are exactly 144 different lexicographic orders that can
be introduced in G. Consequently, it is possible to
characterise the most robust codon groups in terms of
minimising the effect of point mutations.
The definitions 1 and 2 both characterise the prop-
erties of a selected set or group of sets with the same
size. In order to obtain the characteristics of the whole
coding system, we introduced the average conduc-
tance:
Definition 3. The average conductance of a set col-
lection P is defined as:
Φ(P) =
1
|P|
∑
S∈P
φ(S) .
Thanks to that it is possible to measure the quality
of a given group of sets P. A smaller Φ value indicates
that the given code is built of codon groups on average
better resistant to change of coded information due to
point mutations.
3 RESULTS AND DISCUSSION
Similarly to (Nowak et al., 2020), we defined the set
C
k
composed of exactly k codons which encode the
whole canonical genetic information, i.e. 20 amino
acids and stop translation signal. Moreover, we claim
that φ(C
k
) = φ
k
(G), hence C
k
is a set with the mini-
mum possible number of connections to its comple-
ment, for fixed k. In order to obtain this set, we
chose an lexicographic order as presented in (Nowak
et al., 2020) and found exactly k-first codons that at
the same time encode 20 amino acids and stop signal
(Tab. 1)
. Consequently, the set of all 64 codons V , i.e.
vertices of the graph G, has a representation:
V = C
k
∪C
0
k
,
where C
0
k
is a set of vacant codons, which could be
assigned to ncAAs. Moreover, the standard codon as-
signments induces the partition P
k
of the set C
k
into
21 disjoint codon groups encoding canonical genetic
information. In addition, the new genetic information
can creates also a partition P
0
k
, which is the set of va-
cant codons C
0
k
. As a result, the extended genetic code
P has a representation as a union:
P = P
k
∪ P
0
k
.
Table 1 presents a partition of the set of 64 possible
codons into two sets, namely, the canonical set C
28
(in red) consisting of 28 codons encoding the canon-
ical information and the extended C
0
28
of 36 vacant
Table 1: The partition of the set of 64 possible codons into
two sets. The set C
28
(red) contains exactly 28 codons
which encode canonical genetic information. They were
chosen according to a lexicographic order induced by the
linear order of bases U < C < A < G and the order of codon
positions 1 < 2 < 3. The set C
0
28
of 36 vacant codons (blue)
can be split into 16 disjoint codon groups with the same first
two codon positions.
UUU Phe UCU UAU Tyr UGU Cys
UUC UCC UAC UGC
UUA UCA UAA UGA
UUG Leu UCG Ser UAG Stop UGG Trp
CUU Leu CCU CAU His CGU Arg
CUC CCC CAC CGC
CUA CCA CAA CGA
CUG Leu CCG Pro CAG Gln CGG Arg
AUU Ile ACU AAU Asn AGU Ser
AUC ACC AAC AGC
AUA ACA AAA AGA
AUG Met ACG Thr AAG Lys AGG Arg
GUU Val GCU GAU Asp GGU Gly
GUC GCC GAC GGC
GUA GCA GAA GGA
GUG Val GCG Ala GAG Glu GGG Gly
codons (in blue). Clearly, P
28
is in this case a par-
tition of C
28
induced by the canonical codon assign-
ments, whereas codons belonging to C
0
28
may encode
new ncAAs. It was shown in (Nowak et al., 2020)
that k = 28 is the smallest number of codons selected
in a lexicographic order, which is able to encode all 21
canonical items. Thus, the presented code is simulta-
neously the most ’minimalistic’ and optimal. It still
preserves the canonical information of 21 elements,
is the most robust against losing this information due
to point mutations and contains the largest possible
number of vacant codons for these conditions. In this
code, 15 amino acid and stop signal are encoded by
single codons, three amino acids by two codons and
two amino acids by three codons.
3.1 The Extended Genetic Codes
In contrast to the previous work (Nowak et al., 2020),
we considered here another aspect of the SGC struc-
ture. We started with the observation that the set of
all 64 codons in the SGC can be split into 16 dis-
joint codon blocks B
i
, i = 1, 2, . . . , 16 in such a way
that codons belonging to a given group B
i
differ only
in the third codon position. Moreover, it is clearly
visible in the SGC that a group of codons encoding
the same amino acid is generally composed of codons
also with only the third positions different. Using
this property, we investigated a potential extension of
the genetic code according to a similar rule. Here,
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32

we claim that any new non-canonical amino acid can
be encoded by vacant codons belonging only to fixed
blocks B
i
, i = 1, 2, . . . , 16. In consequence, the codons
encoding the same amino acid differ only in the third
position. Mathematically speaking, partition P
0
k
is
composed of codon blocks S
i
, 1 ≤ i ≤ 16 belonging
to the set of vacant codons C
0
k
. These codon blocks
fulfil the following property:
S
i
= B
i
∩C
0
k
, i = 1, 2, . . . , 16 .
Tab. 2, presents an example of codon block of B
i
type. In this case, S
i
= B
i
∩C
0
k
is composed of exactly
two vacant codons (in blue) and belongs to the parti-
tion of the set C
0
28
from the ’minimalistic’ code. All
codons in this group have only the third codon posi-
tions different.
Table 2: The example of codon block B
i
, extracted from
the top left-hand corner of the code shown in Table 1. This
block is divided into two sets. The codons in red encode
canonical genetic information, whereas those in blue are va-
cant and follow the property S
i
= C
0
k
∩ B
i
.
UUU Phe
UUC
UUA
UUG Leu
Interestingly, the family of vacant codons in the
set P
0
28
from the code shown in Table 1 has a
better robustness in terms of Φ than P
28
because
Φ(P
0
28
) = 0.861, whereas Φ(P
28
) = 0.975. This prop-
erty follows from the fact that the canonical amino
acids and stop are in most cases encoded by a single
codon. This causes an imbalance between the ’mini-
malistic’ canonical set P
28
and the non-canonical set
P
0
28
.
In order to improve the robustness of the canon-
ical set, we have to increase the number of codons
by inclusion of consecutive codons in the fixed lexi-
cographic order. However, this procedure causes si-
multaneously deterioration of conductance Φ in the
non-canonical set P
0
k
. It also causes that the num-
ber of newly amino acids incorporated into the code
decreases. To measure and control the properties of
these two sets simultaneously, we investigated their
conductance in relation to k, i.e. the number of codons
building the set C
k
. Thus, we introduced a balance
measure
Ψ(P
0
k
, P
k
) =
Φ(P
0
k
)
Φ(P
k
)
,
which is defined as a ratio of the average conductance
of non-canonical set Φ(P
0
k
) to that of canonical sets
Φ(P
k
). This measure allows us to compare the con-
ductance properties of the non-canonical set in rela-
tion to the canonical set. It is evident that the value
of Ψ near to one means that both P
0
k
and P
k
achieve
the same level of robustness against point mutations,
which could change the coded information. There-
fore, it seems reasonable to find for every k the most
balanced codes that minimize |1 − Ψ(P
0
k
, P
k
)| over all
possible P
0
k
and P
k
for fixed k.
Table 3: The values of selected measures for the most
balanced genetic codes calculated for the fixed number of
codons in the canonical set k = 28, 29, . . . , 63; Ψ - the bal-
ance; Φ(P
0
k
) and Φ(P
k
) - the average conductance for non-
canonical and canonical sets, respectively; |P| - the number
of potentially encoded ncAAs.
k Ψ Φ(P
0
k
) Φ(P
k
) |P|
28 0.8829 0.8611 0.9753 16
29 0.8949 0.8681 0.9700 16
30 0.9053 0.8750 0.9665 16
31 0.9209 0.8819 0.9577 16
32 0.9299 0.8889 0.9559 16
33 0.9424 0.8958 0.9506 16
34 0.9550 0.9028 0.9453 16
35 0.9678 0.9097 0.9400 16
36 0.9807 0.9167 0.9347 16
37 0.9937 0.9236 0.9295 16
38 1.0012 0.9306 0.9295 16
39 1.0043 0.9375 0.9335 16
40 1.0169 0.9444 0.9287 16
41 1.0302 0.9514 0.9235 16
42 1.0458 0.9583 0.9164 16
43 1.0595 0.9653 0.9111 16
44 1.0733 0.9722 0.9058 16
45 1.0863 0.9792 0.9014 16
46 1.1004 0.9861 0.8961 16
47 1.1148 0.9931 0.8908 16
48 1.1293 1.0000 0.8855 16
49 1.1358 1.0000 0.8804 15
50 1.1358 1.0000 0.8804 14
51 1.1408 1.0000 0.8765 13
52 0.8963 0.7778 0.8677 4
53 0.9418 0.8056 0.8554 4
54 0.9752 0.8333 0.8545 4
55 1.0026 0.8611 0.8589 4
56 1.0392 0.8889 0.8554 4
57 1.0783 0.9167 0.8501 4
58 1.1180 0.9444 0.8448 4
59 1.1581 0.9722 0.8395 4
60 1.1987 1.0000 0.8342 4
61 0.9525 0.7778 0.8166 1
62 1.0815 0.8889 0.8219 1
63 1.2246 1.0000 0.8166 1
Figure 1 shows the relationship between the Ψ
values and the size of the set C
k
calculated for the
most balanced codes for fixed k. In the plot, we also
The Extension of the Standard Genetic Code via Optimal Codon Blocks Division
33

Figure 1: The values of Ψ, calculated for the most balanced codes, in relation to the size k, i.e. the number of codons encoding
canonical genetic information. The number of newly encoded ncAAs is presented above dots.
included the number of potential ncAAs for the given
code. The numerical details are presented in Table 3.
Interestingly, we can distinguish three increasing
trends in this plot. In one of them, the balance Ψ
is constantly increasing with k ∈ [28, 51], which re-
sults from the fact that the set conductance calcu-
lated for codon groups of the canonical set P
k
is gen-
erally decreasing, whereas that for codon groups of
the non-canonical set P
0
k
is increasing (Table 3). For
k < 38, the set conductance Φ of the canonical set
is generally higher than that calculated for respective
codon groups belonging to the non-canonical set. For
k = 38, the Φ values of these sets are the most sim-
ilar and the Ψ value is most close to one. Thereby,
it is possible to extend the SGC by 16 amino acids
and achieve a good balance between the canonical and
non-canonical set. Ψ is still growing till k = 51 and
in the range k = [38, 51], the set conductance of the
canonical set is smaller than that of the non-canonical
set (Table 3).
The value of Ψ calculated for the most balanced
extended genetic codes declines sharply for k = 52,
in comparison to Ψ for k ≤ 51 (Figure 1). What is
more, the number of possibly encoded ncAAs also de-
creases dramatically till only four and persists for the
range of k = [52, 60]. It is mainly related with a much
smaller number of vacant codons, which were left for
k > 51. The increasing trend of the balance in this
range results from a gradual dropping of Φ calculated
for the canonical set and its rise for the non-canonical
set (Table 3). Within the range of k = [52, 60], we can
also find the most balanced code for k = 55. In this
case, we can extend the SGC with four ncAAS. The
third growing trend in this plot, for k = 61, 62, 63, is
mainly associated with an increase in the set conduc-
tance of the non-canonical set because this measure
for the canonical set is rather stable (Table 3). These
codes can be extended with only one ncAA.
3.2 The Most Balanced Extended
Genetic Codes
Here, we present two examples of the most bal-
anced extended genetic codes. These coding systems
achieve the values of Ψ most close to 1 among all
genetic codes generated in the lexicographic order
method.
Table 4 shows the most balanced code that con-
tains k = 38 codons in the canonical set (in red) and
encodes up to 16 non-canonical amino acids. The po-
tential ncAAs can be coded by also 16 codon blocks
(in blue), which are induced by codons with the same
the first and the second positions. In the case of the
non-canonical set, the size of the codon groups is one
or two, whereas in the canonical set, the codon groups
encoding an amino acid or stop signal has one, two,
three or four codons. The average conductance for
the canonical set P
k
and the non-canonical set P
0
k
are
nearly the same, i.e. 0.93, which causes that the bal-
ance Ψ(P
0
k
, P
k
) is 1.001 in this case.
Another example of the most balanced code that
is able to encode up to four ncAAs is given in Ta-
ble 5. As we can see, the canonical set contains 55
BIOINFORMATICS 2021 - 12th International Conference on Bioinformatics Models, Methods and Algorithms
34

Table 4: The extended genetic code that encodes at most
16 ncAAs by new blocks with 26 codons (blue) and is the
most balanced among all extended genetic codes achieving
Ψ = 1.001. The set encoding canonical information con-
tains k = 38 codons (red).
UUU Phe UCU Ser UAU Tyr UGU Cys
UUC Phe UCC UAC UGC Cys
UUA UCA UAA UGA
UUG Leu UCG Ser UAG Stop UGG Trp
CUU Leu CCU Pro CAU His CGU Arg
CUC CCC CAC CGC Arg
CUA CCA CAA CGA
CUG Leu CCG Pro CAG Gln CGG Arg
AUU Ile ACU Thr AAU Asn AGU Ser
AUC ACC AAC AGC Ser
AUA ACA AAA AGA
AUG Met ACG Thr AAG Lys AGG Arg
GUU Val GCU Ala GAU Asp GGU Gly
GUC Val GCC GAC GGC Gly
GUA GCA GAA GGA
GUG Val GCG Ala GAG Glu GGG Gly
codons (in red) and nine vacant codons belonging to
the non-canonical set (in blue). The non-canonical set
is composed of four groups, three contain two codons
and one has three codons, whereas in the canonical
set there are groups with one, two, three, four or six
codons. The average conductance Φ calculated for
the canonical set Φ(P
55
) and extended set Φ(P
0
55
) are
nearly similar and equal 0.86. Therefore, the balance
measure Ψ is 1.003 for this code.
Table 5: The extended genetic code that encodes at most
four ncAAs by new blocks with nine codons (blue) and is
the most balanced among all extended genetic codes achiev-
ing Ψ = 1.003. The set encoding canonical information
contains k = 55 codons (red).
UUU Phe UCU Ser UAU Tyr UGU Cys
UUC Phe UCC Ser UAC Tyr UGC Cys
UUA Leu UCA Ser UAA Stop UGA Stop
UUG Leu UCG Ser UAG Stop UGG Trp
CUU Leu CCU Pro CAU His CGU Arg
CUC Leu CCC Pro CAC His CGC Arg
CUA Leu CCA Pro CAA Gln CGA Arg
CUG Leu CCG Pro CAG Gln CGG Arg
AUU Ile ACU Thr AAU Asn AGU Ser
AUC Ile ACC Thr AAC Asn AGC Ser
AUA Ile ACA Thr AAA Lys AGA Arg
AUG Met ACG Thr AAG Lys AGG Arg
GUU Val GCU Ala GAU Asp GGU
GUC GCC GAC GGC
GUA Val GCA Ala GAA Glu GGA Gly
GUG GCG GAG GGG
4 CONCLUSIONS
We presented a potential method of genetic code ex-
tension. Using it, we searched for codes that encode
all 21 elements, i.e. 20 amino acids and one stop
translation signal, but can simultaneously release as
many as possible vacant codons, which can be assign
to non-canonical amino acids. We also imposed con-
ditions for the codes to minimize consequences of the
point mutations, which could change the coded infor-
mation.
This assumption is in good agreement with the hy-
pothesis, that the SGC evolved to minimize the dam-
aging effects of mutations or mistranslations of coded
proteins (Woese, 1965; Sonneborn, 1965; Epstein,
1966; Goldberg and Wittes, 1966; Haig and Hurst,
1991; Freeland and Hurst, 1998; Freeland et al., 2000;
Gilis et al., 2001). Detailed studies revealed that
the code is not ideally optimized in this respect but
shows a global tendency to minimization this harm-
ful consequences (Bła
˙
zej et al., 2016; Massey, 2008;
Novozhilov et al., 2007; Santos et al., 2011; San-
tos and Monteagudo, 2017; Wnetrzak et al., 2018;
Bła
˙
zej et al., 2018b; Bła
˙
zej et al., 2019b; Wnetrzak
et al., 2019). Thus, our assumption seems reason-
able because the biological systems require the opti-
mization in terms of mutations (Radman et al., 1999;
Sniegowski et al., 2000; Dudkiewicz et al., 2005;
Mackiewicz et al., 2008; Bła
˙
zej et al., 2015; Bła
˙
zej
et al., 2017).
Therefore, we used the set conductance, i.e. the
fraction of mutations changing genetic information,
as a measure of the code robustness against point
mutations of individual codon blocks encoding the
same information. Accordingly, the applied algorithm
found the new codon groups for non-canonical amino
acids consisted of codons that differ only in the third
codon position for a given group. This is in line with
the general structure of canonical codon blocks ob-
served in the standard genetic code and very good op-
timization of this code in this codon position in terms
of minimization of point mutations (Santos and Mon-
teagudo, 2010; Bła
˙
zej et al., 2018b).
Following these assumptions and using the
methodology borrowed from graph theory, we
showed several examples of the extended genetic
codes, which potentially could encode up to 16 non-
canonical amino acids. We also searched for the ex-
tended genetic code in which both the canonical part
and the extended part possess the same level of ro-
bustness against point mutations. We found two such
the most balanced codes. One includes 38 codons
for the canonical information and 26 codons for 16
ncAAs, and another contains 55 codons for the canon-
The Extension of the Standard Genetic Code via Optimal Codon Blocks Division
35

ical elements and nine codons for encoding four non-
canonical amino acids. The proposed extended codes
can be useful in designing artificial codes encoding
new amino acid with specific properties, which can
find application in various branches of biotechnology
and synthetic biology.
5 FUNDING STATEMENT
This work was supported by the National Science
Centre, Poland (Narodowe Centrum Nauki, Polska)
under Grant number 2017/27/N/NZ2/00403.
REFERENCES
Aloqalaa, D. A., Kowalski, D. R., Blazej, P., Wnetrzak, M.,
Mackiewicz, D., and Mackiewicz, P. (2019). The im-
pact of the transversion/transition ratio on the opti-
mal genetic code graph partition. In Proceedings of
the 12th International Joint Conference on Biomedi-
cal Engineering Systems and Technologies (BIOSTEC
2019) - Volume 3: BIOINFORMATICS, pages 55–65.
Anderson, J. C., Wu, N., Santoro, S. W., Lakshman, V.,
King, D. S., and Schultz, P. G. (2004). An expanded
genetic code with a functional quadruplet codon. Proc
Natl Acad Sci U S A, 101(20):7566–7571.
Bezrukov, S. L. (1999). Edge isoperimetic problems on
graphs., volume 7, pages 157–197. Akademia Kiado,
Budapest.
Bła
˙
zej, P., Kowalski, D., Mackiewicz, D., Wnetrzak,
M., Aloqalaa, D., and Mackiewicz, P.
(2018a). The structure of the genetic code
as an optimal graph clustering problem.
www.biorxiv.org/content/early/2018/05/28/332478.
Bła
˙
zej, P., Mackiewicz, D., Grabinska, M., Wnetrzak, M.,
and Mackiewicz, P. (2017). Optimization of amino
acid replacement costs by mutational pressure in bac-
terial genomes. Scientific Reports, 7:1061.
Bła
˙
zej, P., Miasojedow, B., Grabinska, M., and Mack-
iewicz, P. (2015). Optimization of mutation pressure
in relation to properties of protein-coding sequences
in bacterial genomes. PLoS One, 10:e0130411.
Bła
˙
zej, P., Wnetrzak, M., Mackiewicz, D., Gagat, P., and
Mackiewicz, P. (2019a). Many alternative and theo-
retical genetic codes are more robust to amino acid
replacements than the standard genetic code. Journal
of Theoretical Biology, 464:21–32.
Bła
˙
zej, P., Wnetrzak, M., Mackiewicz, D., and Mackiewicz,
P. (2018b). Optimization of the standard genetic code
according to three codon positions using an evolution-
ary algorithm. PLoS One, 13(8):e0201715.
Bła
˙
zej, P., Wnetrzak, M., Mackiewicz, D., and Mackiewicz,
P. (2019b). The influence of different types of transla-
tional inaccuracies on the genetic code structure. BMC
Bioinformatics, 20(1):114.
Bła
˙
zej, P., Wnetrzak, M., Mackiewicz, D., and Mackiewicz,
P. (2020). Basic principles of the genetic code exten-
sion. Royal Society Open Science, 7(2):191384.
Bła
˙
zej, P., Wnetrzak, M., and Mackiewicz, P. (2016). The
role of crossover operator in evolutionary-based ap-
proach to the problem of genetic code optimization.
BioSystems, 150:61–72.
Chin, J. W. (2014). Expanding and reprogramming the ge-
netic code of cells and animals. Annu Rev Biochem,
83:379–408.
Chin, J. W. (2017). Expanding and reprogramming the ge-
netic code. Nature, 550(7674):53–60.
Dudkiewicz, A., Mackiewicz, P., Nowicka, A., Kowalezuk,
M., Mackiewicz, D., Polak, N., Smolarczyk, K., Ba-
naszak, J., Dudek, M. R., and Cebrat, S. (2005). Cor-
respondence between mutation and selection pressure
and the genetic code degeneracy in the gene evolution.
Future Generation Computer Systems, 21(7):1033–
1039.
Epstein, C. J. (1966). Role of the amino-acid ”code” and of
selection for conformation in the evolution of proteins.
Nature, 210(5031):25–8.
Freeland, S. J. and Hurst, L. D. (1998). The genetic code
is one in a million. Journal of Molecular Evolution,
47(3):238–248.
Freeland, S. J., Knight, R. D., and Landweber, L. F. (2000).
Measuring adaptation within the genetic code. Trends
Biochem Sci, 25(2):44–5.
Gilis, D., Massar, S., Cerf, N. J., and Rooman, M. (2001).
Optimality of the genetic code with respect to protein
stability and amino-acid frequencies. Genome Biol,
2(11):research0049.1–0049.12.
Goldberg, A. L. and Wittes, R. E. (1966). Genetic code:
aspects of organization. Science, 153(3734):420–4.
Haig, D. and Hurst, L. D. (1991). A quantitative measure
of error minimization in the genetic code. Journal of
Molecular Evolution, 33(5):412–417.
Hohsaka, T., Ashizuka, Y., Murakami, H., and Sisido, M.
(1996). Incorporation of nonnatural amino acids into
streptavidin through in vitro frame-shift suppression.
J Am Chem Soc, 118(40):9778–9779.
Italia, J. S., Addy, P. S., Wrobel, C. J., Crawford, L. A.,
Lajoie, M. J., Zheng, Y., and Chatterjee, A. (2017).
An orthogonalized platform for genetic code expan-
sion in both bacteria and eukaryotes. Nat Chem Biol,
13(4):446–450.
Iwane, Y., Hitomi, A., Murakami, H., Katoh, T., Goto, Y.,
and Suga, H. (2016). Expanding the amino acid reper-
toire of ribosomal polypeptide synthesis via the ar-
tificial division of codon boxes. Nature Chemistry,
8(4):317–325.
Mackiewicz, P., Biecek, P., Mackiewicz, D., Kiraga, J.,
Baczkowski, K., Sobczynski, M., and Cebrat, S.
(2008). Optimisation of asymmetric mutational pres-
sure and selection pressure around the universal ge-
netic code. Computational Science - ICCS 2008, Pt 3,
Lecture Notes in Computer Science, 5103:100–109.
Massey, S. E. (2008). A neutral origin for error minimiza-
tion in the genetic code. Journal of Molecular Evolu-
tion, 67(5):510–516.
BIOINFORMATICS 2021 - 12th International Conference on Bioinformatics Models, Methods and Algorithms
36

Neumann, H., Wang, K., Davis, L., Garcia-Alai, M., and
Chin, J. W. (2010). Encoding multiple unnatural
amino acids via evolution of a quadruplet-decoding ri-
bosome. Nature, 464(7287):441–4.
Noren, C. J., Anthony-Cahill, S. J., Griffith, M. C., and
Schultz, P. G. (1989). A general method for site-
specific incorporation of unnatural amino acids into
proteins. Science, 244(4901):182–8.
Novozhilov, A. S., Wolf, Y. I., and Koonin, E. V. (2007).
Evolution of the genetic code: partial optimization of
a random code for robustness to translation error in a
rugged fitness landscape. Biol Direct, 2:24.
Nowak, K., Bła
˙
zej, P., Wnetrzak, M., Mackiewicz, D.,
and Mackiewicz, P. (2020). Some theoretical as-
pects of reprogramming the standard genetic code.
www.biorxiv.org/content/10.1101/2020.09.12.294553v1.
Radman, M., Matic, I., and Taddei, F. (1999). Evolution
of evolvability a. Annals of the New York Academy of
Sciences, 870(1):146–155.
Santos, J. and Monteagudo, A. (2010). Study of the ge-
netic code adaptability by means of a genetic algo-
rithm. Journal of Theoretical Biology, 264(3):854–
865.
Santos, J. and Monteagudo, A. (2017). Inclusion of the fit-
ness sharing technique in an evolutionary algorithm
to analyze the fitness landscape of the genetic code
adaptability. BMC Bioinformatics, 18(1):195.
Santos, M. A., Moura, G., Massey, S. E., and Tuite, M. F.
(2004). Driving change: the evolution of alternative
genetic codes. Trends in Genetics, 20(2):95–102.
Santos, M. A. S., Gomes, A. C., Santos, M. C., Carreto,
L. C., and Moura, G. R. (2011). The genetic code
of the fungal ctg clade. Comptes Rendus Biologies,
334(8-9):607–611.
Sengupta, S. and Higgs, P. G. (2005). A unified model of
codon reassignment in alternative genetic codes. Ge-
netics, 170(2):831–40.
Sniegowski, P. D., Gerrish, P. J., Johnson, T., and Shaver,
A. (2000). The evolution of mutation rates: separating
causes from consequences. Bioessays, 22(12):1057–
1066.
Sonneborn, T. (1965). Degeneracy of the genetic code:
extent, nature, and genetic implications., pages 377–
397. Academic Press, New York.
Wnetrzak, M., Bła
˙
zej, P., and Mackiewicz, P. (2019). Op-
timization of the standard genetic code in terms of
two mutation types: Point mutations and frameshifts.
BioSystems, 181(181):44–50.
Wnetrzak, M., Bła
˙
zej, P., Mackiewicz, D., and Mackiewicz,
P. (2018). The optimality of the standard genetic code
assessed by an eight-objective evolutionary algorithm.
BMC Evolutionary Biology, 18:192.
Woese, C. R. (1965). On the evolution of the genetic code.
Proc Natl Acad Sci U S A, 54(6):1546–52.
Young, D. D. and Schultz, P. G. (2018). Playing with the
molecules of life. ACS Chem Biol, 13(4):854–870.
The Extension of the Standard Genetic Code via Optimal Codon Blocks Division
37