Design of a genetic algorithm for the simulated evolution of a library of asymmetric transfer hydrogenation catalysts

Article abstract of DOI:10.1002/chem.200802192

A library of catalysts was designed for asymmetric-hydrogen transfer to acetophenone. At first, the whole library was submitted to evaluation using high-throughput experiments (HTE). The catalysts were listed in ascending order, with respect to their performance, and best catalysts were identified. In the second step, various simulated evolution experiments, based on a genetic algorithm, were applied to this library. A small part of the library, called the mother generation (GO), thus evolved from generation to generation. The goal was to use our collection of HTE data to adjust the parameters of the genetic algorithm, in order to obtain a maximum of the best catalysts within a minimal number of gen-erations. It was namely found that simulated evolution's results depended on the selection of GO and that a random GO should be preferred. We also demonstrated that it was possible to get 5 to 6 of the ten best catalysts while investigating only 10% of the library. Moreover, we developed a double algorithm making this result still achievable if the evolution started with one of the worst GO.

Full text of DOI:10.1002/chem.200802192

FULL PAPER
DOI: 10.1002/chem.200802192
Design of a Genetic Algorithm for the Simulated Evolution of a Library of
Asymmetric Transfer Hydrogenation Catalysts
Nicolas Vriamont,[a] Bernadette Govaerts,[b] Pierre Grenouillet,[c]
Claude de Bellefon,*[c] and Olivier Riant*[a]
Abstract: A library of catalysts was de-
signed for asymmetric-hydrogen trans-
fer to acetophenone. At first, the
whole library was submitted to evalua-
tion using high-throughput experiments
(HTE). The catalysts were listed in as-
cending order, with respect to their
performance, and best catalysts were
identified. In the second step, various
simulated evolution experiments, based
on a genetic algorithm, were applied to
this library. A small part of the library,
called the mother generation (G0),
thus evolved from generation to gener-
ation. The goal was to use our collec-
tion of HTE data to adjust the parame-
ters of the genetic algorithm, in order
to obtain a maximum of the best cata-
lysts within a minimal number of gen-
erations. It was namely found that si-
mulated evolutionꢀs results depended
on the selection of G0 and that a
random G0 should be preferred. We
also demonstrated that it was possible
to get 5 to 6 of the ten best catalysts
while investigating only 10% of the li-
brary. Moreover, we developed
a
double algorithm making this result
still achievable if the evolution started
with one of the worst G0.
Keywords: asymmetric catalysis
·
genetic algorithm · simulated evolu-
tion · transfer hydrogenation
Introduction
enantioselective chemical transformations of molecules of
high interest.[1]
Over the last decades, the importance of chirality has been
widely recognized in the medicinal, pharmaceutical and agri-
cultural chemistry. It makes it a centre of interest for syn-
thetic organic chemist trying to develop methodologies that
provide high levels of enantiodiscrimination, and asymmet-
ric catalysis is by far the most appealing way to get highly
In this paper, we focus on the particular case of carbonyl
reductions, with regards to the importance of chiral alcohols
as essential building blocks.[2] The development of a new
asymmetric catalyst, is a challenging and time-consuming
task: A good catalyst must combine a robust structure and
proper kinetics, which requires the adjustment of a large
number of parameters. A common way to develop new cata-
lysts is to imagine a general structure, which combines a
metallic centre with a chiral ligand that leads to the forma-
tion of a chiral catalyst that could efficiently promote a re-
action, in terms of both ee and yield. Analogs of this general
structure are then synthesized and tested, which may then
provide general trends for improving the catalyst design.[3]
Better structures can then be synthesized to obtain en-
hanced or at least satisfactory performances. Certainly, gen-
eralities can be drawn regarding the connection between the
structure of catalysts and their potential application.
The “rate-limiting step” of such a procedure is the time a
chemist can work within a defined period. Therefore, the
part of the chemical space (chiral ligands, metallic precur-
sors, solvents, concentrations, temperatures, pressures, etc.)
that can be explored remains rather small. High-throughput
screenings and high-throughput experiments techniques
(HTS and HTE) have been set up to help chemists perform-
[a] N. Vriamont, Prof. O. Riant
Departement de Chimie Organique et Mꢁdicinale
Universitꢁ catholique de Louvain, Bꢂtiment Lavoisier
Place Pasteur, 1, 1348 Louvain-la-Neuve (Belgium)
Fax : (+32)104-741-68
E-mail: olivier.riant@uclouvain.be
[b] Prof. B. Govaerts
Institut de Statistique
Universitꢁ catholique de Louvain
20 voie du roman pays, 1348 Louvain-la-Neuve (Belgium)
[c] P. Grenouillet, Dr. C. de Bellefon
Laboratoire de Gꢁnie des Procꢁdꢁs Catalytiques
CNRS-ESCPE Lyon, BP2077, 69616 Villeurbanne (France)
Fax : (+33)4-7243-1754
E-mail: claude.debellefon@lgpc.cpe.fr
Supporting information for this article is available on the WWW
under http://dx.doi.org/10.1002/chem.200802192.
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ing more synthesis and, consequently, more tests within a
given time. Combinatorial chemistry has also been fruitfully
combined with HTE/HTS to allow researchers to explore a
wider chemical space.[4] It is now possible to get access to
some structures faster, as well as speeding up the evaluation
phase of catalysts (Figure 1).
Scheme 1. Metal-catalyzed hydride transfer to acetophenone, as a bench-
work reaction.
To validate the methodology, we first considered the syn-
thesis of whole building blocks of the catalysts and HTE
evaluation of all the possible combinations. We then con-
structed a genetic algorithm that was applied to a small part
of the library, with systematic variation of the adjustable pa-
rameters of the genetic algorithm. We performed simulated
evolutions to evaluate the ability of our algorithm to find
the best catalysts without testing the entire library. Our
main result is that it was sufficient to evaluate about 10%
of the whole library to get the best catalysts.
Figure 1. Comparison of the usual steps in the classical way and the HTE
way on engineering structures.
Despite the distinct advantage in the principles of combi-
natorial chemistry and the alarming rise in HTE/HTS tech-
niques, they still suffer from the same limitations as classical
experiments: All arrays have to undergo synthesis and eval-
uation before any statement concerning a high-quality cata-
lyst(s) can be released. Even though the chemical space is
now wider, it still has to be fully explored.
Results and Discussion
Framework of simulated evolution: We first built a library
of chiral catalysts by considering a family of ligands with a
chiral b-amino alcohol structure bearing a substituent on the
nitrogen atom. Such ligands have been reported to provide
high activity and enantioselectivity in the ruthenium asym-
metric catalyzed transfer hydride reaction to prochiral ke-
tones and can be easily prepared from commercially avail-
able starting materials.[11] We introduced chemical diversity
on those structures through alkylation of the primary amine
group by reductive amination with various aldehydes and
ketones, yielding a sub-library of chiral ligands AxBy. The
third variation was introduced through the metal complex
precursor Mz, giving the final library of chiral catalysts
AxByMz (Scheme 2).
Faster access to relevant catalysts might arise from the
ability to predict catalyst behavior directly from its struc-
ture. The efforts made in this field occasionally gave very at-
tractive results, but such an approach still requires high-
quality data and time-consuming calculations.[5] Alternative-
ly, scientists were inspired by nature for improving the
design of catalysts. Every lifeform on Earth is the result of
an evolution over billions of years, and results from the
amazing capacity of life to accommodate to the environment
by self-modification processes. The genetic code of live or-
ganisms is organized in building blocks, the position of
which can endure some variations. Sporadically, these varia-
tions produce a slightly modified organism, which is better
adapted to its environment. The adaptation of such concepts
to the codification of possible variations of the backbone of
a synthetic target has led some groups of combinatorial
chemists to see them as pieces of a large puzzle that can in-
finitely re-arrange.[6] The possibility to mimic Natureꢀs ma-
chinery with evolutionary chemistry is an attractive ap-
proach, which allows transmitting only the most interesting
features during the optimization of a structure for a chosen
chemical or biological property.[7] This approach has been
investigated by several groups and designated as “directed
evolution”[8] or “simulated evolution”[9] depending on the
chosen pathway for the evolution process.
Scheme 2. Generation of a library of chiral catalysts from a metal precur-
sor and a chiral b-amino-alcohol ligand.
A set of 11 enantiopure b-amino alcohols (A1-A11) was se-
lected according to their commercial availability and/or sim-
plicity of synthesis (from the corresponding amino-acids),
and diversity in the substituent of the b-amino alcohol back-
bone (Scheme 3).[12]
We introduced the substituents on the nitrogen atom
through reductive alkylation involving various aldehydes
and ketones. The set of 30 carbonyl groups (B1–B30) selected
for this transformation is given in Scheme 4.
In this paper, we decided to apply the principle of simu-
lated evolution to a library of chiral catalysts that have been
used in asymmetric hydride transfer reduction of ketones
(Scheme 1), a reaction extensively explored by Noyori
et al.[10]
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Catalyst Library Evolution
FULL PAPER
amino-alcohol with 1 equivalent of the carbonyl compound
and 1 equivalent of acetic acid in methanol, which generated
a mixture of oxazolidine and imine. The cyanoborohydride
supported reagent was then added to reduce the intermedi-
ate oxazolidine. The alkylated ligand was released by addi-
tion of an excess of carbonate supported reagent, followed
by filtration and evaporation of the solvent (Scheme 5).
1
The purity of the 330 ligands was evaluated by H NMR
analysis of a statistical choice of molecules of the library
(see the Supporting Information, average purity: 76%). A
procedure for the formation of “in situ” catalysts was also
chosen by mixing the amino-alcohol ligands with six metal
precursors M1–M6 (Scheme 6). M1 and M6 were commercial-
ly available; M2, M3 and M4 were synthesized according to
literature procedures,[13] as well as for M5.[14]
Scheme 3. The set of b-amino alcohols from A1–A11.
Evaluation by high throughput experiments (HTE): The
combination of 330 chiral ligands and 6 metallic precursors
provided a library of 1980 catalysts. Each catalyst was tested
regarding the reduction of acetophenone by isopropanol in
the presence of potassium hydroxide by using high through-
put experiments (HTE). Reactions (Scheme 7) were carried
out in standard 2 mL glass vials under an inert atmosphere,
and all the operations were monitored by a robot (Gilson
215). The stock solutions of metal, ligands, acetophenone,
and KOH were freshly prepared before use and stored
under argon. Catalyst solutions were prepared by mixing
equimolecular amount of ligand and metal precursor solu-
tion (1:1 ratio, 1 mol% of metal loading), and the solutions
were aged for 30 minutes at room temperature. After injec-
tion of acetophenone, each reaction was initiated by injec-
tion of the KOH solution, with a total volume of 400 mL for
each vial (substrate concentration, 0.1m). Reactions were
performed for 90 minutes at room temperature under argon.
Each reaction was stopped by addition of aqueous ammoni-
um chloride solution and Et2O, which caused a phase sepa-
ration. We used an optimized pressure and temperature GC
program that allowed us to perform 20 analyses per hour.
For a given catalyst tested within specified conditions, gas
chromatography gave us direct access to the conversion rate
and the enantiomeric excess. Although optimization of these
two factors is required to develop a performing catalytic
system, genetic algorithms are usually designed for the opti-
mization of a single parameter. The weight attributed to the
conversion with respect to the ee could possibly be worked
out thanks to a desirability index,[15] but would not necessa-
Scheme 4. The set of carbonyl groups from B1–B30.
The reductive amination was
carried out by parallel liquid
phase synthesis using polymer
supported reagents in order to
speed up the synthesis of the
sub-library and to avoid purifi-
cation of each chiral ligand.
About 0.2 mmol of each ligand
was prepared by reaction of the Scheme 5. Preparation of a sub-library of chiral ligands AxBy.
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O. Riant, C. de Bellefon et al.
Figure 2. Definition of the normalized performance factor (NPF).
M3 and M6 displayed a weak activity, whereas those involv-
ing M5 were almost inactive.
The A1 and A7 series provided the best catalysts. Some
other series (A2, A3, A6, and A11) gave medium results.
Their conversion rates as well as their enantioselectivities
led to an NPF value typically around 0.55 (to be compared
to an NPF of 1 for the best catalyst). The average enantiose-
lectivity of the best catalysts of these series ranged from 50
to 65%. Here again, M3, M5, and M6 provided poorly active
catalysts. Most of the catalysts derived from the A4, A5, A8,
A9, and A10 series were almost inactive. The A5 series was
by far the worst one, the best catalyst being only associated
to an NPF of 0.06. Considering all the results, we identified
the best catalysts, which are listed in Table 1 with their relat-
ed NPF, conversion rate and enantioselectivity (for details
of the data of other catalysts, see the Supporting Informa-
tion). The three best structures, associated to the first line of
the table, are also shown at the bottom of the Table 1. The 9
first catalysts (NPF column) are linked to the highest con-
version rates, larger than 30%. Catalysts A7B4M1 and
A7B19M1 had the highest conversion rates of the library, up
to 61%. If we continued to explore this table until the
bottom of the library, we would find the first catalysts with
conversion rates lower than 20% and 10% at the 26th and
108th positions respectively. The ee of the best catalysts are
all higher than 83%, the best ones being very close to 90%.
Here again, would we descend the table, first catalysts with
enantioselectivity lower than 80% and 50% would be at the
26th and 93rd positions respectively.
Scheme 6. The set of metallic precursors from M1–M6.
Scheme 7. Enantioselective hydrogen transfer to acetophenone.
rily match with our desire, which is to give a priority to en-
antiomeric excess over the conversion rate of the reaction.
It was necessary to create a single parameter that accounted
for both conversion and enantioselectivity. Thus, for each
AxByMz catalyst, we calculated the value of a normalized
performance factor (NPF). The NPF is defined as the sum
of the enantioselectivity and twice the conversion rate, di-
vided by the sum of the enantioselectivity and twice the con-
version rate of the best catalyst of the library (Figure 2). A
catalyst NPF was thus com-
prised between 0 and 1.
Results: We first focus on the
results obtained with the A1
series, which provided some of
the best catalysts. The NPF ob-
tained with the 6 metallic pre-
cursors and some of the nitro-
gen substituents are depicted in
Figure 3. The NPF obtained
with M1, M2 and M4 are from
good to excellent, in particular
for the best catalyst of the
series, A1B19M2, whose struc-
ture is depicted in the inset of
the Figure 3. The NPF for
A1B19M2 was then 1, and result-
ed from a conversion rate of
36% and an enantioselectivity
of 73%. The catalysts involving Figure 3. NPF of the 180 catalysts from the A1 series.
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Catalyst Library Evolution
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Table 1. List of the 20 best catalysts.
quired for an accurate measure-
ment of the enantioselectivity.
Thus, when a conversion of less
than 5% was measured, the
enantioselectivity was assessed
to 0%. This Figure shows that
only about 40% of the whole li-
brary displays a catalytic activi-
ty. Although this could appear
at first sight as a poorly effec-
tive library, it seems especially
representative of what could be
expected from a large library of
chiral catalysts when evaluated
by optimizing a target reaction.
Entry
Performance
Conversion [%]
NPF
ee [%]
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
A1B19M2
A1B17M2
A1B4M1
A7B4M1
A7B19M1
A1B20M2
A1B11M2
A1B22M2
A1B15M2
A1B9M1
A1B20M1
A1B12M2
A1B12M1
A1B4M2
A1B4M4
A1B17M1
A1B11M1
A1B30M2
A1B3M4
A11B4M1
1.00
0.96
0.95
0.91
0.89
0.88
0.86
0.82
0.81
0.80
0.78
0.75
0.74
0.74
0.73
0.72
0.72
0.72
0.72
0.71
A7B4M1
61.5
56.0
43.9
38.2
37.9
36.4
36.3
35.7
35.5
27.5
26.2
26.2
25.8
24.9
24.8
24.7
24.1
22.2
22.0
21.9
A1B3M4
A1B11M3
A1B20M1
A1B11M4
A1B22M4
A1B4M4
A1B17M1
A1B24M4
A1B22M1
A1B11M1
A1B25M1
A1B4M1
A1B12M1
A1B5M1
A1B3M1
A1B17M4
A1B19M4
A1B19M1
A1B24M1
A1B15M1
88.9
88.5
88.3
88.2
88.1
88.1
88.0
87.2
86.7
86.6
86.5
86.5
86.2
86.1
86.1
85.7
85.6
85.5
84.9
83.3
A7B19M1
A7B8M1
A7B1M1
A7B6M1
A1B19M2
A1B17M2
A7B13M1
A7B3M2
A3B2M1
A1B20M2
A1B11M2
A1B4M1
A3B1M1
A1B22M2
A7B23M1
A1B15M2
A7B10M1
A3B3M4
A3B1M2
Simulated evolution: The main
goal of our study was to devel-
op a genetic algorithm (GA)
that reproduces an evolution
system and optimizes a small
collection of chiral catalysts
randomly chosen in a larger li-
brary. We used our collection of
HTE data to adjust the GA pa-
rameters, to obtain a maximum
of the best catalysts in a mini-
mal number of generations.
Starting from around 1% of the
A1B19M2
A7B4M1
A1B3M4
Attention can be paid to the constitutive building blocks
whole library, our method should avoid the use of expensive
HTS/HTE technologies and could be carried out using
simple laboratory techniques, as a limited number of cata-
lysts synthesis and following evaluations are required at
each generation. Moreover, no molecular descriptors are
pre-required and a simple “genetic code” can be drawn
from the building blocks of our catalysts.
of the catalysts of the Table 1. An analysis of the structures
of the catalysts with the best conversion rates and enantiose-
lectivities reveals that A1 and M1 have a 67.5% and 57.5%
rate of occurrence respectively, which indicates that A1 and
M1 bear interesting features regarding the catalytic process.
Unfortunately, a similar trend could not be found for “B”
(carbonyl groups).
The principle of the genetic algorithm is depicted in
Figure 5. A set of catalysts (usually 24 catalysts) was consid-
The evaluation of the whole library is depicted in FigACHTUNTRGNEUNGure 4
in which the NPF values are listed in ascending order. The
figure shape clearly depicts a zone of inactivity of the cata-
lysts, or at best, rather poor activity, as well as a discontin-
ued line around 1600 evaluations. This discontinuity origi-
nates from an arbitrary threshold of 5% conversion re-
Figure 5. Principle of a genetic algorithm applied to a library of AxByMz
catalysts.
Figure 4. Classification of the NPF in ascending order.
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O. Riant, C. de Bellefon et al.
ered as the mother generation (G0), defined as the first gen-
eration from which the GA starts. The evolution process
usually stopped when about 200 HTE had been performed,
which corresponds to an evaluation of about 10% of the li-
brary. The evolution process between each generation con-
sisted in the application of three genetic operators
(Figure 5). The crossover operator (first operator) generated
two catalysts by rearranging two catalysts of the previous
generation. The mutation operator (second operator) pro-
duced new catalysts by a random variation of one of the
three components of the catalysts. The evolution ended with
the replication operator, which kept the best catalysts
throughout the evolution process.
for transmitting the unmodified catalysts to the next genera-
tion, and the evolution process was resumed. Two additional
features of the GA should be noted. First, the algorithm
could detect a catalyst that already had been proposed; in
this case, the GA searched for another catalyst. Second, the
GA generated a minimum of six new combinations per evo-
lution loop, which corresponds to a feasible number of cata-
lysts synthesis and subsequent evaluation by the chemist.
The following parameters of the GA were adjusted for
optimization of the evolution process:
G0: Mother generation. This set of catalysts was chosen
either randomly or by the chemist.
The Figure 6 depicts the building of the genetic algorithm
(GA) and the iterative loop associated to the evolution pro-
cess. The GA started by creating a mother generation,
R: Size of each generation of catalysts. The value of R was
24, 30, 36 or 48 (see below).
RE: Rate of exchange, or crossover rate. Since a crossover
step involved 2 catalysts, 2 RE new catalysts were generated
at this stage.
RM: Rate of mutation. RM new catalysts were produced at
each generation.
RR: Number of catalysts which could be replaced during an
evolution loop. RR could be the number of catalysts gener-
ated by crossover and mutation; in this case, the new cata-
lysts replaced the poorest catalysts of the previous genera-
tion. RR could also be larger than the sum of 2 RE and
RM. In this case, the replacements occurred within the RR
poorest catalysts, with a higher probability for the worst cat-
alysts.
NI: Number of evolution loops in a completed evolution
process.
The genetic algorithm was programmed using the R 2.6.1
software available for free from the R Foundation for Statis-
tical Computing.[16] The first step was to create the table of
catalysts, described by their respective genetic code. This
table was linked to a second table containing the NPFꢀs of
each catalyst. For the second step, the parameters of the
GA were written in R 2.6.1 code.[17] The implementation of
the GA resulted in an evolution process throughout our li-
brary of asymmetric catalysts. Thus, the goal was to use our
collection of data to simulate the evolution of sub-libraries
of catalysts, trying to improve the efficacy of our catalysts
from generation to generation.
Figure 6. Building the genetic algorithm.
which was extracted from the whole library either randomly
or by the chemist. Each catalyst of the whole library was as-
sociated to an NPF. Each catalyst of the mother generation
was weighted by its NPF, allowing the GA to order the cata-
lysts from the worst (smallest NPF) to the best one (highest
NPF). The high-ranked catalysts were selected with a higher
probability for crossover operation. Then the GA applied
the mutation step, randomly within the generation. Both
crossover and mutation rates could be specified, as ex-
plained below. After the crossover and mutation steps, some
of the mother generation catalysts were replaced by new
catalysts, the lowest NPF catalysts having a highest probabil-
ity of being replaced. The replication step was then applied,
Selection of the mother generation (G0): We first consid-
ered simulated evolutions in which G0 was randomly ex-
tracted from the whole library. To obtain a statistically reli-
AHCTUNGTREGaNNNU ble result, 20 simulations were performed for each set of
catalysts. The GA was first implemented with the following
parameters: R=24; RE=3; RM=2; RR=16; NI=20. The
results of a typical simulation are depicted in Figure 7
wherein every dot stands for a generation. The Figure 7A
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Catalyst Library Evolution
FULL PAPER
(lower curve) gives the mean
catalyst NPF value as a func-
tion of the number of evaluated
catalysts (HTE), and the evolu-
tion of the mean NPF value of
the 10 best catalysts of a given
generation (Figure 7A, upper
curve). 176 HTE were carried
out within 20 evolution loops,
that is, 24 HTE for the mother
Figure 8. Selection of the G0 members.
ketones, aromatic aldehydes and aromatic aldehydes with a
potentially coordinating heteroatom. Finally, the associated
metal precursors (M) were split into two groups: the four
[RuCl2ACTHNUGTRNE(UNG arene)]2 and the two remaining complexes. The re-
sulting combinations were supposed to maximize the chemi-
cal diversity in a mother generation of 24 catalysts.
This mother generation was submitted to the GA, which,
however, was unable to perform a single evolution loop be-
cause most of the catalysts were associated to a null NPF.
Therefore the GA was unable to decide which catalysts of
G0 had to undergo crossover and mutation steps. Neverthe-
less, by randomly choosing the B and M building blocks as-
sociated to A3, A5 and A7, the GA was capable to complete
the evolution process.
We compared the results of two sets of 20 evolutions
starting from either random or partially-selected mother
generation. For this purpose, five parameters were evaluat-
ed:
1) The mean number of top 10 catalysts found at the end of
the evolutions (mean top 10).
2) The mean number of tests (MNT), which were required
to find one of the ten best catalysts. The MNT can be
considered as a measure of the speed of the evolution
process to create a catalyst from the top 10, even if the
lower the MNT, the faster the evolution creates catalysts
from top 10.
3) The standard deviation of the MNT (sMNT).
4) The occurrence of the best catalyst structure (A1B19M2),
given in percent.
5) The percentage of evolutions that were unable to find
any of the top 10 catalysts (no top 10).
Figure 7. Simulated evolution with random G0. GA parameters: R=24;
RE=3; RM=2; RR=16; NI=20.
Results are given in Table 2.
generation and 8 HTE per evolution loop. The performance
of an evolution process can also be estimated by considering
the number of created catalysts that are in the top 10 list of
the entire library (Figure 7B).
The highest number of best catalysts was obtained from
simulations starting from random mother generations, which
also triggered the lowest MNT, meaning the highest evolu-
Alternatively, we directly selected the mother generation.
We choose to introduce chemical diversity in G0, assuming
that it would be a prerequisite for successful evolutions. We
divided the constitutive catalysts building blocks (A, B, and
M) into families (Figure 8). We selected the b-amino alco-
hols A3, A5 and A7 as representatives of three chemical fam-
ilies. Each amino-alcohol (A) was combined with carbonyl
groups (B) randomly selected among aliphatic aldehydes,
Table 2. Comparison of two sets of evolutions with random or selected
G0.
G0
Mean top 10 MNT[b] sMNT A1B19M2 [%] no top 10 [%]
random[a] 3.8
selected[a] 2.7
62
79
56
54
35
30
35
30
[a] Results given for 20 simulated evolutions in every set. [b] The lower
the MNT, the faster the evolution is.
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O. Riant, C. de Bellefon et al.
tion speed. The standard deviations of the MNTꢀs were high
and rather similar, as well as the occurrence of A1B19M2 and
the percentage of evolutions without top 10 catalysts. Thus,
a random choice of the mother generation is statistically
more efficient than trying to guess a “right” G0.
Influence of the parameters of the genetic algorithm: We in-
vestigated the effect of the cross-over (RE) and mutation
(RM) rates on the GA performance, the mother generation
being randomly chosen and the size R of the generation
being fixed. Since a minimum rate of mutation was necessa-
ry for introducing novelty, we first considered evolutions
that involved only one mutation (RM=1) and crossover
rates RE ranging from 1 to 4. We performed 10 evolutions
for each RE value, and noticed only a slight increase of the
GA performance with increasing RE. We then considered
evolution processes with RE=1 and RM=2, 4, 6 and 8, and
for each value of RE we performed 10 evolutions. Increas-
ing RM affected the GA performance only slightly. For in-
stance, the mean number of top 10 catalysts for RM=2 and
RM=8 was 1.4 and 2.4 respectively, whereas the MNT was
53 and 101 respectively, in both cases with a large standard
deviation (sMNT of 29 and 80 respectively). These results can
be understood by considering that, at low cross-over rate, a
novelty introduced by a mutation has a low probability of
being transmitted, because the probability of being replaced
by next mutations before rearrangement is high.
We also performed simulated evolutions in which the
preference was given to either crossover, with RE=4 and
RM=2, or mutation, with RE=2 and RM=4. Since such
rates could enable the GA to find more catalysts from the
top 10, we increased the size of the mother generation G0
from 24 to 30, in order to be sure that the top 10 catalyst
found by the GA were preserved during the evolution pro-
cess. The number of required tests was thus increased to
220. Both evolutions provided similar results (Table 3). In
particular, the MNT does not depend on the RE/RM ratio,
only sMNT is slightly reduced when the priority is given to
mutations.
Figure 9. Simulated evolution with high crossover and mutation rates.
GA parameters: R=30; RE=4; RM=8; RR=20; NI=19.
Table 4. Set of evolution with high crossover and mutation rates.
Preference
Mean
top 10
MNT[b] sMNT A1B19M2 no top
[%]
10 [%]
high RE and high RM[a] 5.7
59
22
70
0
[a] Results given for 10 simulated evolutions in every set. [b] The lower
the MNT, the faster the evolution is.
Table 3. Comparison of two sets of evolutions with preference to either
crossover or mutation rates.
evolutions. In most cases, however, the mean NPF remained
rather low (Figure 9 A, lower curve) as expected with so
high perturbation rates, when the mean NPF value of the 10
best catalysts of a given generation (Figure 9A, upper curve)
kept rising. Thus, high perturbation rates promoted the find-
ing of top 10 catalysts rather than an increase of the mean
NPF. The number of required test was also largely in-
creased, and 344 evaluations were necessary to drive each si-
mulated evolution.
We also modified the number of catalysts, which were re-
placed at each generation (RR). As explained before, the
smaller RR, the more the replacements happened within
the less competitive catalysts. Ten evolution processes were
performed for RR=6, 12 and 18. The cross-over and muta-
tion rates were RE=2 and RM=2, and the mother genera-
Preference
Mean
top 10
MNT[b]
sMNT
A1B19M2
[%]
no top 10
[%]
crossover (RE)[a]
mutation (RM)[a]
2.4
2.6
100
79
73
43
15
15
10
0
[a] Results given for 20 simulated evolutions in every set. [b] The lower
the MNT, the faster the evolution is.
We also addressed the impact of both high crossover and
mutation rates. Ten simulated evolutions were performed
with RE=4 and RM=8 in order to estimate the effect of
these large rates on the 24 members of the mother genera-
tion. As shown in Figure 9 and Table 4, the GA performance
was increased. The mean number of top 10 catalysts was 5.7,
the MNT was 59, and A1B19M2 was found in 70% of the
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Chem. Eur. J. 2009, 15, 6267 – 6278

Catalyst Library Evolution
FULL PAPER
tion G0 was randomly selected. Simulated evolution results
were not affected by RR variations (data not shown). The
explanation lies on the size of replacement space compared
to the proportion (about 20%) of the library that contains
moderate to efficient catalysts (Figure 4). One can assume
that a randomly selected G0 contains the same proportion
of efficient catalysts. The maximum size of the replacement
space we tested corresponds to RR=18, that is, a replace-
ment space of 75% of each generation. Since an influence
of RR on the first evolution loops is expected only if RR is
larger than 80% of the G0 size, simulated evolution results
were therefore not affected by RR variations. It also implies
that the algorithm should be robust with regards to RR var-
iations during the next evolution loops.
At last, we studied the effect of the size of the mother
generation G0. We expected that increasing the size of G0
would incorporate more chemical diversity and thus increase
the GA performance, in the cost of more HTE required at
each generation. The G0 sizes we implemented were 24, 36
and 48, the catalysts being randomly selected. Taking into
account the lack of influence of the RR variations on the
GA performance, we selected a maximum RR (14, 26 and
38 respectively, so the 10 best catalysts could eventually be
recovered and kept throughout the simulated evolution ex-
periments). Finally, NI was set to 40 to bring to light any
generation size effect. The mutation and crossover rates
were RE=2 and RM=3. To our surprise, the size of G0 did
not seem to have any influence on the GA performance
(Table 5). The MNT was unaffected by G0 size variations, as
learned from former simulations that it is advantageous to
start with a randomly selected mother generation. On the
other hand, this first generation could contain only ineffi-
cient catalysts, which can seriously impede the evolution
process, as demonstrated previously when we selected the
mother generation.
The efficiency of an optimization process is thus directly
linked to the quality of the mother generation. But we also
know, since we evaluated the whole library, that it contains
about 75% of inefficient catalysts. The probability P that n
members of G0 originate from this zone of inactivity can be
approximated by Equation (1).
ꢀ
ꢁ
n
m
N
Pðc ¼ nÞ ¼
ð1Þ
In which N is the total number of catalysts and m the
number of catalysts in the zone of inactivity. For the library
(m/N ꢀ0.75), the probability that the mother generation
contains only inefficient catalysts is thus P
N
Even if this probability is low, we have already shown that a
simulated evolution starting from such a mother generation
is unsuccessful. We forced the GA to select G0 randomly,
but solely from the zone of inactivity, that is, catalysts built
with A1, A7 and A11 were excluded from G0. The GA pa-
rameters were RE=2, RM=3 and RR=14. In addition, the
GA could perform a maximum of 199 evaluations, which is
close to 10% of the library. As shown in Figure 10, the per-
formance of the GA was low: first generations were associ-
ated to small NPF and only two of top ten catalysts were
found.
Table 5. Variation of the size of G0.
To incorporate more chemical diversity and thus to im-
prove the performance of the evolution process, one could
increase the number of catalysts in the mother generation,
from 24 to 48 for instance. However, it would prevent the
GA from meeting our requirement of 10% catalysts to be
tested. One could also increase RE and RM, but we have
shown that only 3 catalysts from top 10 were found within
the 200 first experiments (3ꢀ5.7*(200 HTE/340 HTE),
Table 4) which is a rather low improvement.
To deal with simulated evolutions that could start from a
mother generation containing only inefficient catalysts, we
developed a double algorithm (DA) which was evaluated by
simulated evolution. The first step of this algorithm consist-
ed in turning G0 into G1 using 14 mutations. Thus, the 10
best catalysts from G0 were transmitted to G1, and the
other catalysts underwent a mutation, which introduced
more chemical diversity in the mother generation. After this
high-mutation-rate step, the probability that all catalysts
from G1 came from the inefficient part of the library dra-
matically decreased to about 0.001%, that is, a very small
probability. We then applied to G1 the “common” algorithm
with RE=2 and RM=3 for the next 23 generations and for
a total of 199 evaluations (including the 14 tests necessary
for the G0–G1 high-mutation step). As depicted in
Figure 11, the results of the GA were significantly improved:
the mean NPF was increased, as well as the number of top
Size of G0
Mean top 10
MNT[b]
sMNT
A1B19M2 [%]
24[a]
36[a]
48[a]
6.5
6.5
6.1
40
41
48
14
9
15
90
80
70
[a] Results given for 10 simulated evolutions in every set. [b] The lower
the MNT, the faster the evolution is.
well as the number of top 10 recovered catalysts, which nev-
ertheless was more than doubled due to a larger NI. Thus, a
mother generation of 24 catalysts was sufficient to find the
best catalysts. The simulated evolution processes performed
with these RE and RM intermediate values provided good
results. Finally, the size of G0 might have more influence on
simulated evolution performed within a larger library, as a
G0 of 24 members, that is, more than 1% of this library, is
still a large mother generation. Note that each simulation
process led to at least one catalyst from the top 10, which
gives the reason why the column dedicated to processes
with zero top 10 catalysts is no longer presented.
Simulated evolution with a double algorithm (DA): We now
address a real case of optimization as must be managed by a
simulated evolution process: The whole library can surely
be pictured by the chemist, but only a few catalysts would
really be synthesized and evaluated. On one hand, we
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6275

O. Riant, C. de Bellefon et al.
Figure 11. Simulated evolution starting from random G0 taken in the in-
activity zone and using a double algorithm (DA). 1st GA parameters:
R=24; RE=0; RM=14; RR=14; NI=1. 2nd GA parameters: R=24;
RE=2; RM=3; RR=14; NI=23.
Figure 10. Simulated evolution starting from random G0 taken in the in-
activity zone. GA parameters: R=24; RE=2; RM=3; RR=14; NI=25.
10 catalysts. The introduction of new catalysts by mutation
was thus sufficient to ensure a successful evolution process.
The table 6 summarizes the results obtained with/without
the double algorithm. When the high-mutation step was not
applied to the mother generation randomly selected among
the zone of inefficiency (entry 1, Table 6), the mean number
of top 10 catalysts was low, and the MNT depicted a slow
evolution process, whereas the associated sMNT reveals dis-
similar behaviors throughout evaluations. When the double
algorithm was applied to the same mother generation
(entry 2, Table 6), the performance of the GA was quantita-
tively enhanced: on average more than five catalysts from
top 10 were found, the process was almost three times
faster, with a MNT of 36, roughly constant throughout eval-
uations, as demonstrated by the value of sMNT. Moreover,
A1B19M2 was found for 70% of the evolutions. Finally, we
compared the results obtained from a double algorithm
starting either from the zone of inefficient catalysts or from
a G0 randomly selected amongst the whole library (entry 3,
Table 6). Comparison of the data shows similar performan-
ces, which confirms the efficiency of the double algorithm
technique.
Table 6. Comparison of sets of evolutions made without and with DA.
Entry G0
DA Mean top 10 MNT[b] sMNT A1B19M2 [%]
1[a]
2[a]
3[a]
G0 from z.i.[c] no 2.1
99
36
40
55
9
14
10
70
90
G0 from z.i.[c] yes 5.2
random G0[d] yes 6.5
[a] Results given for 10 simulated evolutions in every set. [b] The lower
the MNT, the faster the evolution is. [c] G0 randomly selected among cat-
alysts from the zone of inefficiency. [d] G0 randomly selected among the
library.
Conclusion
In this study, we developed a genetic algorithm that mimics
an evolution process. This algorithm was devoted to the cre-
ation of the best catalysts within a library designed for the
asymmetric-hydrogen transfer to acetophenone. To both val-
idate and optimize our algorithm, we considered a library of
1980 catalysts that were evaluated by HTE, and from which
we found out the 10 best catalysts. Our genetic algorithm
was able to find most of these best catalysts evaluating only
10% of the whole catalyst library.
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Catalyst Library Evolution
FULL PAPER
the reaction, and Et2O was added to the mixture. Chemical analysis of
the reaction mixture was performed by gas chromatography.
The algorithm gave the best results when the mother gen-
eration was randomly chosen. The results of the simulated
evolutions were found to be only slightly affected by varia-
tions of the algorithm parameters (size of the mother gener-
ation, mutation and cross-over rates, number of evolution
loops…). Those results also show that the algorithm intro-
duced enough chemical diversity during the evolution pro-
cess. For a mother generation of 24 catalysts, however, the
best results were obtained with crossover and mutation rates
of 2 and 3 respectively. Using these values, the algorithm
was typically able to find 3–5 catalysts of the top 10, the
number of catalysts to be synthesized and evaluated ranging
from 176 to 350.
Acknowledgements
The “Fonds pour la formation ꢆ la Recherche dans l’Industrie et dans
l’Agriculture” (FRIA) from Belgian government is gratefully acknowl-
edged for their financial support of this research. The authors also want
to thank the “R Foundation for Statistical Computing” for the free use of
the R 2.6.1 software. Dr Pierre Desbiolles is also gratefully acknowledged
for help with the corrections of the manuscript.
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lytic enantioselective reactions.
Experimental Section
General procedure of the AxBy ligand synthesis: To a solution of amino-
alcohol Ax (0.2 mmol, 1 equiv) and aldehyde (2 mmol, 1 equiv) in 2 mL
of MeOH was added AcOH (0.012 mL, 0.2 mmol, 1 equiv). The reaction
mixture was stirred and heated to reflux for 4 h. Resin supported BH3CN
(1.5 equiv) was then added and reflux continued for 15 h with occasional
orbital stirring. Resin supported CO3 (1.1 equiv) was finally added, and
reflux continued for an additional 4 h. The reaction mixture was then fil-
trated and supported reagents washed with 3 mL of a hot solution of
MeOH/CH2Cl2 (1:1). The solvents were evaporated under vacuum and
1
the mixture analyzed by H NMR.
General procedure of the AxByMz catalyst evaluation: Into a vial flushed
with Ar and capped with a Teflon system was injected 4ꢅ10ꢁ7 mol
(0.01 equiv) of metal precursor Mz (diluted in isopropanol/cosolvent: 3:1)
directly followed by injection of 4ꢅ10ꢁ7 mol (0.01 equiv) of the chiral
ligand AxBy diluted in isopropanol. 30 minutes later, acetophenone (4ꢅ
10ꢁ5 mol, 1 equiv) diluted in isopropanol was added to the preformed cat-
alyst solution, directly followed by injection of 4ꢅ10ꢁ6 mol (0.1 equiv) of
KOH in isopropanol. The reaction was allowed to progress for 90 mi-
nutes at room temperature. The addition of saturated NH4Cl quenched
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Received: October 23, 2008
Published online: May 12, 2009
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