Use of Boolean and fuzzy logics in lactose glycocluster research

Article abstract of DOI:10.1039/c3cc44615h

Fuzzy logic systems can be exploited for defining the degrees of true or false binding between calcium mediated multivalent lactose and peanut agglutinin lectin, which are difficult to define with Boolean logic.

Full text of DOI:10.1039/c3cc44615h

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Use of Boolean and fuzzy logics in lactose glycocluster
research†
Cite this: Chem. Commun., 2013,
49, 9185
Harikrishna Bavireddi,z Priya Bharatez and Raghavendra Kikkeri*
Received 19th June 2013,
Accepted 7th August 2013
DOI: 10.1039/c3cc44615h
www.rsc.org/chemcomm
Fuzzy logic systems can be exploited for defining the degrees of
The experimental setup was based on a newly synthesized
true or false binding between calcium mediated multivalent lactose lactose-modified b-cyclodextrin (1) and the two glycodendrimers
and peanut agglutinin lectin, which are difficult to define with (2 and 3), which were prepared by exploiting the tendency
Boolean logic.
of adamantane and benzene to form stable complexes with
b-cylodextrin and its derivatives used as the ‘hosts’ in complexes
Carbohydrate–protein interactions (CPIs) play a crucial role in 2 and 3 with compounds 4 and 5, respectively, used as the
many biological events, such as cell–cell adhesion, proliferation, ‘guests’ (Fig. 1A). The syntheses of compounds 1 and 2 were
bacterial and viral infections.1 Since CPIs in normal and malignant described previously.6 Compound 4 was prepared by reacting the
cells differ significantly, it is crucial to understand them both dichloride of ferrocene dicarboxylic acid, prepared by reaction
qualitatively and quantitatively.2 A variety of techniques, such as with oxalyl chloride, and adamantyl 20-amino-b-alanine amide
surface plasmon resonance (SPR), microarray, quartz crystal (Fig. 1B). Complexes 2 and 3 include guest molecules having azo
microbalance (QCM), and enzyme-linked immunosorbent assay and ferrocene templates. The glycodendrimers were used as
(ELISA),3 were used for analyzing these interactions. All methods active components for the performance of logic operations and
require expensive instruments, laborious experiments and extensive for construction of truth tables based on chemical inputs. PNA
technical expertise. Recently, Boolean logic (BL)4 was used for lectin, which recognizes lactose specifically,7 and calcium ions,
real-time and straightforward analysis of CPIs to select the best
scaffolds for specific interaction and also for sensing processes.5
Although the BL model is simple and very effective in differentiating
true and false interactions, it is not adequate for describing
fine-tuned systems and degrees of truthfulness. The fuzzy logic
system (FLS) is a superset of BL extended to characterize
partially true values between completely true (1) and completely
false (0). It is one of the automatic fine-tuning control systems
that can handle several middle steps and define degrees of
truth. It stems from the notion that human reasoning and
decision making is too complex to be precisely defined.
We have applied BL and FL for optimization of CPIs
mediated by Ca2+ ions, with emphasis on the multivalent ionic
interactions between lactose, appended on a b-cyclodextrin
skeleton, and peanut agglutinin (PNA) lectin. We have compared
the two methods and concluded that the logic operation of FL is
more appropriate for analyzing CPI than BL.
Indian Institute of Science Education and Research, Pune 411021, India.
E-mail: rkikkeri@iiserpune.ac.in; Fax: +91-20-25899790; Tel: +91-20-25908207
† Electronic supplementary information (ESI) available: The synthesis of 3 and
Fig. 1 (A) Structures of lactose glycodendrimers (2 and 3); (B) schematic
additional spectral data. See DOI: 10.1039/c3cc44615h
‡ Equal contribution.
diagram of the mechanism of interactions.
c
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which interact with lactose, were used as input signals.8
Isothermal titration calorimetry (ITC), used to determine the
thermodynamic parameters of interactions in solution, was utilized
for measuring the association constants between PNA lectin and
compounds 2 and 3 that were used as output.
For demonstrating the use of the operation AND gate in
Boolean logic, PNA lectin and Ca2+ ions, separately or in a
mixture, were titrated with the glycoclusters 2 and 3 and the
process was followed by ITC. The binding processes are accom-
panied by release of heat and typical isotherms were recorded.
Based on the qualitative assessment, the isotherms were fitted
to a model containing one set of binding sites. ‘N’ values
represent the number of carbohydrates on the glycoclusters
that are available for binding to PNA lectin or to the Ca2+ ions
and ‘K’ represents the formation constants. (Table 1) For
complex 2, the best fit was obtained for ‘N’ values of E21
and E232 for Ca2+ and PNA, respectively. Since the CCIs are
weak, addition of Ca2+ ions resulted in weak binding affinity
(115 Mꢀ1) (Fig. 2a). For PNA lectin interactions, a significant
increase in the binding affinity of 2 as compared to CCIs (3.18 ꢁ
106 Mꢀ1) was observed (Fig. 2b). In the presence of both, Ca2+
ions and PNA lectin, the binding affinity was increased, ‘N’
value E334 (Fig. 2c), indicating that Ca2+ ions not only assist
lectin amino acids in positioning for achieving maximum
binding, but also induce inter/intra CCIs and increase the
number of binding sites. By setting the binding affinity of CPIs
in the presence of Ca2+ ions as the threshold level (red line
Fig. 3a), 2 exhibited the behavior of the AND logic; in the
presence of a single input signal ((1.0) and (0.1)), 2 displayed a
low output or no binding at all (0) while with both inputs high
Fig. 3 (a) Boolean logic: if binding affinity Z 9 ꢁ 106 Mꢀ1, it is specific CPI (1 or
true) and if binding affinity r 9 ꢁ 106, it is not specific CPI (0 or false). (b) Truth
table.
(1, 1) the output is high and represents binding (1). The truth
table is presented in Fig. 3b. A major limiting feature of BL is
that the values 0 and 1 are mutually exclusive and it is not
possible to define a transition from one state to the other, i.e.,
‘non-binding’ to ‘binding’, by considering a single value. This
limitation is overcome by using the fuzzy logic systems (FLSs)
for presentation.
FLS can be defined as the nonlinear mapping of an input
dataset to a scalar output data. The parameters obtained from
the ITC measurements, which reflect the degrees of interaction,
were used for the construction of a fuzzy subset. They have
degrees of membership ranging between 0 and 1. A subset of
‘strong binding’, defined in the following way, was used as the
‘rule base’.
Strong binding (x) = {0, if DK r 1 ꢁ 106
M
ꢀ1; 0–1 if 1 ꢁ
106 o DK r 9 ꢁ 106 Mꢀ1, 1 if DK Z 9 ꢁ 106 Mꢀ1
}
Based on this definition we have built the truth table
(Fig. 4b) from which we conclude that PNA lectin binding to
2 is ‘35% strong binding’. Similarly, from the experiment with 3
we received the value 0.28, which is also found to be ‘strong
binding’.
Table 1 Thermodynamic parameters of cis–trans isomers in 2 measured by
isothermal titration calorimetry; N = 1/n
From the above presentation it seems clear what the statement
‘degree of strong binding’ means. In order to interpret ‘weak’,
‘medium’ and ‘strong’ binding affinities in fuzzy linguistic terms,
we have performed a set of operations (union, intersection and
complement). ‘Intersection’ and ‘union’ are defined as minimum
and maximum of two interactions and ‘complement’ is defined as
the negation of specific interaction. Using these operations, fuzzy
sets (weak, medium and strong binding) are constructed in which
‘weak binding’ is defined for systems of binding affinity (x) =
{1 (FL) or 0 (BL), if (DK) r 200 Mꢀ1 and gradient binding (0–1)
(FW) between 200 Z DK r 250 Mꢀ1}. ‘Medium binding’ affinity
is defined as (y) = {0–1, if 100 Z DK r 250 Mꢀ1 (SM) or 1 ꢁ
Binding
DH
Ligand
n
N
constant (Mꢀ1
)
(Kcal molꢀ1) 106
2 & Ca2+
2 & PNA
E0.047 E21 115 ꢂ 23.0
ꢀ3.43 ꢂ 0.81
E0.0043 E232 3.18 ꢂ 0.79 ꢁ 106 ꢀ0.71 ꢂ 0.005
2 & Ca2+ & PNA E0.003 E334 9.12 ꢂ 4.87 ꢁ 106 ꢀ0.37 ꢂ 0.002
3 & Ca2+
3 & PNA
E0.041 E24 178 ꢂ 21.7
ꢀ1.79 ꢂ 0.9
E0.005 E200 2.59 ꢂ 0.37 ꢁ 106 ꢀ0.768 ꢂ 0.009
3 & Ca2+ & PNA E0.002 E500 13.7 ꢂ 1.13 ꢁ 106 ꢀ0.32 ꢂ 0.027
106 Z DK r 9 ꢁ 106 Mꢀ1(FM); 1, if 250 Z DK r 1 ꢁ 106 Mꢀ1
}
Fig. 2 ITC profile for 2 in H2O with CaCl2, PNA and both, PNA + CaCl2 at 298 K.
Top panels represent the energy (mcal sꢀ1) required to maintain isothermal
conditions with respect to the reference cells and lower panels represent the
heat evolved from each injection per mole of Ca2+ versus the molar ratio of
(a) conc of 2 = 0.05 mM and CaCl2 solution = 20 mM; (b) conc of 2 = 0.05 mM and
PNA = 0.01 mM (c) conc of 2 = 0.05 mM, CaCl2 = 20 mM PNA = 0.01 mM in
phosphate buffer pH 7.4.
Fig. 4 (a) Fuzzy logic of strong binding. (b) Truth table.
c
9186 Chem. Commun., 2013, 49, 9185--9187
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R.K, H.B and P.B are thankful to IISER, Pune, the Indo-
German (DST-MPG) program and DAE (Grant No. 2011/37C/20/
BRNS) and CSIR, India for financial support. We thank Dr Rina
Arad Yellin for critically reviewing the manuscript.
References
1 (a) R. A. Dwek, Chem. Rev., 1996, 96, 683; (b) C. R. Bertozzi and
L. L Kiessling, Science, 2001, 291, 2357; (c) A. Dove, Nat. Biotechnol.,
2001, 19, 913; (d) K. Drickamer and M. E. Taylor, Annu. Rev. Cell Biol.,
1993, 9, 237; (e) F. T. Liu, Clin. Immunol., 2000, 97, 79; ( f ) K. N.
Konstantinov, B. A. Robbin and F. T. Liu, Am. J. Pathol., 1996, 148, 25;
(g) K. T. Pilobello, D. E. Slawek and L. K. Mahal, Proc. Natl. Acad. Sci.
U. S. A., 2007, 104, 11534; (h) H. Lis and N. Sharon, Chem. Rev., 1998,
98, 637.
2 (a) R. Kikkeri, L. H. Hossain and P. H. Seeberger, Chem. Commun.,
2008, 2127; (b) J. L. De Paz, C. Note, F. Boehm, S. Werner and
P. H. Seeberger, Chem. Biol., 2007, 14, 879; (c) M. D. Disney,
J. Zheng, T. M. Swager and P. H. Seeberger, J. Am. Chem. Soc., 2004,
126, 13343; (d) P. Laurino, R. Kikkeri, N. Azzouz and P. H. Seeberger,
Nano Lett., 2011, 11, 73; (e) R. Kikkeri, P. Laurino, A. Odedra and
P. H. Seeberger, Angew. Chem., Int. Ed., 2010, 49, 2054.
Fig. 5 FLS rules: DK r 250 Mꢀ1 – weak interaction, 100 r DK r 9 ꢁ 106 Mꢀ1
–
medium interaction and for DK Z 1 ꢁ 106 Mꢀ1 – strong binding. SM (slightly
medium); TW (true weak); SS (slightly strong); FM (fairly medium); FW (fairly
weak); (b) truth table.
`
¨
3 (a) S. Andre, Z. Pei, H.-C. Siebert, O. Ramstrom and H.-J. Gabius,
Bioorg. Med. Chem., 2006, 18, 6314; (b) X. Wang, E. Matei,
¨
A. M. Gronenborn, O. Ramstrom and M. Yan, Anal. Chem., 2012,
84, 4248; (c) O. Norberg, L. Deng, T. Aastrup, M. Yan and
¨
O. Ramstrom, Anal. Chem., 2011, 83, 1000; (d) T. Horlacher and
P. H. Seeberger, Chem. Soc. Rev., 2008, 37, 1414; (e) J. L. de Paz and
P. H. Seeberger, Methods Mol. Biol., 2012, 808, 1; ( f ) E. M. Munoz,
J. Correa, R. Riguera and E. Fernandez-Megia, J. Am. Chem. Soc., 2013,
135, 5966; (g) E. M. Munoz, J. Correa, E. Fernandez-Megia and
R. Riguera, J. Am. Chem. Soc., 2009, 131, 17765.
finally, ‘strong binding’ (z) = {0–1, if 1 ꢁ 106 Z DK r 9 ꢁ
106 Mꢀ1; 1, if DK Z 9 ꢁ 106 Mꢀ1}. The FLS that characterizes
specific CPIs of 2 is presented in Fig. 5a. The red vertical line
represents the Ca2+ binding of 2 ({1, 0}) with binding affinity
115 Mꢀ1 and three degrees of interaction. The pointing of the
red arrow to zero may be interpreted as ‘no-binding’ or low
output (0) (as in BL). The black arrow (pointing to 0.11) may be
described as ‘slightly medium (SM) binding’ and light blue
arrow (pointing to 1.0) – ‘true weak (TW) binding’. In general,
Ca2+ ions mediated interactions can be considered as real
values, ranging from 0 to 1, with three degrees of weak inter-
actions. Similarly, PNA lectin interactions with 2 (green vertical
line) again displayed three degrees of medium interaction. The
red arrow indicates ‘no-binding’ and black arrow (pointing to
0.35) may be described as ‘slightly strong (SS) binding’. The
light blue arrow at 0.74 indicates ‘fairly medium (FM) binding’.
Similarly, the black line ({1, 1}) represents ‘strong binding’ or
output 1. Similarly, the experiment with 3 showed three degrees
of interactions.
4 (a) A. P. de Silva, H. Q. N. Gunaratne and C. P. A. McCoy, Nature, 1993,
364, 42; (b) A. Credit, V. Balzani, S. J. Langford and J. F. Stoddart,
J. Am. Chem. Soc., 1997, 119, 2679; (c) A. P. de Silva and
N. D. McClenaghan, Chem.–Eur. J., 2002, 8, 4935; (d) D. Margulies,
G. Melman, C. E. Felder, R. Arad-Yellin and A. Shanzer, J. Am. Chem.
Soc., 2004, 126, 15400; (e) D. Margulies, G. Melman and A. Shanzer,
Nat. Mater., 2005, 4, 768; ( f ) G. de Ruiter, L. Motiei, J. Chowdhury,
N. Oded and M. E. van der Boom, Angew. Chem., Int. Ed., 2010,
49, 4780; (g) G. de Ruiter, E. Tartakovsky, N. Oded and M. E. van der
Boom, Angew. Chem., Int. Ed., 2010, 49, 169; (h) T. Gupta and
M. E. van der Boom, Angew. Chem., Int. Ed., 2008, 47, 5322;
(i) P. Ceroni, G. Bergamini and V. Balzani, Angew. Chem., 2009,
121, 8668; ( j) B. Rout, L. Unger, G. HArmony, M. E. Iron and
D. Margulies, Angew. Chem., Int. Ed., 2012, 51, 12477; (k) Z. Li,
M. A. Rosenbaum, A. Venkataraman, T. K. Tam, E. Katz and
L. T. Angenent, Chem. Commun., 2011, 47, 3060; (l) M. A. Arugula,
D. Saffarini, E. Katz and Z. He, Chem. Commun., 2012, 48, 10174;
(m) M. Zhou, Y. Du, C. G. Chen, B. L. Li, D. Wen, S. J. Dong and
E. K. Wang, J. Am. Chem. Soc., 2010, 132, 2172; (n) T. K. Tam,
G. Strack, M. Pita and E. Katz, J. Am. Chem. Soc., 2009, 131, 11670;
(o) L. Amir, T. K. Tam, M. Pita, M. M. Meijler, L. Alfonta and E. Katz,
J. Am. Chem. Soc., 2009, 131, 826.
In this communication, we have introduced the use of the
two logic systems, FLS and BL, for presenting carbohydrate–
protein interactions in glycoclusters composed of multivalent
b-cyclodextrin appended with lactose molecules and peanut
agglutinin lectin. We compare between the two logic systems,
emphasize and demonstrate the preference of FLS over BL,
which describes only the two states 1 and 0. FLS provides a
real-time analytical tool for exploring these systems, and is
adequate for presenting transitions from one state to the other,
namely from ‘non-binding’ to ‘binding’ states. Degrees of
interactions between the glycoclusters and PNA lectin, with
and without calcium Ca2+ ions, were used as the linguistic
variables for the fuzzy logic sets. The association constants,
between these parameters, measured by ITC, were the output.
5 (a) R. Kikkeri, D. Grunstein and P. H. Seeberger, J. Am. Chem. Soc.,
2010, 132, 10230; (b) M. Elstner, K. Weisshart, K. Mullen and
A. Schiller, J. Am. Chem. Soc., 2012, 134, 8098; (c) W. Shi, X. Ji,
M. Wei, D. G. Evans and X. Duan, Langmuir, 2012, 28, 7119;
(d) B. K. Gorityala, Z. Lu, M. L. Leow, J. Ma and X.-W. Liu, J. Am.
Chem. Soc., 2012, 134, 15229.
6 H. Bavireddi, P. Bharate and R. Kikkeri, Chem. Commun., 2013,
49, 3988.
7 K.-R. Wang, H.-W. An, L. Wu, J.-C. Zhang and X.-L. Li, Chem.
Commun., 2012, 48, 5644.
8 (a) J. M. de la Fuente, P. Eaton, A. G. Barrientos, M. Menendez and
´
S. Penades, J. Am. Chem. Soc., 2005, 127, 6192; (b) A. J. Reynolds,
A. H. Haines and D. A. Russell, Langmuir, 2006, 22, 1156; (c) J. M. de la
´
Fuente and S. Penades, Glycoconjugate J., 2004, 21, 149;
(d) A. Carvalho de Souza and J. P. Kamerling, Methods Enzymol.,
´
2006, 417, 221; (e) M. Fuss, M. Luna, D. Alcantara, J. M. de la Fuente,
´
´
P. M. Enrıquez-navas, J. Angulo, S. Penades and F. Briones, J. Phys.
Chem. B, 2008, 112, 11595.
c
This journal is The Royal Society of Chemistry 2013
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