A Network of Networks to Reproduce the Electrical Features of an

Aptamer-ligand Complex

What an Electrical Network Tells about Affinity

Eleonora Alfinito

, Rosella Cataldo

and Lino Reggiani

Dipartimento di Ingegneria dell’Innovazione, Salento University, Lecce, Italy

Dipartiemnto di Matematica e Fisica “Ennio de Giorgi”, Salento University, Lecce, Italy

Keywords: Networks, Proteotronics, Aptamers, Aptasensors.

Abstract: The increasing interest in the production and selection of aptamers for therapeutic and diagnostic applications

yields many studies in recent years. Most of them investigated the production techniques, usually performed

in vitro, but also the possibility of an in silico selection. Due to their specific ability of target-inhibition, some

aptamers are under clinical trials, and some other were just patented by several pharmaceutical companies.

However, the mechanism of aptamer-ligand formation is not completely understood. In this paper we explore

the possibility to describe some topological and electrical features of the aptamer TBA alone and complexed

with thrombin, its specific ligand, by using a network consisting of two different networks. The results are

quite intriguing, confirming some conjectures about the different role of two cations, i.e. Na

and K

, in

stabilizing the compound. Furthermore, this study suggests the use of resistance measurements to discriminate

among different affinities.

1 INTRODUCTION

The current trend in medicine is the improvement of

prevention (vaccination, disease screening, correct

lifestyle, etc.), the personalization of treatments and a

less invasive and friendly (for example, point-of-care)

diagnostics. Accordingly, the development of new

techniques and therapies is widely explored.

Outstanding results are given by aptamers, which are

small fragments of ssDNA or RNA, artificially

produced to perfectly adapt to an assigned ligand

(from small molecules to large proteins).

The selection and amplification technique used to

produce aptamers is called SELEX (Systematic

Evolution of Ligands by EXponential Enrichment)

(Oliphant, 1989, Ellington, 1990, Tuerk, 1990). This

technique seems so powerful to produce, in principle,

an aptamer for each specific pathogen or

macromolecule found at the origin of a disease. It

could be a revolution in medicine.

In the last 20 years, big efforts have been devoted

to the production of even more efficient aptamers, by

using both biochemical and computational techniques

(Yüce, 2015, Jo, 2016). Some of them are at the

first/second stage of clinical trials, and this result

gives hope of a more and more massive use in

medicine (Ni, 2011).

The mechanism of ligand binding has been

compared to the structural recognition process used

by antibodies to capture antigens, therefore aptamers

are also known as “chemical antibodies” (Sun, 2014).

Like antibodies, they bind the target with high

specificity and selectivity and, therefore, this has

awakened a wide interest for the possible

technological uses. As a consequence, a rapid

development of aptasensors, i.e. sensors based on

aptamers (Iliuk, 2011) has taken place. Indeed,

aptamers are used in biosensors in substitution of

antibodies, which are, usually, more difficult to

produce and often require animal sacrifice. Despite

all the progresses made in the field of aptamer

production and selection, so as in the aptamer

technological and medical applications, the

understanding of the biochemical and physical

processes underling the aptamer/protein-ligand

interaction is still quite poor (Du, 2016).

In this paper we focus attention on the small 15-

mer TBA (5’-GGT TGG TGT GGT TGG-3` ), whose

ability in the inhibition of the enzyme thrombin is

well known. Thrombin is an enzyme present in

Alﬁnito, E., Cataldo, R. and Reggiani, L.

A Network of Networks to Reproduce the Electrical Features of an Aptamer-ligand Complex - What an Electrical Network Tells about Afﬁnity.

DOI: 10.5220/0006361000620069

In Proceedings of the 2nd International Conference on Complexity, Future Information Systems and Risk (COMPLEXIS 2017), pages 62-69

ISBN: 978-989-758-244-8

mammals blood where rules coagulation. Therefore,

in some diseases, like heart attack, its inhibition is

part of the therapy. TBA passed the first step of the

clinical trials; at present, a modified version of this

aptamer, which ensures a longer permanence in

human body, has been patented and is currently used

in clinics.

Recently, TBA has been successfully used in a

prototype of thrombin sensor (Cai, 2005). This device

is sensitive to thrombin in a range of 6 orders of

magnitude and selective with respect non-thrombin

molecules. Furthermore, the detection technique,

based on electrochemical impedance spectroscopy, is

well consolidated. At present, the only -although

quite serious- constraint to its large scale diffusion is

miniaturization, which should allow for point-of-care

uses.

The aim of this paper is to show that a network of

networks can be a good tool for investigating some

electrical properties of the complex TBA-thrombin,

each of them represented by a specific network.

Specifically, this tool, which is contained in a more

wide approach called proteotronics (Alfinito, 2015),

is able to correctly describe and interpret some

relevant results obtained by using X-ray spectrometry

(Russo–Krauss, 2012), and electrochemical

impedance spectroscopy (EIS) measurements (Cai,

2005). In particular, this approach is able to foresee

the reduced affinity of the TBA-thrombin composite,

when produced in the presence of Na

, with respect

to that of the same compound, produced in a solution

containing K

. Furthermore, the resistance variation

observed in EIS measurement is also well

reproduced. Finally, the results reveal a very

interesting feature: the protein binding lowers instead

of increasing the aptamer resistance. As a matter of

fact, compared to the aptamer in the native state, there

is an increase of resistance, in agreement with

experiments, but, compared to the aptamer in the

active state, the resistance decreases. This is an

unexpected result, which is mainly related to the

complex structure of the associated interconnected

networks.

2 MATERIALS AND METHODS

The network of networks is built up starting from the

single networks representing the protein and the

aptamer, respectively. In particular, to build up the

networks we use:

a. the aptamer in its native state, i.e. its lowest

free energy state;

b. The aptamer in its active form, i.e. the

aptamer with the structure deformed due to

the binding but deprived of the protein, in

the presence of both K

and Na

;

c. The aptamer-enzyme complex, in the

presence of both K

and Na

;

d. The enzyme alone in the presence of both K

and Na

Structure a. is available from the Protein Data

Bank (Berman, 2000) at the entry 148D (Schultze,

1994), while structures b-d are available from the

Protein Data Bank at the entries: 4DII and 4DIH

(Russo-Krauss, 2012).

Furthermore, each network has been equipped

with specific electrical features and can be used to

explore the topological and electrical properties of the

corresponding biomolecule. The complete network,

the network of networks, is obtained by using the 3D

structure of the complex aptamer-thrombin and

allowing appropriate electrical interactions between

the different macromolecules, as described in Section

2.2

2.1 Topological Methods

Each structure is mapped into a complex network

whose nodes correspond to the position of the C

carbon atoms, for the aptamer, and to that of the C



carbon atoms for the enzyme. The nodes are

connected with a simple cut-off rule, i.e. only if the

distance is smaller than an assigned value, R

In such a way, some topological features, like the

structure deformation subsequent to the protein

attachment, can be easily described. Figure 1 shows

the adjacency matrix, also known as contact map

(each point represents the link between the nodes

corresponding to the point coordinates) of the

aptamer in the active form, in the presence of Na

and

. The value of the interaction radius is 10Å.

The contact maps are equal. Nevertheless, the

aptamer-thrombin complex shows tiny differences in

the structure when produced in the presence of the

two different cations, see Figure 2.

In brief, these results tell us that the cations

slightly affect the topological structure of the

complex. Anyway, it is well known that affinity does

depend on the solvent (Russo-Krauss, 2012),

therefore we proceed with a more detailed

investigation.

A Network of Networks to Reproduce the Electrical Features of an Aptamer-ligand Complex - What an Electrical Network Tells about

Afﬁnity

Figure 1: Contact map of TBA in the active state, in solution

with two different cations, Na

, magenta, and K

, black

(color online).

Figure 2: Contact map of the complex TBA-thrombin in

solution with two different cations, Na

, black, and K

green (color online).

Complementary information concerning the network

structure is given by the degree distribution. Figure 3

reports the degree distribution of the TBA in the

native structure and active state, R

=10Å.

Figure 3. Degree distribution of TBA in the native and

active state, R

=10Ǻ. The degree distribution of the active

state does not depend on the ion in solution (color online).

The degree distribution of the native state has a

typical Poisson-like shape. The degree distribution of

the active state does not depend on the kind of ions

used in the solution; the maximum has shifted at the

value 2, and there are not more nodes with more 5

links. This means that the structure is more dilated

than the native one.

On the other hand, when we give a look to the

degree distribution of the enzyme alone (Figure 4, full

histograms), we notice small but noticeable

differences depending on the used ions.

Figure 4: Degree distribution of the TBA-thrombin

complex, R

=10Ǻ (empty histogram) and the thrombin

alone (full histogram).

As expected, in the TBA-thrombin complex

(empty histograms) the number of nodes with a small

number of links is larger (due to the dilated structure

of the aptamer).

The structure resolved in the solution containing

potassium has a Poisson-like degree distribution,

while the structure resolved in a solution containing

sodium is more flat. A more detailed investigation on

this topic is in progress.

In conclusion, the topological analysis reveals that

the differences between the macromolecules in the

presence of the cations K

and Na

are quite subtle

and mainly concern the degree distribution. These

differences are amplified by the electrical response,

as described in the following section.

2.2 Electrical Methods

To investigate the electrical response of the

macromolecules we built up the corresponding

electrical network.

The single protein electrical network is produced

as in previous investigations (Alfinito, 2009, Alfinito,

2010). In particular, each link is thought as an

electrical line with a specific resistance and

COMPLEXIS 2017 - 2nd International Conference on Complexity, Future Information Systems and Risk

capacitance. Each passive element of this line is

geometrically represented by a cylinder of height l,

the distance between the nodes, and basis area A, the

intersection area of two spheres of radius R

centred

in each of the nodes. The resulting electrical

impedance depends on the kind of nodes (here amino

acids or nucleobases) and on their distance. Finally,

the impedance of the link between the nodes a,b

writes:

a,b

1+iϱε

a,b

(1)

where



a,b

and



a,b

are the resistivity and the

dielectric constant of the link,  is the frequency of

the applied voltage. The polarizability values are

quite different for amino acids and nucleic bases (and,

in principle, also the macroscopic electric response of

aptamers could be not the same observed in proteins

(Akimov, 2008)). Here we assume that, in similar

experimental conditions, aptamers and proteins have

similar electrical behaviors and formulate our model

accordingly.

The aptamer electrical features are modelled by

using the values of resistivity and polarizability of the

AGCTU set, recently published (Ohshiro, 2012,

Šponer, 2001). Specifically, the relative dielectric

constant of the couple of the a-th and b-th nodes,

a,b

is expressed in terms of the intrinsic polarizability of

each isolated amino acid/nucleobase, α

elec

(Šponer,

2001) , and writes:





elect a elect b

 







(2)

where the second term in the r.h.s. describes the

mean value of the polarizability of the couple of

nodes.

The resistivities of the nucleobases are taken by

(Ohshiro, 2012) ,





, where



is the mean

value calculated upon the AGCTU set and  is the

fraction /ρ for each nucleobase.

Therefore, the resistivity of the link drawn between

the a-th and the b-th nucleobase is defined as :





 







(3)

Since analogous data are not given for amino

acids, for the sake of simplicity, we assume that their

resistivities are all the same. In particular, the link

resistance of a couple of amino acids is:



a,b



. (4)

The region between the networks, where the

hooking happens, is the most interesting. Here the

protein perfectly matches the aptamer and combines

with it via van der Waals forces. It has been revealed

that the presence of some ions like Na

and K

gives

TBA a different ability to inhibit thrombin (Russo-

Krauss, 2012). Furthermore, in previous sections we

have seen that these cations poorly affect the TBA-

enzyme structure.

Accordingly, we conjecture that most of these

differences are due to the small interaction region.

Therefore, we assume that previous formulas still

hold in each part of the network of networks. This is

also true in the aptamer-thrombin contact region, but

with features intermediate between those of amino

acids and nucleobases. In particular, for the couple of

the a-th nucleobase and b-th amino acid, the link

resistance is:











 (5)

Equation (2) is modified accordingly.

Each electrical network is ideally contacted to an

external bias, by using the first and the last node as

terminals. The electrical features of this linear

network are calculated by using the Kirchhoff laws,

applied to a set of linear equations. Finally, the

equations are numerically solved by a standard

computational procedure which has its roots in the so-

called random resistor network method (De

Arcangelis, 1985, Pennetta, 2004) and has driven to

the proteotronic approach (Alfinito, 2015, Alfinito,

2009).

2.3 Thrombin Inhibition - the Energy

Funnel Framework

The exact mechanism of thrombin inhibition is, at

present, quite unclear and, in general, the protein

activation due to a specific ligand is a long time

debated problem (Onuchic, 1994, Kobilka, 2007).

Here we describe the process of TBA-thrombin

conjugation from the point of view of the energy

transitions the single macromolecule and the

compound perform (Alfinito, 2017, Alfinito, 2016).

First of all, when the protein/aptamer assumes its

native and stable configuration, its energy is on the

bottom of a configurational energy funnel (the native

funnel) which corresponds to the set of energies the

macromolecule has when it goes from the molten to

A Network of Networks to Reproduce the Electrical Features of an Aptamer-ligand Complex - What an Electrical Network Tells about

Afﬁnity

the native state. When it receives energy from the

environment it can go up in the funnel. A way to

receive energy is to be surrounded by the specific

ligands. The ligands can smoothly improve the

aptamer energy simply striking it. Otherwise, when

they bind the aptamers, they produce a sharp energy

jump into a different funnel, the bond funnel. As a

final result, the macromolecule changes its

conformation and binds the ligand. Therefore, the

energy funnel changes (binding funnel). In

conclusion, the addition of specific ligands produces

both the shift of energy in the native funnel and the

transition to the binding energy funnel. A cartoon

describing these two mechanisms is given in Figure

5. This complex mechanism is described, inside the

impedance network analogue, with a change of the

value of R

(Alfinito, 2017, Alfinito, 2016). In doing

so, we follow the model proposed by Kobilka and

Deupi (Kobilka, 2007) which describes the protein

dynamics in a process of binding as a transition

between a couple of energy funnels. Furthermore, this

induces a change of the number of internal bonds,

preserving only those useful for stabilizing the final

configuration.

Figure 5: Sketch of the two possible energy transformations

between two contiguous energy funnels, due to the aptmer-

ligand interaction. Continuous line represents a smooth

transition and dashed line an abrupt transition.

3 THEORY AND EXPERIMENTS

In this section we compare some experimental data

concerning the structural and inhibitory properties of

TBA with theoretical data coming from our model.

3.1 Resistance Data

It is well known that ions play an important role in

stabilizing the 3D structure of TBA, the so-called G-

quadruplex. In particular, by adding K

ions, the

result is a more stable G-quadruplex and an increased

inhibitory activity of thrombin (Russo- Krauss, 2012)

The resistance spectra produced within the

proteotronic approach are represented in Figure (6).

In particular, in Figure 6a, the resistance of TBA

activated in the presence of K

and Na

is reported in

comparison with the resistance of TBA in the native

state, for different values of R

. Activation produces

a resistance increase mainly in the region 8-16 Ǻ. The

main difference is obtained for R

=10Ǻ and is the

same for both the activated structures.

Figure 6. Relative resistance variation of TBA in the active

state (a), or complexed with thrombin (b), vs. TBA in the

native state. Turquoise lines refer to structures in the

presence of K

, black lines refer to structures in the

presence of Na

(color online).

On the other hand, when the protein is added,

Figure 6b, the resistance variation becomes strongly

depend on the kind of ions in solution. Furthermore,

it is quite smaller than that observed for the activated

structures (notice the different scales in Figures (6a)

and (6b)). Therefore, the protein does not produce a

simple passivation, but it integrates the network of the

TBA in the active state and globally reduces its

resistance.

The TBA-thrombin structure obtained in the

presence of K

has a larger resistance compared to the

same structure obtained in the presence of Na

, more

close to that observed in experiments. This prompt us

to explore this structure for further investigations.

Free

energy

Conformational entropy

native

bond

COMPLEXIS 2017 - 2nd International Conference on Complexity, Future Information Systems and Risk

3.2 EIS Data: Experiment

The experimental outcomes we refer for testing our

model concern with the use of TBA in an

electrochemical impedance spectroscopy assay (Cai,

2005).

In particular, a gold electrode, functionalized with

TBA, was used to perform electrochemical

measurements in the absence of thrombin and after

incubation with different concentrations of the

enzyme (from to 1 pM to 1 M). The increasing

protein concentration produced an increase of the

electron transfer resistance, sufficient to fairly resolve

different concentrations (a variation larger than

150 % for the highest concentration was measured).

A sketch of the experiment is shown in Figure 7.

Figure 7. Schematic view of the experiment by Cai and co-

workers. On top, the gold electrode functionalized with

TBA without (left) and with (right) thrombin. On bottom

the EIS response, with a sensitive variation of impedance

due to thrombin.

3.3 EIS Measurements: Theory

Our model describes the behaviour of a single

macromolecule, therefore, to compare our data with

experiments, it is necessary to perform a rescaling. In

particular, we are interested in the comparison of

resistance data and it is made by using the following

formula (Alfinito, 2017):



sample com nat

rNfr(1f)r 

(6)

where r

sample

the sample resistance, r

com

the

resistance of a single TBA-thrombin complex, and

nat

the resistance of the single TBA in the native state. N

is the total number of aptamers on the electrode and f

is the fraction of them bound to the protein. We

estimate the f value by assuming it is described by the

Hill-like equation:





(7)

where

0C0

)/RR(R x

, R

is the value of R

corresponding to f=0 i.e. a sample consisting only of

TBAs in their native state, and a and b are numerical

fitting parameters. Equation (7) states a functional

dependence between f and the value of the interaction

radius, in agreement with Sec.2.3.



In the present case, we assume R

=13.3Å, which

is the value corresponding to zero difference between

the resistance of the aptamer alone and that of the

complete macromolecule. Furthermore, this value is

the largest corresponding to the region in which, in

agreement with experiments, the resistance of the

complex TBA-thrombin is larger than that of the TBA

in the native state (see Figure 6). By simultaneously

using Equations (6,7) we are able to reproduce the

experimental data. In particular, by using in Equation

(7) the fitting parameters, a=2.99 and b=2.7 10

-4

Equation (6) reproduces the sample resistance

variation observed by Cai and coworkers.

The results are given in Table 1.

Table 1: The rate r/r

of the sample electron-transfer

resistance, R

, measured for different thrombin

concentrations with respect the sample R

without

thrombin; the corresponding theoretical quantities

calculated for the values of R

shown in column 3,

and the

fraction, f, of aptamer-thrombin complex.

r/r

experiment

r/r

theory

(Å)

2.6±0.6 3.2 11.3 0.93

2.2±0.5 2.1 11.5 0.90

2.2±0.7 1.8 11.7 0.87

1.7±0.5 1.2 12.7 0.26

4 CONCLUSIONS

We have used a network of networks for analysing

the electrical features of the complex constituted by

the aptamer TBA and its specific ligand, the enzyme

thrombin. The inhibition activity of TBA on this

protein is a long time known result, also investigated

to produce a targeted therapy with reduced side

A Network of Networks to Reproduce the Electrical Features of an Aptamer-ligand Complex - What an Electrical Network Tells about

Afﬁnity

effects. Furthermore, it has been also considered for

producing a thrombin biosensor.

We have adapted a procedure previously used for

a single protein to the aptamer alone, complexed with

the specific ligand, and also without the ligand but

with the modified structure it assumes when binds the

ligand. The aptamer structures, taken by the Protein

Data Bank, describe the oligomers in two different

solutions. We observe that the electrical responses of

the corresponding networks do not depend on the

kind of solution (with Na

or K

), for the case of the

aptamer alone. On the other hand, when the protein

binds the aptamer, the different action of the two

cations is reflected by a different resistance response.

Thus, this definitely confirms the relevant role of the

cations in the binding mechanism. In other words, the

cation steric action determines the shape of the

network, and finally, the inhibition activity of TBA.

In a more pragmatic approach this results suggest that

a measure of resistance could be a test of affinity.

Another important result obtained with the

technique of the network of networks is that by

adding a large protein like the thrombin to TBA in its

active form, the global resistance is lower than that of

the aptamer. This is an important information

concerning the mechanism of binding because it

reveals that the protein efficaciously completes the

not trivial structure of the aptamer, producing a global

improvement of its conductance. Of course, and in

agreement with experiments, the final resistance

value is lower than that of the aptamer in the native

state, but larger than that of the aptamer in the active

state.

This enforces the conclusion that, at this level of

microscopic interactions, the bulk approximation

fails.

REFERENCES

Akimov, V., Alfinito, E., Bausells, J., Benilova, I., Paramo,

I.C., Errachid, A., Ferrari, G., Fumagalli, L., Gomila,

G., Grosclaude, J. and Hou, Y., 2008. Nanobiosensors

based on individual olfactory receptors. Analog

Integrated Circuits and Signal Processing, 57(3),

pp.197-203.

Alfinito, E., Pennetta, C. and Reggiani, L., 2009.

Topological change and impedance spectrum of rat

olfactory receptor I7: A comparative analysis with

bovine rhodopsin and bacteriorhodopsin. Journal of

Applied Physics, 105(8), p.084703.

Alfinito, E., Pennetta, C. and Reggiani, L., 2010. Olfactory

receptor-based smell nanobiosensors: an overview of

theoretical and experimental results. Sensors and

Actuators B: Chemical, 146(2), pp.554-558.

Alfinito E., Pousset J., and Reggiani L.,2015 Proteotronics:

Development of Protein-Based Electronics. CRC Press.

Alfinito, E. and Reggiani, L., 2016. Current-voltage

characteristics of seven-helix proteins from a cubic

array of amino acids. Physical Review E, 93(6),

p.062401.

Alfinito, E., Reggiani, L., Cataldo, R., De Nunzio, G.,

Giotta, L. and Guascito, M.R., 2017. Modeling the

microscopic electrical properties of thrombin binding

aptamer (TBA) for label-free biosensors.

Nanotechnology, 28(6), p.065502.

Berman, H.M., Westbrook, J., Feng, Z., Gilliland, G., Bhat,

T.N., Weissig, H., Shindyalov, I.N. and Bourne, P.E.,

2000. The protein data bank. Nucleic acids research,

28(1), pp.235-242.

De Arcangelis, L., Redner, S. and Coniglio, A., 1985.

Anomalous voltage distribution of random resistor

networks and a new model for the backbone at the

percolation threshold. Physical Review B, 31(7),

p.4725.

Du, X., Li, Y., Xia, Y. L., Ai, S. M., Liang, J., Sang, P., Ji,

X.-L. and Liu, S. Q., 2016. Insights into Protein–Ligand

interactions: mechanisms, models, and methods.

International journal of molecular sciences, 17(2),

pp.144-177.

Iliuk, A.B., Hu, L. and Tao, W.A., 2011. Aptamer in

bioanalytical applications. Analytical chemistry.

83(12), pp. 4440-52.

Ellington, A.D. and Szostak, J.W., 1990. In vitro selection

of RNA molecules that bind specific ligands. Nature,

346, pp.818–822.

Jo, H. and Ban, C., 2016. Aptamer–nanoparticle complexes

as powerful diagnostic and therapeutic tools.

Experimental & Molecular Medicine. 48(5). e230.

Kobilka, B.K. and Deupi, X., 2007. Conformational

complexity of G-protein-coupled receptors. Trends in

pharmacological sciences, 28(8), pp.397-406.

Ni, X., Castanares, M., Mukherjee, A., Lupold, SE., 2011.

Nucleic acid aptamers: clinical applications and

promising new horizons. Current medicinal chemistry.

18(27), p.4206.

Ohshiro, T., Matsubara, K., Tsutsui, M., Furuhashi, M.,

Taniguchi, M. and Kawai, T., 2012. Single-molecule

electrical random resequencing of DNA and RNA.

Scientific reports, 2, p.501.

Oliphant, AR, Brandl, C.J. and Struhl, K., 1989. Defining

the sequence specificity of DNA-binding proteins by

selecting binding sites from random-sequence

oligonucleotides: analysis of yeast GCN4 proteins.

Mol. Cell. Biol. 9, pp. 2944–2949.

Onuchic, J.N., Luthey-Schulten, Z. and Wolynes, P.G.,

1997. Theory of protein folding: the energy landscape

perspective. Annual review of physical chemistry,

48(1), pp.545-600.

Pennetta, C., Alfinito, E., Reggiani, L., Fantini, F.,

DeMunari, I. and Scorzoni, A., 2004. Biased resistor

network model for electromigration failure and related

phenomena in metallic lines. Physical Review B,

70(17), p.174305.

COMPLEXIS 2017 - 2nd International Conference on Complexity, Future Information Systems and Risk

Russo-Krauss, I., Merlino, A., Randazzo, A., Novellino, E.,

Mazzarella, L. and Sica, F.,2012. High-resolution

structures of two complexes between thrombin and

thrombin-binding aptamer shed light on the role of

cations in the aptamer inhibitory activity. Nucleic Acids

Research. 40, gks 512.

Schultze, P., Macaya, R.F. and Feigon, J., 1994. Three-

dimension al solution structure of the thrombin-binding

DNA aptamer d (GGTTGGTGTGGTTGG). Journal of

molecular biology. 235, pp. 1532-1547.

Šponer, J., Leszczynski, J. and Hobza, P ., 2001. Electronic

Properties, Hydrogen Bonding, Stacking,and Cation

Binding of DNA and RNA Bases. Nucleic Acid Sci.,

(61), pp.3–31.

Sun, H., Zhu, X., Lu, P. Y., Rosato, R.R., Tan, W. and Zu,

Y., 2014. Oligonucleotide aptamers: new tools for

targeted cancer therapy, Molecular Therapy-Nucleic

Acids 3, e182.

Tuerk, C. and Gold, L., 1990. Systematic evolution of

ligands by exponential enrichment: RNA ligands to

bacteriophage T4 DNA polymerase. Science. 249,

pp.505–510.

Yüce M., Ullah N. and Budak H., 2015. Trends in aptamer

selection methods and applications. Analyst., 140(16) ,

pp.5379-99

A Network of Networks to Reproduce the Electrical Features of an Aptamer-ligand Complex - What an Electrical Network Tells about

Afﬁnity