Nanotechnology. 2017 Feb 10;28(6):065502.

New tools to model and evaluate binding affinity in aptamer-protein complexes

Eleonora Alfinito1, Rosella Cataldo2, Giorgio De Nunzio2, Livia Giotta3, Maria Rachele Guascito3, Francesco Milano4, Lino Reggiani2


1Dipartimento di Ingegneria dell’Innovazione, Università del Salento, via Monteroni, Lecce, Italy

2Dipartimento di Matematica e Fisica “Ennio de Giorgi”, Università del Salento, via Monteroni, Lecce, Italy

3Dipartimento di Scienze e Tecnologie Biologiche e Ambientali, Università del Salento, via Monteroni, Lecce, Italy

4 CNR-IPCF Istituto per i Processi Chimico-Fisici, U.O.S. Bari, via Orabona, 4, Bari, Italy

Running title: new tools to investigate aptamer-protein complexes

To whom correspondence should be addressed: Eleonora Alfinito E-mail:



In the last 25 years, aptamers gained most attention in the scientific community by yielding over 7000 entries in the PubMed. In essence, aptamers are short RNA or single-stranded DNA oligonucleotides functionally used to bind specific ligands. Usually they are generated in vitro and, recently, computational approaches have been developed for optimizing the in silico selection and exploring the affinity performances. However, the mechanism of aptamer-ligand formation is still far from being understood, and not obvious to be predicted. To address this issue we propose a computational model that describes aptamer-ligand binding affinity, by studying: (i) the topological structure of the corresponding graphs through the rank-degree distribution (hierarchy) and the node assortativity; (ii) the linear response (impedance) of the equivalent electrical-circuit. Numerical calculations are applied to the thrombin binding aptamer (TBA), alone and complexed in the presence of sodium and potassium ions. Results are quite intriguing since they reveal the possibility of identifying different affinities of the complex, due to the presence of different ions when looking at the hierarchy-assortativity plot. Furthermore, the analysis of the electrical response of TBA in a specific state is performed by dressing the topological graph with elementary impedances that preserve the electrical features of the original macromolecule. The result reveals that the macromolecule resistance sensitively depends on the presence of sodium or potassium ions, thus indicating the value of the resistance as a crucial parameter for testing affinity.

Keywords: Aptamers, Biomolecule Electrical Properties, Proteotronics, Thrombin, Graph Theory, Electro-chemical Impedance Spectroscopy




Within the framework of Proteotronics [1], an emerging science for the investigation of the electrical and topological properties of biological macromolecules, we develop a procedure based on two fundamental steps: i. the building of a graph analogue of the macromolecule, ii. the conversion of the graph into an interacting network. The procedure is successfully used to describe and interpret a series of relevant experimental results [2], obtained from X-ray spectrometry [3] and electrochemical impedance spectroscopy (EIS) measurements [4].


The building of a graph analogue

The aptamer, alone and complexed with the protein, is represented as a complex network, and studied by means of classical graph properties, measuring global and local features, i.e. the degree and the rank-degree distribution, and the node assortativity [5]. The network is built up, starting from the tertiary structure, available from the Protein Data Bank (PDB) entries [6], related to:

  1. the aptamer in its native state, i.e. its lowest free energy state (148D entry);
  2. 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+ (4DII entry), and Na+ (4DIH) [3,6];
  3. the aptamer-enzyme complex, in the presence of both K+ and Na+ [3,6].


By taking the C1 and Cα carbon atoms as the centroids of each nucleobase/amino acid, their position is mapped into the position of a node in the graph. Then, two nodes are connected to form a link only if their distance is smaller than an assigned cut-off radius, RC. This is a free parameter, whose tuning at increasing values produces a graph more connected, thus determining the degree of the graph nodes.

The result is a small-world network, with significant clusterization, which provides a better understanding of the stability of the protein topology, both in terms of overall structural integrity and robustness against failure of function due to mutations [7].

Hierarchy-assortativity of the networks can be investigated through the degree distribution and node correlation. The more sloped the distribution, the more the network displays hierarchy in the degree of nodes [5]. Networks are assortative/disassortative when displaying a positive/negative correlation degree. A network is assortative when high-degree nodes are connected to other high-degree nodes, and low- degree nodes are preferentially connected to low-degree nodes, so that the degree correlation is positive. A network is disassortative when high-degree nodes tend to connect to low-degree nodes, and vice versa, so that the degree correlation is negative [5].

TBA, in the native state, or in presence of K+ and Na+ ions, presents a quite low hierarchical organization and a degree correlation, strictly non-positive. This classifies the networks as “open”, quite flat and disassortative. Sodium ions allow a better information flow among nodes, with respect to potassium ions, and produce a more robust (flat) network. From another side, this also means that the network does not need to be completed to be stable, i.e. the network is less inclined to accept an external target (low affinity) [8].

Looking at the complex structures, they have the same, assortative behaviour, i.e. they are closed system (nothing more can be added to the structure), and also show a quite similar and very low value of hierarchy. In other terms, the complexed structures are more robust against random attacks or failures than the active structures. Indeed, this could be an alternative definition of high affinity.

Analyzing the evolution of the TBA network, by adding new links through an increase of the value of RC, we found that the network nature does not substantially change; on the other side, the presence of thrombin produces a sharp change in the assortativity behavior. Therefore, the most impressive news is that, by adding the thrombin, the networks go from “open” to “closed” systems, in terms of structure and also of binding affinity.


The building of an interaction network

An exhaustive argumentation of this item is given by Alfinito et al. [1,2], in which a resistance measurement calculated from the graph analogue, has been proposed as an efficient tool for testing different affinities in aptamers.

The single macromolecule impedance (or resistance in the limit of a static bias) is calculated by attributing to each link of the graph analogue the meaning of an elementary RC-parallel-circuit impedance (see Figure). By solving the network, we obtain an impedance spectrum which reveals a larger resistance of the structure obtained in the presence of potassium ions with respect that obtained in the presence of sodium ions [2].

In order to compare calculations with experiments like those reported in [4], data should be rescaled to a set of N macromolecules (the sample). Furthermore, when a sample receives its specific target, only a fraction, f, of its elements binds the target and this is at the origin of the dose-response mechanism, giving the sample resistance as [2]:

where rnat and ract are the single aptamer and the single aptamer-thrombin complex resistances, respectively. Within this model, the value of f is related to the value of RC [2]. In particular, the activation process is the result of multiple pathways along and between energy funnels [1,9,10]. For example, each energy funnel is built up on a specific stable (ground) state, the native state (native funnel) or the binding state (binding funnel). Analogously, we argue that when an aptamer folds from the molten state to the native state, its free energy, so as its conformational entropy, becomes smaller and smaller. This process is described by the aptamer sliding down an energy funnel (the native funnel), toward its minimum energy state (the native state). The interaction with thrombin may produce the binding or simply a variation of its free energy. In terms of the energy funnel description, the aptamer changes its state from native to bound, moving from the native funnel toward the binding funnel, or it stays in the initial funnel, but goes toward a higher energy state. Both these kinds of dynamics go with a change of RC, in analogy with macromolecule dynamics, since in going up and down among the states, the macromolecule changes the number of its internal bonds, retaining only those useful for stabilizing its final configuration [10,2].



Figure. A schematic view of the procedure: from the aptamer-protein complex (in the middle) [3,6] to the graph and the impedance network. The hierarchy-assortativity plot (a) for TBA in different states of activation and in the presence of Na+ and K+[8]; the relative resistance plot (b) for the complex in the presence of both Na+ and K+ ions[2]; the calculated fraction , f, of aptamer-protein complex (coloured dots) and the calculated/measured (coloured/black bars) sample resistance variation (c) [2] are reported.


Independently of the specific results, the graph topological analysis emerges as a novel theoretical tool able to validate hierarchy and assortativity as relevant quantities for investigating affinity in other aptamer-ligand complexes and, in a more pragmatic approach, a measure of resistance could be a significant indicator of affinity performance of aptamers.





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