Linear and Branched Peis (Polyethylenimines) and Their Property Space

International Journal of Molecular Sciences

Article Linear and Branched PEIs (Polyethylenimines) and Their Property Space

Claudiu N. Lungu 1, Mircea V. Diudea 1, Mihai V. Putz 2,3,* and Ireneusz P. Grudzi ´nski 4

1 Department of Chemistry, Faculty of Chemistry and Chemical Engineering, Babes-Bolyai University, 400028 Cluj, Romania; [email protected] (C.N.L.); [email protected] (M.V.D.) 2 Laboratory of Structural and Computational Physical-Chemistry for Nanosciences and QSAR, Biology-Chemistry Department, Faculty of Chemistry, Biology, Geography, West University of Timisoara, Str. Pestalozzi No. 16, 300115 Timisoara, Romania 3 Laboratory of Renewable Energies-Photovoltaics, R&D National Institute for Electrochemistry and Condensed Matter, Dr. A. Paunescu Podeanu Str. No. 144, RO-300569 Timisoara, Romania 4 Faculty of Pharmacy, Medical University of Warsaw, 02-097 Warsaw, Poland; [email protected] * Correspondence: [email protected]; Tel.: +40-(0)-256-592-638; Fax: +40-(0)-256-592-620

Academic Editor: Jesus Vicente De Julián Ortiz Received: 20 February 2016; Accepted: 5 April 2016; Published: 13 April 2016

Abstract: A chemical property space defines the adaptability of a molecule to changing conditions and its interaction with other molecular systems determining a pharmacological response. Within a congeneric molecular series (compounds with the same derivatization algorithm and thus the same brute formula) the chemical properties vary in a monotonic manner, i.e., congeneric compounds share the same chemical property space. The chemical property space is a key component in molecular design, where some building blocks are functionalized, i.e., derivatized, and eventually self-assembled in more complex systems, such as enzyme-ligand systems, of which (physico-chemical) properties/bioactivity may be predicted by QSPR/QSAR (quantitative structure-property/activity relationship) studies. The system structure is determined by the binding type (temporal/permanent; electrostatic/covalent) and is reflected in its local electronic (and/or magnetic) properties. Such nano-systems play the role of molecular devices, important in nano-medicine. In the present article, the behavior of polyethylenimine (PEI) macromolecules (linear LPEI and branched BPEI, respectively) with respect to the glucose oxidase enzyme GOx is described in terms of their (interacting) energy, geometry and topology, in an attempt to find the best shape and size of PEIs to be useful for a chosen (nanochemistry) purpose.

Keywords: chemical property space; QSAR/QSPR; linear PEI (LPEI); branched PEI (BPEI); molecular principal moment of inertia; geometric descriptors; topological descriptors

1. Introduction The concept of chemical space, by its currently accepted deﬁnition, is the space spanned by all possible molecules/chemical compounds, with any stoichiometry of electrons and atomic nuclei, and any possible topology [1]. The topology of the chemical space is not unique, so a variety of isomers exhibiting similar/dissimilar properties may appear. Drug design and molecular design in general involve the screening of the chemical space [2] within which one may move by chemical reactions. A chemical property space is then a multi-dimensional space, where physico-chemical properties of a molecule (or a molecular system) have the highest probability of being found. In drug design, this property space coincides with the drug likeness [3]. Visualization/exploration of the chemical property space may be realized by theoretical (statistics like “principal component analysis”

Int. J. Mol. Sci. 2016, 17, 555; doi:10.3390/ijms17040555 www.mdpi.com/journal/ijms Int. J. Mol. Sci. 2016, 17, 555 2 of 12

PCA, similarity maps, U matrix, clustering, diverse regression algorithms, generative topographic mapping GTM, radar plots, etc.) [4], while “moving” within this space may be accomplished by chemical reactions, resulting in functionalized/derivatized new molecules (or molecular systems). Each of these methods for exploring and/or moving within the chemical property space is applied speciﬁcally, according to the type of compounds under study [4]. In the present study, PEIs (i.e., polyethylenimines) are computationally explored by their chemical property space; for this class of compounds, two-dimensional plots and radar plots are suitable for the design of receptor relevant subspace and for diversity analysis, respectively [4–6]. Using statistical methods in exploring the chemical property space of PEIs, their physico-chemical properties can be predicted even consecutively to derivatization and functionalization. In other words, the physico-chemical behavior of a class of compounds, when moved within its chemical space, can be predicted by computational methods [7]. To properly predict the behavior of the derivatized compounds, the properties of the parent compounds must be computed [8]. PEIs (polyethylenimines) are polymeric molecules composed of repeating units of amine groups and two aliphatic carbons; a branched PEI, BPEI, may have all types of primary, secondary and tertiary amino groups while a linear PEI, LPEI, contains only secondary and primary amino groups. LPEI is solid at room temperature (melting point about 73–75 ˝C) while BPEI is liquid, irrespective of the molecular weight [9]. LPEI is soluble in hot water at low pH, and also in chloroform, ethanol or methanol. PEI has many applications, due to its polycationic character. The PEI property as a transfection reagent is well-studied; polyethylenimine was the second polymeric transfection agent discovered (after poly-L-lysine) and it binds to anionic residues of DNA by its positively charged units [10]. PEI is, however, cytotoxic [11].

2. Computational Methods In order to study PEIs, their chemical property space, i.e., the properties variation consecutive to functionalization and derivatization, were developed to simulate the interaction of PEIs with molecular systems (i.e., nano-devices) for a set of PEI molecules. The method used in designing the PEIs series was (structural) derivatization (e.g., C–C–N unit repetition), producing branched (B) and linear (L) PEIs isomers. Two congeneric PEIs series, namely C14N8 and C18N10 have been designed; each group consists of 4 members, one LPEI and three BPEIs, LPEI 01 and BPEI 02 to 04 (with different branching). These molecules were studied both as free entities and parts of a nano-system (i.e., derivatized/functionalized). The degree of functionalization/derivatization of PEIs is reﬂected in its chemical property space by a property variation. As for the degree of functionalization used in modeling these nano-therapeutic systems, several “generations” (i.e., gen. I, II, III, etc.) may be distinguished within the complex molecular architecture. In the congeneric series of PEI (C14/C18), the magnitude of properties variation enabled the differentiation between the two PEI series. The properties by which variation is relevant in our case reflect variation in the molecular structure: atomic distance, angles, and dihedral angles, with consequences in the energetics (reactivity vs. stability) of the studied molecular systems. In this respect, for each group member (of PEIs), a docking study was performed, using GOx (glucose oxidase) as a receptor. A crystallographic structure of GOx (PDB ID 3QVR) imported from the protein data bank [12], with a resolution of 1.3 Å, was used. Energy minimization and partial charges were performed using an MMFFF94 force field integrated in an online server [13,14]. The site where docking was performed was the active site of GOx for glucose oxidation [15]. All GOx valences, floods, charges, were corrected and the water molecules, other ligands and cofactors were removed. Docking of PEIs to GOx was performed using AutoDock software [16]. Dihedral angle was chosen as the monitored property, since dihedral angle values are sensitive to changes in molecule geometry subsequent to molecular interactions and because they correlate with torsion angles and the system free energy [17]. Dihedral angles [17] were calculated for each member of the two PEI groups, both in the free and docked ligand molecules, and represented as scatter plots (see Figure1). In order to have a Int. J. Mol. Sci. 2016, 17, 555 3 of 12

measureInt. J. Mol. (and Sci. an 2016 illustration), 17, 555 of variation within the chemical property space, the “pairs3 of of values12 comparison”Int. J. Mol. Sci. method 2016, 17, [55518 ] was used (by Ofﬁce 2007 software package) on the dihedral angle3 valuesof 12 of each LPEI/BPEIcomparison” pairmethod [19 ,[18]20]; was the resultingused (by Office “dissimilarity 2007 software cluster” package) representation on the dihedral is shown angle invalues Figure 2. comparison”of each LPEI/BPEI method pair [18] [19,20];was used the (by resulting Office 2007 “dissimilarity software package) cluster” onrepresentation the dihedral angleis shown values in The dihedral angle values of L 01-C14N8 PEI were chosen as the benchmarking term; next, pairs of ofFigure each 2. LPEI/BPEI The dihedral pair angle [19,20]; values the of resulting L 01-C14N8 “dissimilarity PEI were chosen cluster” as therepresentation benchmarking is term;shown next, in valuesFigurepairs were of 2. values compared,The dihedral were withcompared, angle terms values with in of C14N8 termsL 01-C14N8 in series, C14N8 PEI in series,were C18N10 chosen in C18N10 series as the series and benchmarking in and the in combined the term; combined next, (C14N8 &C18N10)pairs(C14N8 of series. values&C18N10) were More series. compared, dissimilar More withdissimilar pair terms molecules pairin C 14N8molecules provide series, provide in more C18N10 more connections series connections and inin thein thecombined cluster cluster graph representation,(C14N8graph representation, &C18N10) with a distinctseries. with More a color distinct dissimilar for color each forpair analyzed each molecules analyzed pair provide [ 17pair,21 [17,21].]. more connections in the cluster graph representation, with a distinct color for each analyzed pair [17,21].

Figure 1. Dihedral angles of free linear polyethylenimine (LPEI) 01 C14N8, represented as a function Figure 1. Dihedral angles of free linear polyethylenimine (LPEI) 01 C14N8, represented as a function Figureof the atom1. Dihedral groups; angles more ofdetails free linear in the polyethyleniminemain text. (LPEI) 01 C14N8, represented as a function of theof atom the atom groups; groups; more more details details in in the the main main text.text.

Figure 2. Dissimilarity of LPEI 01 vs. BPEIs in the C14N8 set (see additional material for the rest of FigureFigurethe 2. clustersDissimilarity 2. Dissimilarity obtained of for LPEIof C18N10 LPEI 01 01vs and .vs BPEIs. BPEIsC14N8 in in the& the C18N10). C14N8 C14N8 set set (see (see additionaladditional material material for for the the rest rest of of the the clusters obtained for C18N10 and C14N8 & C18N10). clusters obtained for C18N10 and C14N8 & C18N10). To get a quantitative measure (mathematically expressed) of the dissimilarity of PEIs dihedralTo getangles, a quantitative a fourth-degree measure equation (mathematically based on a polynomialexpressed) oftrend the line dissimilarity with period of 4 PEIswas dihedralTocalculated get a quantitativeangles, [22]. Ana fourth-degree example measure of polynomial (mathematicallyequation based trend online expressed) a andpolynomial data oflinearization thetrend dissimilarity line iswith given period of in PEIs Figure 4 was dihedral 3 angles,calculated(see a also fourth-degree the [22]. Supplementary An example equation Material).ofbased polynomial on a polynomialtrend line and trend data line linearization with period is given 4 was in calculated Figure 3 [22]. An example(see alsoTo representthe of Supplementary polynomial the chemical trend Material). property line and space data (a linearization multivariate one), is given two inmethods Figure were3 (see chosen: also the Supplementary(i) a To2D representsurface Material). shape the chemicaland (ii) aproperty radial chart. space In (athis multivariate respect, ten one), quantitative two methods variables were (including chosen: (i)Totopological a represent 2D surface and the geometricshape chemical and descriptors) (ii) property a radial space were chart. co (a Inmputed multivariate this respect, and represented one),ten quantitative two as methods discussed variables were above. chosen:(including (i) a 2D topological and geometric descriptors) were computed and represented as discussed above. surface shape and (ii) a radial chart. In this respect, ten quantitative variables (including topological and geometric descriptors) were computed and represented as discussed above.

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Figure 3. Polynomial equation calculated for the dihedral angles cluster of C14N8 BPEI 04 (the “(3)” Figure 3. Polynomial equation calculated for the dihedral angles cluster of C14N8 BPEI 04 (the “(3)” Figurenumber 3. ofPolynomial equation corresponds equation calculated with that for of the dihedralSupplementary angles Material). cluster of C14N8 BPEI 04 (the “(3)” number of equation corresponds with that of the Supplementary Material). number of equation corresponds with that of the Supplementary Material). Data, computed for both docked/undocked PEIs, include the following variables: Connolly Data, computed for both docked/undocked PEIs, include the following variables: Connolly molecularData, area, computed Connolly for bothaccessible docked/undocked area [23], molecular PEIs, includeweight, theovality, following inertial variables: principal Connollymoment, molecular area, Connolly accessible area [23], molecular weight, ovality, inertial principal moment, molecular area,refractivity, Connolly topological accessible areadiameter [23], molecularand Wiener weight, index, ovality, log inertialP and principalanother moment,partition molecular refractivity, topological diameter and Wiener index, log P and another partition molecularcoefficient refractivity,[24,25]. Examples topological of chemical diameter property and Wiener variation index, and logchemicalP and property another partitionspace of coefficient [24,25]. Examples of chemical property variation and chemical property space of coefﬁcientPEIs group [ 24C14N8,25]. Examplesare shown of in chemical Figures property4 and 5 (see variation the Supplementary and chemical Material property for space the ofrest PEIs of PEIs group C14N8 are shown in Figures 4 and 5 (see the Supplementary Material for the rest of groupthe series). C14N8 are shown in Figures4 and5 (see the Supplementary Material for the rest of the series). the series).

Figure 4.4. Chemical properties variation for C14N8C14N8 L/BL/B PEIs in the free (undocked)—((undocked)—(top), and inin Figure 4. Chemical properties variation for C14N8 L/B PEIs in the free (undocked)—(top), and in docked form—(form—(bottombottom).). 1—log 1—logP ;P 2—Connolly; 2—Connolly accessible accessible area area (Å2 );(Å 3—Connolly2); 3—Connolly molecular molecular area (Åarea2); docked form—(bottom). 1—log P; 2—Connolly accessible area (Å2); 3—Connolly molecular area 4—Molecular(Å2); 4—Molecular weight; weight; 5—Ovality; 5—Ovality; 6—Principal 6—Principal moment moment of inertia; of 7—Molar inertia; refractivity7—Molar (cmrefractivity3/mol); (Å2); 4—Molecular weight; 5—Ovality; 6—Principal moment of inertia; 7—Molar refractivity 8—Partition(cm3/mol); 8—Partition coefﬁcient; coefficien 9—Topologicalt; 9—Topological diameter (bonds); diameter and (b 10—Wieneronds); and 10—Wiener index. index. (cm3/mol); 8—Partition coefficient; 9—Topological diameter (bonds); and 10—Wiener index.

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FigureFigure 5. Chemical 5. Chemical property property space spaceof of C14N8C14N8 PEIs PEIs before before (top (top) and) and after after docking docking (bottom (bottom). ).

In order to determine the maximum length of the chain of PEIs docked on GOx, an additional In order to determine the maximum length of the chain of PEIs docked on GOx, an additional docking study was performed. A set of LPEI molecules, from C2 to C70 (see Supplementary dockingMaterial), study waswere performed.docked at Athe set enzyme of LPEI catalyti molecules,c active from site C2 (see to C70the (seeabove Supplementary described docking Material), weremethod). docked After at the docking, enzyme QSAR catalytic models active were site deve (seeloped, the abovewith the described steric energy docking of the method). GOx-PEI After docking,complex QSAR being models the dependent were developed,variable. Independent with the variables steric energy were the of number the GOx-PEI of C atoms, complex number being the dependentof N atoms, variable. number of Independent hydrogen donor variables groups were(HD), the the number mean distance of C atoms, between number two hydrogen of N atoms, numberdonor of hydrogengroups (HD-HD-Mean), donor groups the (HD), maximum the mean dist distanceance between between two twohydrogen hydrogen donor donor groups groups (HD-HD-Mean),(HD-HD-Max), the and maximum Wiener index. distance A multiple between linear two hydrogenregression donor(MLR) groupsmethod (HD-HD-Max),was used. The and Wienermodel index. was Avalidated multiple using linear the regression leave-one-out (MLR) method. method was used. The model was validated using Total hydrogen bonds energy of the GOx-PEI complex together with the steric energy of PEI the leave-one-out method. and torsions of PEI after docking were also calculated in order to give a more detailed view of the Total hydrogen bonds energy of the GOx-PEI complex together with the steric energy of PEI and GOx-PEI interaction. Data were collected for the C14N8 and C18N10 sets while the docking torsionsconditions of PEI were after kept docking as in werethe previous also calculated studies. in order to give a more detailed view of the GOx-PEI interaction. Data were collected for the C14N8 and C18N10 sets while the docking conditions were kept3. as Results in the previousand Discussion studies. Dihedral angle values show four distinct domains for all PEI undocked molecules (see Figure 1); 3. Results and Discussion in the case of docked PEIs, the dihedral angle values are distributed in a rather disordered picture, probablyDihedral taking angle valuesinto account show the four PEI distinct molecule domains “accommodation” for all PEI undocked according molecules to the binding (see Figuresite 1); in theshape case [26]. of docked PEIs, the dihedral angle values are distributed in a rather disordered picture, probablyClusters taking obtained into account from “comparison the PEI molecule of pair va “accommodation”lues” method applied according on dihedral to angle the binding values site for the studied PEIs showed a quite ordered distribution. Let us look at the graph in Figure 2, shape [26]. representing the dissimilarity cluster obtained for the C14N8 PEI set, with the values of LPEI 01 C14N8 Clusters obtained from “comparison of pair values” method applied on dihedral angle values dihedral angles, as the reference: the graph with respect to BPEI 02 has only one edge representing for theits dissimilarity studied PEIs to PEI showed 01; next, a quite BPEI 03 ordered C14N8 distribution.has 8 straight lines, Let usmeaning look atit is the more graph distinct in Figure[27] 2, representingfrom LPEI the 01 dissimilarity in comparison cluster to BPEI obtained 02 C14N8; for thefinally, C14N8 PEI PEI04 C14N8 set, with (gre theen lines) values has of even LPEI more 01 C14N8 dihedral angles, as the reference: the graph with respect to BPEI 02 has only one edge representing its dissimilarity to PEI 01; next, BPEI 03 C14N8 has 8 straight lines, meaning it is more distinct [27] from LPEI 01 in comparison to BPEI 02 C14N8; ﬁnally, PEI 04 C14N8 (green lines) has even more lines in the Int. J. Mol. Sci. 2016, 17, 555 6 of 12 cluster of dihedral angles, making it the most dissimilar to the reference LPEI 01 C14N8. LPEI 01 itself is not represented on the chart, being the comparison (benchmarking) term. To give a quantitative measure of the similarity/dissimilarity, qualitatively shown by the graph in Figure2, a mathematical approach was used: a polynomial trend line of order 4 was calculated for the clusters belonging to BPEI 04 (C14N8 and C18N10), thus obtaining polynomials of the fourth degree (a total of 15 equations were calculated—see the Supplementary Material). The equations (see the Supplementary Material) are:

C14N8 BPEI 04 : y “ 0.0001x4 ´ 2 ˝ 10-5x3 ´ 30.06x2 ` 0.661x ` 97, 401 (1)

C18N10 BPEI 04 : y “ 0.0001x4 ´ 1 ˝ 10-5x3 ´ 14.96x2 ` 0.622x ` 48, 499 (2)

To exemplify such a function expressed by the fourth-degree equation, Equation (1), (3.C14) in the Supplementary Material, is represented in Figure3; the polynomial trend line was calculated for the points belonging to BPEI 04 C14N8. When applied the (dis)similarity operation listed above, a line was obtained composed of all the points that represent the values of BPEIs 04 C14N8 dihedral angles that differ from those of the reference LPEI 01C14N8 (the green line). The polynomial equation for this line is a sinusoidal with 4 points of intersection with the line (see Figure3), according to the degree of the equation. Such representations have been performed for all the cluster series (11 equations and 11 graphs, respectively—see the Supplementary Material). Next, the roots of the above equations were calculated; they consist of real and imaginary numbers (see Table1, for the equation shown in Figure3). The roots calculus was done by using the online computational engine Wolfram Alpha [28].

Table 1. Roots for the fourth-degree equations (1) and (2), Equations (3.C14) and (3.C18) in Supplementary Material.

Equation Root 1 Root 2 Root 3 Root 4 (1)/(3.C14) ´545.181 ´57.254 57.275 545.361 (2)/(3.C18) 20.376 50.003 ´11.684 ´ 18.421i ´11.684 + 18.421i

To escape the complex roots we have eliminated the fourth and third degree terms of the equation, based on their negligible coefﬁcients; thus, the equations (1) and (2) now become

C14N8 BPEI 04 : y – ´30.06x2 ` 0.661x ` 97, 401 (3)

C18N10 BPEI 04 : y – ´14.96x2 ` 0.622x ` 48, 499 (4)

For these new equations, the calculated roots were all real numbers (Table2).

Table 2. Roots for the second degree equations (3) and (4).

Equation Root 1 Root 2 (3) ´56.9119~´57 56.9339~57 (4) ´56.917~´57 56.9586~57

The obtained roots fall in the range (´57, 57) for both PEI series. All these structural variations must be reflected in the variation of chemical properties. To prove this, ten physical-chemical descriptors for C14N8&C18N10 PEIs were calculated. Among these, a significant variation of values (collected before and after docking) was shown by the Connolly accessible area and inertial principal moment of the PEIs molecules; in contrast, Wiener index and the topological diameter do not change after docking, a result just expected (these two topological descriptors follow the topology of structure Int. J. Mol. Sci. 2016, 17, 555 7 of 12 and do not regard the actual geometry, thus remaining constant). Figure4 illustrates the monitored physico-chemical properties of C14N8 PEIs series, before (in the free form) and after docking (bound) on the GOx enzyme. Each PEI structure is represented by a color. On the horizontal axis, the chemical descriptors are: 0—The origin; 1—log P; 2—Connolly accessible area (Å2); 3—Connolly molecular area (Å2); 4—Molecular weight; 5—Ovality; 6—Principal moment of inertia; 7—Molar refractivity (cm3/mol); 8—Partition coefficient, 9—Topological diameter (bonds), 10—Wiener index. On the Int. J. Mol. Sci. 2016, 17, 555 7 of 12 vertical axis, the values of descriptors are represented using the same scale. Similar results, in terms of chemicalinertia; descriptor 7—Molar variation, refractivity were (cm3 obtained/mol); 8—Partition for the C18N10 coefficient, series 9—Topological (see the Supplementary diameter (bonds), Material). In10—Wiener order to index. represent On the in vertical more detailaxis, the the values chemical of descriptors property are space, represented the above using mentioned the same ten molecularscale. Similar descriptors results, were in terms calculated of chemical for PEIs descript andor joined variation, in a 2-dimensional were obtained for shape, the C18N10 and a surface-like series radial(see graph the Supplementary was designed Material). (Figure5 ). EachIn property order towas represent represented in more by detail one edgethe chemical of the radial property graph. space, LPEI the 01 above and BPEI mentioned 02 surfaces ten are not visible,molecular being descriptors covered bywere BPEI calculated 03 and BPEI for PEIs 04 surfaces and joined in the in C14N8 a 2-dimensional free PEI series, shape, while and the a BPEI 03 surfacesurface-like is not radial visible graph because was designed those of BPEI(Figure 02 5). and BPEI 04 surfaces of C14N8 docked PEI series (for Each property was represented by one edge of the radial graph. LPEI 01 and BPEI 02 surfaces more details, see the Supplementary Material). are not visible, being covered by BPEI 03 and BPEI 04 surfaces in the C14N8 free PEI series, while Therethe BPEI are 03 clear surface differences is not visible in the because chemical those property of BPEI 02 space and ofBPEI PEIs, 04 beforesurfaces and of C14N8 after docking. docked ComparingPEI series (for two more molecules details, see is the equivalent Supplementary to formation Material). of a complex cluster (corresponding to their virtual interaction);There are clear according differences to thein the network chemical theory, property the space complexity of PEIs, of before a cluster and after formed docking. between two PEI structuresComparing is directly two proportionalmolecules is equivalent to their dissimilarity to formation ( i.e.of ,a thecomplex more “different”cluster (corresponding the molecules to are, the moretheir complexvirtual interaction); the cluster results;according see to the the scatterplots network theory, in Figure the2 andcomplexity in the rest of ofa thecluster Supplementary formed Material).between two PEI structures is directly proportional to their dissimilarity (i.e., the more “different” Beingthe molecules located are, at thethe uppermore complex limit of the PEI cluster chemical results; space, see BPEIthe scatterplots 04 characterizes in Figure the 2 and upper in the limit of functionalrest of differentiation/functionalization,the Supplementary Material). meaning in this case the highest number of functional Being located at the upper limit of PEI chemical space, BPEI 04 characterizes the upper limit of groups and ramification (i.e., branching). functional differentiation/functionalization, meaning in this case the highest number of functional Thegroups lower and limitramification of chemical (i.e., branching). space is represented by LPEI 01 C14N8; this was taken as the reference of differentiation.The lower Clearly, limit of variations chemical inspace the is structure represente determined by LPEI changes 01 C14N8; in the this chemical was taken property as the space of eachreference PEI. Observe of differentiation. the ”same Clearly, degree“ variations in changes in the of structure the property determine space, changes as suggested in the chemical by the same rootsproperty of the second space degreeof each equationPEI. Observe of BPEI the 04”same in the degree“ two series in changes C14N8 of and the C18N10 property (the space, root as values are nearlysuggested identical; by the seesame the roots Supplementary of the second Material).degree equation of BPEI 04 in the two series C14N8 and TheC18N10 maximum (the root variation values are was nearly observed identical; for see BPEI the Supplementary 04 in both series Material). while LPEI 01 tends to conserve its chemicalThe properties. maximum However,variation was the geometryobserved offor LPEI BPEI 01 04 changes in both drastically series while by LPEI docking, 01 tends a fact to clearly conserve its chemical properties. However, the geometry of LPEI 01 changes drastically by docking, evidenced by the changes in Connolly molecular surface and especially in the principal moment of a fact clearly evidenced by the changes in Connolly molecular surface and especially in the inertia, computed before and after docking (see Figures6 and7). We interpret this result as highly principal moment of inertia, computed before and after docking (see Figures 6 and 7). We interpret suggestivethis result that as LPEI highly 01 issuggestive more susceptible that LPEI to01 bindis more at ansusceptible enzyme siteto bind compared at an enzyme to BPEIs site and compared meanwhile to conserveto BPEIs its and chemical meanwhile property to space;conserve it alsoits meanschemical that property its (topological/functional) space; it also means structurethat its will not be(topological/functional) drastically affected bystructure binding. will not be drastically affected by binding.

FigureFigure 6. Chemical6. Chemical property property spacespace descriptorsdescriptors in in C1 C14N84N8 PEIs, PEIs, before before (free (free of docking) of docking) and and afterafter docking. docking.

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Figure 7. Principal moment of inertia in the C14N8 PEI series before (free of docking) and FigureFigureafter docking. 7.7.Principal Principal moment moment of inertia of inertia in the in C14N8 the C14N8 PEI series PEI before series (free before of docking) (free of and docking) after docking. and after docking. Figure8 8 shows shows the the molecular molecular models models of theof the LPEI LP C14N8EI C14N8 structure, structure, represented represented before before and after and dockingafterFigure docking with 8 GOx;withshows GOx; the the changes themolecular changes in molecule models in molecule geometryof the geometry LP areEI C14N8 clearly are clearly seen.structure, seen. represented before and after docking with GOx; the changes in molecule geometry are clearly seen.

Figure 8. Models of LPEI 01 C14N8 before ( left) and after docking (right) at GOx binding site. Figure 8. Models of LPEI 01 C14N8 before (left) and after docking (right) at GOx binding site. Since any biological receptor/enzyme shows saturation, (i.e., a limit in the number of ligands i.e. that SinceSincemay be any bound) biologicalbiological in terms receptor/enzymereceptor of its/enzyme binding showsshows sites saturation, saturation,while docked ( (i.e., a ,being limita limit inavailable thein the number number to another of ligands of ligands ligand that thatmayacting may be on bound) bethe bound) same in terms binding in terms of its site, bindingof weits performedbinding sites while sites the docked while docking docked being procedure available being foravailable to LPEI another molecules to ligandanother acting C2–C70, ligand on actingtheamong same on which bindingthe same it site,was binding wefound performed site, feasible we theperformed for docking C2–C28 the procedure LPEI; docking for for procedurethe LPEI rest molecules of for LPEI LPEI C2–C70,molecules, molecules among the C2–C70, whichsteric amongitenergy was found whichcalculated feasible it was for forfound the C2–C28 corresponding feasible LPEI; for for C2–C28 theGOx-PEI rest ofLPEI; LPEIcomplex for molecules, the has rest positive, theof LPEI steric increasedmolecules, energy calculated values the steric (see for energytheFigure corresponding 9).calculated Total hydrogen for GOx-PEI the bond corresponding complex energy has of this positive,GOx-PEI series increased (C2–C70complex LPEI) valueshas positive,varies (see Figure within increased9 ).the Total range values hydrogen +50 (seeand ´ Figurebond−40 kcal/mol. energy 9). Total of thishydrogen series (C2–C70bond energy LPEI) of variesthis se withinries (C2–C70 the range LPEI) +50 varies and within40 kcal/mol. the range +50 and −40 kcal/mol.Energetic data for these calculations can be found inin thethe SupplementarySupplementary Material.Material. EnergeticQSAR model data obtained for these for calculations the reasonably can be docked found C2–C28 in the Supplementary molecules is is represented Material. in in Figure Figure 10;10; the regression equation is as follows: y = ´6.382x ´ 884.6 with a Pearson correlation coefﬁcient R2 the regressionQSAR model equation obtained is asfor follows: the reasonably y = −6.382 dockedx − 884.6 C2–C28 with molecules a Pearson is representedcorrelation coefficientin Figure 10; R2 2 theof 0.907. regression equation is as follows: y = −6.382x − 884.6 with a Pearson correlation coefficient R of 0.907.

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Figure 9. Steric energy values of GOx-LPEI complexes. Figure 9. Steric energy values of GOx-LPEI complexes. Figure 9. Steric energy values of GOx-LPEI complexes. Figure 9. Steric energy values of GOx-LPEI complexes.

Figure 10. QSAR model for GOx-LPEI complex (data computed by docking).

We also Figurecompared 10. QSAR the docking model forenergy GOx-LPEI (steric complex total energy) (data computed after docking, by docking). for LPEIs and BPEIs Figure 10. QSAR model for GOx-LPEI complex (data computed by docking). with similar numbersFigure 10. of QSAR carbon model atoms, for GOx-LPEIsee Figures complex 11 and (data 12. Nevertheless,computed by docking). Figure 12 gives more detailsWe also on the compared results in the Figure docking 11. energy (steric total energy) after docking, for LPEIs and BPEIs withWe Wesimilar also also compared numberscompared of the the carbon docking docking atoms, energyenergy see (stericFigures(steric totalto 11tal and energy) 12. Nevertheless, after after docking, docking, Figure for for LPEIs LPEIs12 gives and and BPEIsmore BPEIs withdetailswith similar similar on the numbers numbers results in of of Figure carbon carbon 11. atoms, atoms, seesee FiguresFigures 11 and 12.12. Nevertheless, Nevertheless, Figure Figure 12 12 gives gives more more detailsdetails on on the the results results in in Figure Figure 11 11..

Figure 11. Steric energy for GOx-L/B PEI; the energy of BPEIs (C14 and C18 groups) is represented in yellow; the energy of LPEI C14 and C18 is shown in red; the energy of LPEI C16 is represented in green.

Figure 11. Steric energy for GOx-L/B PEI; the energy of BPEIs (C14 and C18 groups) is represented FigureinFigure yellow; 11. 11.Steric theSteric energy energy energy of for forLPEI GOx-L/B GOx-L/B C14 and PEI; PEI; C18 the the is energy energyshownof inofBPEIs red;BPEIs the (C14(C14 energy andand C18ofC18 LPEI groups)groups) C16 isis representedrepresented in yellow;inin green.yellow; the energy the energy of LPEI of C14LPEI and C14 C18 and is C18 shown is shown in red; in the red; energy the energy of LPEI of C16 LPEI is representedC16 is represented in green. in green.

Int. J. Mol. Sci. 2016, 17, 555 10 of 12 Int. J. Mol. Sci. 2016, 17, 555 10 of 12

FigureFigure 12.12. StericSteric energy of GOx-L/B PEIs PEIs complex complex (from (from left left to to right): right): 1 and 1 and 6 L 6 PEI L PEI C14 C14 and and C18 C18 (in (inred); red); 2 to 2 to4 and 4 and 7 7to to 9 9represent represent the the corresponding corresponding branched branched isomers isomers B PEIs (in(in yellow);yellow); LPEILPEI C16C16 isomerisomer is is represented represented in in green green (see (see also also Figure Figure 11 11).).

4.4. Conclusions LPEIsLPEIs modifymodify their their geometry geometry more more easily easily in comparisonin comparison to BPEIs, to BPEIs, meaning meaning that LPEIsthat LPEIs are more are adaptablemore adaptable at a certain at bindinga certain site. binding LPEIs are site. site-adaptive LPEIs are and site-adaptive chemical property and space–stable.chemical property From thespace–stable. perspective From of variation the perspective interval, the of PEI variation C18N10 interval, set is more the favorable PEI C18N10 compared set is to more C14N8 favorable PEIs. If onecompared wishes toto buildC14N8 a nano-device PEIs. If one using wishes PEIs withto bu GOxild a as nano-device a component, using then LPEIsPEIs arewith preferred, GOx as ata leastcomponent, in the first-generation then LPEIs are devices preferred, (in which at least LPEI in is the docked first-generation to GOx); if additional devices (in functionalization which LPEI is isdocked needed, to thenGOx); C18N10 if additional PEI have functionalization to be chosen at is the needed, expense then of C18N10 C14N8. Also,PEI have when to speakingbe chosen aboutat the thermo-responsiveexpense of C14N8. properties, Also, when which speaking are correlated about th withermo-responsive the principal properties, moment of inertia,which are LPEIs correlated should bewith chosen the principal over BPEIs. moment The structural of inertia, principal LPEIs should moment be is chosen related over to temperature BPEIs. The and structural thus the principal thermal (in)stabilitymoment is ofrelated the GOx-PEI to temperature complex and [29]. thus The optimalthe thermal size of(in)stability PEI must beof aroundthe GOx-PEI C18N10, complex which is[29]. at aboutThe optimal the middle size ofof thePEI length must ofbe PEIaround chain, C18N10, as suggested which by is theat about QSAR the model middle developed of the length in this study,of PEI inchain, view as of suggested getting evidence by the of QSAR a certain model “saturation” developed of GOxin this by study, PEI, and in viceview versa of getting, when theevidence size of of the a PEIcertain molecule “saturation” increases. of GOx Overall, by branchedPEI, and vice PEIs versa have, when a relatively the size small of energeticthe PEI molecule influence increases. on GOx bindingOverall, when branched compared PEIs have to linear a relatively PEIs. small energetic influence on GOx binding when compared to linear PEIs. Supplementary Materials: Supplementary materials can be found at http://www.mdpi.com/1422-0067/17/ 4/555/s1.Supplementary Materials: Supplementary materials can be found at http://www.mdpi.com/1422-0067/17/ Acknowledgments:4/555/s1. This work was financially supported by GEMNS project granted in the European Union’s Seventh Framework Programme, under the framework of the ERA-NET EuroNanoMed II (European Innovative ResearchAcknowledgments: and Technological This work Development was financially Projects supported in Nanomedicine). by GEMNS Mihai project V. Putz granted acknowledges in the European his contribution Union’s toSeventh this work Framework within the Nucleus-ProgrammeProgramme, under underthe framewor the projectk PN-16-14-03-01of the ERA-NET funded EuroNanoMed by the Romanian II (European National AuthorityInnovative for Research Scientific and Research Technological and Innovation Development (ANCSI). Projects in Nanomedicine). Mihai V. Putz acknowledges Authorhis contribution Contributions: to thisClaudiu work with N. Lunguin the Nucleus-Programme and Mircea V. Diudea under established the project the conceptual PN-16-14-03-01 framework, funded produced by the theRomanian results, National discussion Authority and conclusions, for Scientific and Research assembled and the Innovation paper; Mihai (ANCSI). V. Putz and Ireneusz P. Grudziński performed the literature screening of concerned compounds and methods and contributed the references and resultsAuthor discussion; Contributions: all authors Claudiu refined N. Lungu and agreedand Mircea on the V. finalDiudea manuscript. established the conceptual framework, produced the results, discussion and conclusions, and assembled the paper; Mihai V. Putz and Ireneusz P. Grudziński Conflicts of Interest: The authors declare no conflict of interest. performed the literature screening of concerned compounds and methods and contributed the references and results discussion; all authors refined and agreed on the final manuscript.

Conflicts of Interest: The authors declare no conflict of interest.

Int. J. Mol. Sci. 2016, 17, 555 11 of 12

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