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MD and MC models are used to study the performance of dendrimers in biological systems including structural configuration and thermodynamic calculations. In general, dendrimers are defined with a starting configuration and then by assuming ergodic conditions, the system is minimized towards a low free energy. In this process, MC simulations use iterative random atomic displacements of the initial configuration to generate a new energy value which is then accepted or rejected by association of a probability function using Boltzmann statistics. This will depend on whether the study is performed in NVT (number of particles, volume and temperature constant) or NPT (number of particles, pressure and temperature constant) ensemble. The system is therefore evaluated to find a minimum configuration potential energy. By setting up constrains, the number of degrees of freedom can be reduced to decrease the computational demand. For this reason, allowing only important rotatable bonds to change is usually a good approximation.
Before performing the actual measurement, energy minimization is advised. This can be achieved with a short simulation with restrictions to the degrees of freedom. For example, in the case of a peptide bond, these can be restrained to maintain planarity. At this point it is necessary to be careful so that the initial structure does not end in a local minimum, which can be difficult to reverse. An interesting approach to circumvent this was proposed by changing the partial charge to +0.1e of all atoms followed by an increase in temperature to 500 K. This promotes the extension of the structure to be evaluated [105]. Another approach that can guarantee that the dendrimer branches are the farthest away from each other can be the addition of NOE constraints during the assembly of monomers using XPLOR [71].
A good solvent system is essential for a reliable prediction of dendrimer size and conformation, and the evaluation of solvent penetration into dendrimer void spaces [113]. The water behaves differently depending on its position to a dendrimer. In the case of PAMAM dendrimers three classes of water have been described: (i) buried water; (ii) surface water at the dendrimer-solvent interface and (iii) bulk water (i.e., solvent) [113,114]. Water molecules are enthalpy favored near the dendrimer and buried water has lower entropy in relation to the bulk water. Therefore, the binding of a water molecule to a dendrimers molecule results in release of this difference of free energy [114].
These are encouraging results has one can predict from a pool of interesting drugs which ones will fit best into the features of a given dendrimer. This kind of approach has been tested on PAMAM G5 dendrimers with different drugs (salicylic acid, L-alanine, phenylbytazone and primidone) [98]. These drugs were docked to the dendrimer via AutoDock Vina and then the best scoring conformations were selected for MD simulations using AMBER with explicit water solvent. Umbrella samplings were performed between the center of mass of the dendrimer and the drugs. When plotting the potential mean force (PMF) among all drugs studied l-alanine showed lower free energy (better ability to be released) followed by salicylic acid, primidone and phenylbutazone. However, taking into account the experimental data, although l-alanine and salicylic acid had a lower free energy (semi-empirical calculations) they were difficult to encapsulate in the dendrimer due to absence of nonpolar groups. This is due to less van der Waals contributions and the hydrogen bonding that did not contribute significantly to the free energy barrier. The PMF was also found to be less when the drugs are bound to the non-protonated dendrimer. The authors suggest that drugs should be encapsulated at higher pH and once in physiological pH they will be more tightly bond making the release controlled [97].
Proposed alteration of pH to modulate the interaction, encapsulation and release of drugs was observed from MD/MM simulations of PAMAM G5 and folic acid-terminated PAMAM G5 with tramadol and morphine [96] as well as PPI dendrimers G5 with Famotidine and Indomethacin [44] where the affinity of these drugs decreased with the decrease in pH. Similarly, PAMAM G4 equilibrated using MM+ FF were docked with resveratrol, genistein and curcumin [55]. The MD simulations revealed that the free energy binding followed genistein > curcumin > resveratrol which was in different binding constants determined experimentally which followed the order of curcumin > genistein > resveratrol. The difference between the calculation of energy of binding and the binding constants found experimentally was attributed to the difficulty of the drug to access the interior of the dendrimer.
The sequence of the DNA also takes a role in the dendrimer-nucleic acid complex formation and thus the importance of using computational methods to predict this interaction. Using MD simulations with different strand composition it was found that the binding constant follows as polyG > polyC > polyA > polyT sequence as observed by the free energy calculations [49]. The flexibility or rigidity of dendrimers is another crucial point to form the polyelectrolyte complexes which was described to be due to the balance between the enthalpy and entropy of binding [98].
We attempted to measure Ca2+ binding properties of native and mutated hOtolC1q and dOtolC1q. However, upon the removal of Ca2+ by overnight incubation with buffered Chelex 100 resin (Bio-Rad, Hercules, CA, USA)38, native hOtolC1q and dOtolC1q precipitated completely. Dialysis against Ca2+-depleted buffer did not result in satisfactory removal of bound Ca2+. Upon concluding that the proteins were not obtainable in a Ca2+-free form without the addition of EDTA or EGTA, we decided to indirectly estimate the affinity of the proteins to Ca2+ by measuring the binding of terbium(III) ions (Tb3+), as Ca2+-binding proteins can also bind lanthanide ions due to similar effective ionic radii and positive charges of Ca2+ and lanthanide ions39. The binding of lanthanide ions by Ca2+-binding proteins is usually stronger than the binding of Ca2+, due mainly to a higher positive charge40,41,42. Therefore, protein-bound Ca2+ should be substituted by Tb3+. Specifically, the use of Tb3+ in such studies gives a significant advantage, as when bound to proteins, Tb3+ can be detected thanks to luminescence resonance energy transfer (LRET) from aromatic side chains (phenylalanine, tryptophan and tyrosine) to the bound Tb3+. Upon excitation of the proteins at the aromatic absorption band (280 nm), sensitized emission from the bound Tb3+ can be observed with a maximum at 545 nm39,43. Both hOtolC1q and dOtolC1q contain numerous aromatic residues, which are a prerequisite for LRET to occur. The results of the titration experiments are shown in Fig. 2.
In summary, we discovered that the basis of the engagement of Ca2+ in the formation of gC1q domain trimers is the neutralization of the negative charge at the Ca2+ binding site. Despite the apparently stabilizing effect of substitutions of acidic Ca2+-binding residues with neutral alanine residues, hOtolC1q and dOtolC1q were ultimately the most stable in their native forms saturated with Ca2+. We also determined that hOtolC1q and its mutants were more stable than dOtolC1q and its mutants under all tested conditions, including a Ca2+-free environment. Apparently, the human protein became optimized to function at lower concentrations of Ca2+. We conclude that this predisposes otolin-1 to years-long function in biomineral organic matrices.
Synthetic cDNAs encoding full-length otolin-1 from human and zebrafish were codon-optimized for E. coli and provided by GeneArt (currently Thermo Fisher Scientific, Warsaw, Poland). Nucleotide primers were provided by Genomed (Warsaw, Poland). The pQE-80 L plasmid expression vector was purchased from Qiagen (Hilden, Germany). E. coli Top10 cells, Phusion DNA polymerase, restriction enzymes, T4 DNA ligase and LB broth were obtained from Thermo Fisher Scientific. One-fusion DNA polymerase was obtained from GeneOn (Ludwigshafen am Rhein, Germany; distributed by ABO, Gdańsk, Poland). Agar, agarose, tris(hydroxymethyl)aminomethane (Tris), ethylenediaminetetraacetic acid (EDTA), carbenicillin, isopropyl β-d-1-thiogalactopyranoside (IPTG), NaCl, glycerol, 2-mercaptoethanol, imidazole, glycine, sodium dodecyl sulfate (SDS) and CaCl2 were obtained from Carl Roth (Karlsruhe, Germany; distributed by Linegal Chemicals, Warsaw, Poland). E. coli BL21(DE3) cells, TB broth, 4-(2-hydroxyethyl)-1-piperazineethanesulfonic acid (HEPES), lysozyme, phenylmethylsulfonyl fluoride (PMSF), DNase I, RNase A, terbium(III) chloride hexahydrate, xylenol orange disodium salt and SYPRO Orange were from Sigma (currently Merck, Warsaw, Poland). The NP40 substitute was from Amresco (currently VWR, Gliwice, Poland). Empty Tricorn, Superdex 200 Increase 10/300 GL and Superdex 75 16/60 Prep Grade columns were obtained from GE Healthcare Life Sciences (currently Cytiva, Warsaw, Poland). TALON Metal Affinity resin and 6xHis monoclonal antibody (albumin-free) were purchased from Takara Bio (Mountain View, CA, USA; distributed by Biokom, Janki, Poland). HRP horse anti-mouse IgG antibody was purchased from Vector Laboratories (Burlingame, CA, USA; distributed by Biokom, Janki, Poland). 350c69d7ab