Figure 1.
The atom numbering in α-D-galacturonic acid monomer.
Figure 2.
The scheme of stretching forces.
The scheme of external stretching force actions on O1a and O4a oxygen atoms in α-D-galacturonic acid (a) monomer, (b) dimer, (c) trimer. Og indicates the oxygen atom involved in the glycosidic bond. The characteristic dihedral angles are defined as: φ1 = H1C1O1gC2, ψ1 = C1O1gC2H2 and φ2 = H3C3O2gC4, ψ2 = C3O2gC4H4).
Figure 3.
The energy of stretched and relaxed molecules.
The energy of the stretched (forced) and corresponding relaxed (a) monomer, (b) dimer, (c) trimer structures as a function of applied external force. 1au = 82.39 nN.
Figure 4.
Monomer structures obtained as a result of external forces.
The selected structures obtained as a result of external forces applied to oxygen atoms in 1,4 position in 4C1 conformer of α-D-galacturonic acid molecule with a marked distance between oxygen atoms O1 and O4.
Figure 5.
History of 4C1 conformer optimization.
History of 4C1 conformer optimization in the presence of external force f = 0.055 au (f = 4.53 nN) applied to atoms O1 and O4 with the structures from selected optimization cycles (1, 21, 32, 48, 68).
Table 1.
The values of energy and O4aO1a distance corresponding to molecular structures obtained in selected cycles of forced geometry optimization and the energy of relaxed structures with the lowest harmonic vibration frequencies.
Table 2.
Experimental (AFM experiment) and theoretical (MD method, EGO model) lengths of α-D-galacturonic acid conformers.
Figure 6.
Stretched and relaxed dimer structures.
The selected stretched and corresponding relaxed dimer structures with marked oligomer unit lengths.
Figure 7.
Theoretical force extension curves for mono-, di and trimer structures.
Table 3.
The distances between distinctive oxygen atoms (O4a, O1a and Og) of the stretched and corresponding relaxed α-D-galacturonic acid oligomer molecules obtained for the selected force value f = 0.07 au (5.77 nN).
Figure 8.
Structural parameters as a function of the optimization cycle.
The selected structural parameters as a function of the optimization cycle number; the enforced optimization in the presence of external force f = 0.07 au applied to terminal oxygen atoms O4a and O1a; a) L = O4aO1a distance, b) angles φ3 and c) ψ3 defined similarly as in Figure 1, d) ∠O4aCCC is the dihedral angle in the ring of the terminal monomer units with the unbounded O4a atom.
Figure 9.
Possible monomer conformations after the EGO procedure.
Possible conformations of monomer units in relaxed oligomer structures obtained after the EGO procedure.