Influence of Calcium Binding on Conformations and Motions of Anionic Polyamino Acids. Effect of Side Chain Length

Abstract

Investigation of the effect of CaCl₂ salt on conformations of two anionic poly(amino acids) with different side chain lengths, poly-(α-l glutamic acid) (PGA) and poly-(α-l aspartic acid) (PASA), was performed by atomistic molecular dynamics (MD) simulations. The simulations were performed using both unbiased MD and the Hamiltonian replica exchange (HRE) method. The results show that at low CaCl₂ concentration adsorption of Ca²⁺ ions lead to a significant chain size reduction for both PGA and PASA. With the increase in concentration, the chains sizes partially recover due to electrostatic repulsion between the adsorbed Ca²⁺ ions. Here, the side chain length becomes important. Due to the longer side chain and its ability to distance the charged groups with adsorbed ions from both each other and the backbone, PGA remains longer in the collapsed state as the CaCl₂ concentration is increased. The analysis of the distribution of the mineral ions suggests that both poly(amino acids) should induce the formation of mineral with the same structure of the crystal cell.

Keywords: Hamiltonian replica exchange; mineralization; molecular dynamic simulation; poly(amino acids); poly-(α-l aspartic acid); poly-(α-l glutamic acid); salt solutions.

Figure 1

The chemical structures of (a) poly-(α-l aspartic acid) (PASA) and (b) poly-(α-l glutamic acid) (PGA) molecules. The degree of polymerization (n) in the simulations was 32.

Figure 2

(a) Radius of gyration and (b) charge of the complex formed by the poly(amino acid) and adsorbed ions (both Ca²⁺ and Cl⁻) as a function of salt concentration. The horizontal dashed line corresponds to zero charge (exact charge neutralization).

Figure 3

Transition frequencies of the φ and ψ dihedral angles for each monomer in the classical unbiased molecular dynamics (MD) simulations. Pink—all transitions, green—transitions through high-energy barriers. (a) PASA in water (b) PASA in 0.07 mol/kg CaCl₂ solution, (c) PASA in 0.29 mol/kg CaCl₂ solution, (d) PGA in water (e) PGA in 0.07 mol/kg CaCl₂ solution, (f) PGA in 0.29 mol/kg CaCl₂ solution.

Figure 4

The distribution of calcium bridge lifetimes in the highest replica (replica number 21 in Table 2) without exchanges (data from the equilibration stage).

Figure 5

The exchange frequencies between neighbor replicas for all considered systems (a) PASA-0.07 mol/kg CaCl₂ (b) PASA-0.29 mol/kg CaCl₂ (c) PGA-0.07 mol/kg CaCl₂ (d) PGA-0.29 mol/kg CaCl₂.

Figure 6

Radius of gyration distributions of PASA in 0.07 mol/kg CaCl₂ solution for all simulated replicas (a) 0–7 replicas (b) 8–13 replicas (c) 14–20 replicas.

Figure 7

The change of the dihedral angles of the main chain in each monomer in a typical section of a trajectory obtained from (a) HRE simulation and (b) MD simulation. Each pixel illustrates the conformation of one monomer during 100 ps. The colors indicate the combination of φ and ψ dihedral angles corresponding to specific secondary structures (see Figure S2): PPII helix—pink, 2.5₁₀ helix—blue, 3₁₀ helix—yellow, right-handed α helix—green, left-handed α helix—red.

Figure 8

The radius of gyration distributions obtained from (a) HRE simulations and (b) classical non-biased MD simulation.

Figure 9

Distribution of the distances along the chain between monomers connected by calcium bridges.

Figure 10

Snapshots of typical chain conformations with Ca²⁺ ions bridging the carboxyl groups. (a) PASA and (b) PGA at 0.29 mol/kg CaCl2 solution.

Figure 11

The results from the integration of the areas of the Ramachandran plots related to different secondary structures (more stretched (PPII and 2.5₁ helices) and less stretched (α (left-handed and right-handed) and 3₁₀ helices). The Ramachandran plot with the specified areas is shown in Figure S2. (a) PASA (b) PGA.

Figure 12

The pair distribution functions obtained from our simulations compared to the distribution obtained for calcium tri-hydrated and di-hydrated oxalates extracted from [75]. Comparison between calcium oxalate tri-hydrate (COT) and (a) PASA, (b) PGA. Comparison between calcium oxalate di-hydrate (COD) and (c) PASA, (d) PGA.