Effect of hydrogen bond networks on the nucleation mechanism of protein folding

Y. S. Djikaev and Eli Ruckenstein

Phys. Rev. E 80, 061918 – Published 29 December 2009

Abstract

We have recently developed a kinetic model for the nucleation mechanism of protein folding (NMPF) in terms of ternary nucleation by using the first passage time analysis. A protein was considered as a random heteropolymer consisting of hydrophobic, hydrophilic (some of which are negatively or positively ionizable), and neutral beads. The main idea of the NMPF model consisted of averaging the dihedral potential in which a selected residue is involved over all possible configurations of all neighboring residues along the protein chain. The combination of the average dihedral, effective pairwise (due to Lennard-Jones-type and electrostatic interactions), and confining (due to the polymer connectivity constraint) potentials gives rise to an overall potential around the cluster that, as a function of the distance from the cluster center, has a double-well shape. This allows one to evaluate the protein folding time. In the original NMPF model hydrogen bonding was not taken into account explicitly. To improve the NMPF model and make it more realistic, in this paper we modify our (previously developed) probabilistic hydrogen bond model and combine it with the former. Thus, a contribution due to the disruption of hydrogen bond networks around the interacting particles (cluster of native residues and residue in the protein unfolded part) appears in the overall potential field around a cluster. The modified model is applied to the folding of the same model proteins that were examined in the original model: a short protein consisting of 124 residues (roughly mimicking bovine pancreatic ribonuclease) and a long one consisting of 2500 residues (as a representative of large proteins with superlong polypeptide chains), at $p H = 8.3$ , 7.3, and 6.3. The hydrogen bond contribution now plays a dominant role in the total potential field around the cluster (except for very short distances thereto where the repulsive energy tends to infinity). It is by an order of magnitude stronger for hydrophobic residues than for hydrophilic ones. The range of “residue-cluster” distances, at which the hydrogen bond effect exists, is twice as long for hydrophobic residues as for hydrophilic ones.

Received 30 July 2009

DOI:https://doi.org/10.1103/PhysRevE.80.061918

Authors & Affiliations

Y. S. Djikaev^* and Eli Ruckenstein^†

Department of Chemical and Biological Engineering, SUNY at Buffalo, Buffalo, New York 14260, USA

^*idjikaev@buffalo.edu
^†Corresponding author. FAX: (716) 645-3822; feaeliru@buffalo.edu

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Vol. 80, Iss. 6 — December 2009

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Images

Figure 1
A schematic representation of the first two hydration layers two spherical solutes of radii $R$ and $R^{'}$ at a distance $r$ between their centers. The surface of each particle is shown as a thick solid line. The circles of diameter $η_{w}$ represent water molecules. The dashed circle of radius $η$ represents a molecule of the solute particle.Reuse & Permissions
Figure 2
A schematic representation of a water molecule in the first hydration shell (1HS) of the planar substrate surface (shadowed area). The lower and upper boundaries of the 1HS are marked as the planes $L 1$ and $U 1$ and shown as long-dashed lines. The molecule, shown as a disk $S$ , is at the distance $ξ$ from the lower boundary (closest to the hydrophobic surface) of 1HS. The four hb arms of the molecule are shown as short-dashed lines with the empty circles as the arm tips. Arms 1 and 2 are in the plane of the figure, whereas arms 3 and 4 are located out of the figure plane (one of them under it, the other above it). The angle between any two hb arms is $α$ . The angle $Θ$ is the angle formed between the hb arm and its tangential projection (parallel to the lower boundary of the 1HS). In this figure, the origin of the Cartesian coordinate system lies at the hydrophobic surface with the $z$ axis being normal thereto. It is assumed that $- π / 2 \leq Θ \leq π / 2$ with $Θ < 0$ if the $z$ coordinate of the hb-arm tip is greater than $(η + η_{w}) / 2 + ξ$ and $Θ > 0$ , otherwise. The large dashed circle represents a water molecule, while the smaller dashed semicircles represent the substrate molecules.Reuse & Permissions
Figure 3
The boundary hydrogen bond networks contribution $ϕ^{hb}$ to the total interaction potential between two spherical solutes, one of which is a composite particle of radius $R = 5 η_{w}$ (and of hydrophobic surface fraction $ω_{b} = 0.4$ ) and the other is either a hydrophobic (thick dashed curve) or hydrophilic (thin continuous curve) particle of radius $R^{'} = 0$ (which corresponds to a single protein residue). The potential is plotted as $ϕ^{hb} / | Φ^{'} |$ vs $r / η_{w}$ , where $Φ^{'} = ϵ_{b} n_{b} ρ_{w} η_{w}^{3}$ is twice the energy of water-water hydrogen bonds in the volume $η_{w}^{3}$ of bulk water. The leftmost dotted-dashed vertical line indicates the location of $r_{1}$ , whereas the middle and rightmost lines indicate the location of $r_{0}$ for hydrophilic and hydrophobic beads, respectively. The solvent (water) is under such conditions that $n_{b} = 3.65$ .Reuse & Permissions
Figure 4
A piece of a heteropolymer chain around a spherical cluster consisting of $ν_{b}$ hydrophobic, $ν_{l}$ hydrophilic, and $ν_{n}$ neutral beads. Among the hydrophilic beads themselves $ν_{l}^{o}$ are uncharged, $ν_{l}^{-}$ are negatively charged, and $ν_{l}^{+}$ are positively charged. Bead 1 is in the plane of the figure, whereas other beads may all lie in different planes. All bond angles are equal to $β_{0}$ and their lengths are equal to $η$ . The radius of the cluster is $R$ and the distance from the selected bead 1 to the cluster center is $r$ Reuse & Permissions
Figure 5
(a) The potentials $ϕ_{b} (r) + ϕ_{b}^{hb}$ (lower dashed curve), $ϕ_{b} (r)$ (upper dashed curve), ${\bar{ϕ}}_{b}^{δ} (r)$ (dotted-dashed curve), and $ψ_{b} (r)$ (solid curve), for a hydrophobic bead around a cluster with $ν_{b} = 23, ν_{l} = 41, ν_{l}^{-} = 4.5, ν_{l}^{+} = 6.5, ν_{n} = 2$ at $p H = 7.3$ [ $ϕ_{b} (r)$ , ${\bar{ϕ}}_{b}^{δ} (r)$ , $ϕ_{cp}$ , $ϕ^{hb}$ , and $ψ_{b} (r)$ are the effective pairwise, average dihedral angle, confining, solvent-mediated (hydrogen bond), and total potentials for a hydrophobic bead around the cluster of folded protein]. The confining potential is shown as a solid vertical line at $r_{cp} ≃ 18.5 η_{w}$ whereas the hydrogen bond contribution is plotted separately in Fig. 3. All the potentials are given in units of $ϵ_{b b}$ , the energy parameter in the Lennard-Jones potential of pairwise interactions between two hydrophobic beads. (b) shows the curve $ψ_{b} (r)$ alone for the better visualization of its double-well shape.Reuse & Permissions

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