Geofold: topology-based protein unfolding pathways capture the effects of engineered disulfides on kinetic stability

Abstract

Protein unfolding is modeled as an ensemble of pathways, where each step in each pathway is the addition of one topologically possible conformational degree of freedom. Starting with a known protein structure, GeoFold hierarchically partitions (cuts) the native structure into substructures using revolute joints and translations. The energy of each cut and its activation barrier are calculated using buried solvent accessible surface area, side chain entropy, hydrogen bonding, buried cavities, and backbone degrees of freedom. A directed acyclic graph is constructed from the cuts, representing a network of simultaneous equilibria. Finite difference simulations on this graph simulate native unfolding pathways. Experimentally observed changes in the unfolding rates for disulfide mutants of barnase, T4 lysozyme, dihydrofolate reductase, and factor for inversion stimulation were qualitatively reproduced in these simulations. Detailed unfolding pathways for each case explain the effects of changes in the chain topology on the folding energy landscape. GeoFold is a useful tool for the inference of the effects of disulfide engineering on the energy landscape of protein unfolding.

Figure 1

(a) Elemental subsystem for the kinetic model, a cut. f is any spatially contiguous substructure of a protein, and is partitioned into spatially contiguous substructures u₁ and u₂. (b) Diamond shapes represent the cuts, each having a type (color) and an associated energy barrier ‡. A pivot motion is single point revolute joint. A hinge rotates around two points. A break is a pure translational motion. Rotations and translations must not cross chains. (c) Top portion of an unfolding pathway DAG for DHFR. Node 1 is the fully folded state. Green lines indicate the pathway of maximum unfolding traffic; grey lines are other significant pathways. Unfolding simulations start with all of the protein in node 1, and end when node concentrations reach equilibrium.

Figure 2

(a) Barnase ribbon showing locations of first four pivot locations and the disulfide positions. (b) Secondary structure element diagram of barnase showing locations of disulfide linkages. Online color version shows the predominant pathway of unfolding from red (early unfolding) to blue (late unfolding). (c) Simulated unfolding kinetics, showing a slowing effect for mutants 85-102 and 70-92, a result of blocking early unfolding steps. Note that slow unfolding rates with ln(k_u) < −5 cannot be measured. (d) Equilbrium unfolding simulation, varying desolvation energy ω.

Figure 3

(a) Figure 2 from Matsumura et al, used by permission, showing the changes in melting temperature for reduced versus oxidized disulfide mutants of T4 lysozyme. (b) Changes in equilibrium unfolding point, as ω value, in GeoFold simulations. Mutants 127-154 and 90-122 unfold at the same w at WT*. (c-d) Age plot for unfolding pathway of (c) wild type T4 lysozyme, or reduced, or 127-154 or 90-122 mutants, and (d) oxidized 21-142 or 9-164 mutants, with contacts colored red to blue according to unfolding order. Upper inset in (c-d): first unfolding step, a pivot move in (c), a hinge move in (d). Lower inset: ribbon drawing showing how the structure is divided in the first unfolding step by (c) the pivot move p, and (d) the hinge move h.

Figure 4

DHFR. (a) Figure 4 from Villafranca et al, used by permission, showing urea gradient gel electrophoresis equilibrium denaturation of reduced and oxidized P39C DHFR. (b) Simulated equilibrium denaturation curve from GeoFold. The axes have been reversed to match the image. (c) DHFR ribbon showing location of engineered disulfide and first unfolding steps in the inside-out pathway, hinge h, and the outside-in pathway, pivot p.

Figure 5

FIS. (a) Figure 4 from Meinhold et al, used by permission, showing equilibrium unfolding circular dichroism data for FIS disulfide variants. (b) Simulated equilibrium unfolding curves from GeoFold for the same variants. Note that axes are reversed to conform with (a). (c) Ribbon diagram for alpha helical part of FIS dimer, showing principle cleavage points and locations of mutations.

Figure 6

GeoFOLD algorithm.