Anders Irbäck

Quantum heuristics have shown promise in solving various optimization problems, including lattice protein folding. Equally relevant is the inverse problem, protein design, where one seeks sequences that fold to a given target structure. The latter problem is often split into two steps: (i) searching for sequences that minimize the energy in the target structure, and (ii) testing whether the generated sequences fold to the desired structure. Here, we investigate the utility of variational quantum algorithms for the first of these two steps on today’s noisy intermediate-scale quantum devices. We focus on the sequence optimization task, which is less resource-demanding than folding computations. We test the quantum approximate optimization algorithm and variants of it, with problem-informed quantum circuits, as well as the hardware-efficient ansatz, with problem-agnostic quantum circuits. While the former approach, with a careful choice of mixer, yields good results in noiseless simulations (success probability ≥ 0.95 in all instances), its performance drops drastically under noise. With the problem-agnostic circuits, which are more compatible with hardware constraints, improved performance is observed in noisy simulations, compared to their problem-informed counterparts. When running the problem-agnostic circuits on a real quantum device, with parameters taken from simulations, we obtain a significant success probability ( ≥ 0.2 ) in most instances.

Steric clashes pose a challenge when exploring dense protein systems using conventional explicit-chain methods. A minimal example is a single lattice protein confined on a minimal grid, with no free sites. Finding its minimum energy is a hard optimization problem, with similarities to scheduling problems. It can be recast as a quadratic unconstrained binary optimization (QUBO) problem amenable to classical and quantum approaches. We show that this problem in its QUBO form can be swiftly and consistently solved for chain length 48, using either classical simulated annealing or hybrid quantum-classical annealing on a D-Wave system. In fact, the latter computations required about 10 s. We also test linear and quadratic programming methods, which work well for a lattice gas but struggle with chain constraints. All methods are benchmarked against exact results obtained from exhaustive structure enumeration, at a high computational cost.

Field-theory simulation by the complex Langevin method offers an alternative to conventional sampling techniques for exploring the forces driving biomolecular liquid–liquid phase separation. Such simulations have recently been used to study several polyampholyte systems. Here, we formulate a field theory corresponding to the hydrophobic/polar (HP) lattice protein model, with finite same-site repulsion and nearest-neighbor attraction between HH bead pairs. By direct comparison with particle-based Monte Carlo simulations, we show that complex Langevin sampling of the field theory reproduces the thermodynamic properties of the HP model only if the same-site repulsion is not too strong. Unfortunately, the repulsion has to be taken weaker than what is needed to prevent condensed droplets from assuming an artificially compact shape. Analysis of a minimal and analytically solvable toy model hints that the sampling problems caused by repulsive interaction may stem from loss of ergodicity.

Computer simulation can provide valuable insight into the forces driving biomolecular liquid–liquid phase separation. However, the simulated systems have a limited size, which makes it important to minimize and control finite-size effects. Here, using a phenomenological free-energy ansatz, we investigate how the single-phase densities observed in a canonical system under coexistence conditions depend on the system size and the total density. We compare the theoretical expectations with results from Monte Carlo simulations based on a simple hydrophobic/polar protein model. We consider both cubic systems with spherical droplets and elongated systems with slab-like droplets. The results presented suggest that the slab simulation method greatly facilitates the estimation of the coexistence densities in the large-system limit.

Duplicative horizontal gene transfer may bring two previously separated homologous genes together, which may raise questions about the interplay between the gene products. One such gene pair is the “native” PgiC1 and “foreign” PgiC2 in the perennial grass Festuca ovina. Both PgiC1 and PgiC2 encode cytosolic phosphoglucose isomerase, a dimeric enzyme whose proper binding is functionally essential. Here, we use biophysical simulations to explore the inter-monomer binding of the two homodimers and the heterodimer that can be produced by PgiC1 and PgiC2 in F. ovina. Using simulated native-state ensembles, we examine the structural properties and binding tightness of the dimers. In addition, we investigate their ability to withstand dissociation when pulled by a force. Our results suggest that the inter-monomer binding is tighter in the PgiC2 than the PgiC1 homodimer, which could explain the more frequent occurrence of the foreign PgiC2 homodimer in dry habitats. We further find that the PgiC1 and PgiC2 monomers are compatible with heterodimer formation; the computed binding tightness is comparable to that of the PgiC1 homodimer. Enhanced homodimer stability and capability of heterodimer formation with PgiC1 are properties of PgiC2 that may contribute to the retaining of the otherwise redundant PgiC2 gene.

The formation of biomolecular condensates inside cells often involve intrinsically disordered proteins (IDPs), and several of these IDPs are also capable of forming dropletlike dense assemblies on their own, through liquid-liquid phase separation. When modeling thermodynamic phase changes, it is well known that finite-size scaling analysis can be a valuable tool. However, to our knowledge, this approach has not been applied before to the computationally challenging problem of modeling sequence-dependent biomolecular phase separation. Here we implement finite-size scaling methods to investigate the phase behavior of two 10-bead sequences in a continuous hydrophobic-polar protein model. Combined with reversible explicit-chain Monte Carlo simulations of these sequences, finite-size scaling analysis turns out to be both feasible and rewarding, despite relying on theoretical results for asymptotically large systems. While both sequences form dense clusters at low temperature, this analysis shows that only one of them undergoes liquid-liquid phase separation. Furthermore, the transition temperature at which droplet formation sets in is observed to converge slowly with system size, so that even for our largest systems the transition is shifted by about 8%. Using finite-size scaling analysis, this shift can be estimated and corrected for.

Using NMR and Monte Carlo (MC) methods, we investigate the stability and dynamics of superoxide dismutase 1 (SOD1) in homogeneous crowding environments, where either bovine pancreatic trypsin inhibitor (BPTI) or the B1 domain of streptococcal protein G (PGB1) serves as a crowding agent. By NMR, we show that both crowders, and especially BPTI, cause a drastic loss in the overall stability of SOD1 in its apo monomeric form. Additionally, we determine chemical shift perturbations indicating that SOD1 interacts with the crowder proteins in a residue-specific manner that further depends on the identity of the crowding protein. Furthermore, the specificity of SOD1-crowder interactions is reciprocal: chemical shift perturbations on BPTI and PGB1 identify regions that interact preferentially with SOD1. By MC simulations, we investigate the local unfolding of SOD1 in the absence and presence of the crowders. We find that the crowders primarily interact with the long flexible loops of the folded SOD1 monomer. The basic mechanisms by which the SOD1 β-barrel core unfolds remain unchanged when adding the crowders. In particular, both with and without the crowders, the second β-sheet of the barrel is more dynamic and unfolding-prone than the first. Notably, the MC simulations (exploring the early stages of SOD1 unfolding) and the NMR experiments (under equilibrium conditions) identify largely the same set of PGB1 and BPTI residues as prone to form SOD1 contacts. Thus, contacts stabilizing the unfolded state of SOD1 in many cases appear to form early in the unfolding reaction.