The B-domain of staphylococcal protein A (BdpA), a 60-residue three-helix bundle and classic ultrafast two-state folder, was simulated in 2008 with the activation-relaxation technique (ART) and the coarse-grained OPEP force field; the resulting low-energy minima organized into multiple funnels - the native basin plus off-pathway funnels containing ordered non-native topologies, including mirror-image helix packings and fully ordered structures resembling the native states of nonhomologous proteins. Because ART does not satisfy detailed balance and OPEP omits explicit solvent, vibrational entropy, and a consistent temperature dependence, the physical status, equilibrium populations, and kinetics of these competing funnels could not be established. Later work has addressed these limitations only in part - reversible explicit-solvent folding with extracted equilibrium and kinetics for the native basin (2011), a report across several method families, including explicit-solvent replica exchange, of a mirror-image topology competitive with the native state (2012), and a metastable mirror-image basin in coarse-grained UNRES dynamics (2014) - while single-molecule experiments find apparent two-state behavior with heterogeneous ensembles and no detected off-pathway intermediate, and a 2019 proposal to detect the mirror image in solution via a Q10H pKa shift has not been executed. No converged free-energy map of the alternative funnels under physically consistent treatments exists, and no experimental detection has been reported, leaving a precise open core: whether the competing funnels carry non-negligible equilibrium populations, with force-field robustness and experimental detection as corroborating lines of evidence.

Background

The B-domain of staphylococcal protein A (BdpA) is a 60-residue, three-alpha-helix bundle that folds on a microsecond timescale and is a standard model system for protein folding: its thermodynamics and kinetics appear two-state, and it has been studied by phi-value analysis and psi-analysis (methods that infer the structure of the folding transition state from how point mutations, or engineered metal-ion binding sites, change the folding and unfolding rates), hydrogen/deuterium isotope effects, single-molecule fluorescence, and many simulations. In the energy-landscape picture of folding, a denatured chain descends a biased free-energy surface toward the native state; the surface is often idealized as a single funnel, but residual frustration can in principle produce several competing low-free-energy funnels corresponding to distinct folded topologies, which would imply populated alternative structures, complex kinetics, and misfolding routes. A mirror-image conformation is the competing topology of a helical bundle in which the secondary structure is native-like but the handedness of the helix packing is reversed. In 2008, St-Pierre, Mousseau, and Derreumaux studied BdpA with the activation-relaxation technique (ART) - an event-based sampling method that walks between potential-energy minima through first-order saddle points and, as a Langevin-free discrete explorer, does not obey detailed balance, so no equilibrium weights or rates can be read from it - coupled to OPEP (Optimized Potential for Efficient structure Prediction), an implicit-solvent coarse-grained protein force field. Across more than 50 unbiased folding trajectories they found diverse folding pathways and a set of low-energy minima partitioned into multiple funnels: the native basin (their lowest funnel, labeled LE1 in the paper) plus off-pathway funnels containing non-native beta and alpha structure, including fully ordered minima resembling native states of nonhomologous proteins, with reported energy separations of about 14 kcal/mol. The authors explicitly acknowledged that this picture carries method limitations: the effective potential neglects explicit vibrational entropy and a physically consistent temperature dependence (the Metropolis temperatures used are sampling parameters, not thermodynamic temperatures), so equilibrium probabilities and relative rates of the funnels cannot be established from these trajectories; the coarse-grained implicit-solvent treatment may over-stabilize helices and intermediates and reproduce folding cooperativity imperfectly; and the predicted rare ordered off-pathway minima had no experimental detection. Direct detection of the mirror-image funnel in solution was later proposed but has not been performed: Martin, Vorobjev, Scheraga and Vila (PeerJ Phys. Chem. 1, e2, 2019) outline a mutational experiment in which a Q10H (glutamine-10-to-histidine) variant of protein A is predicted to show a histidine pKa of about 6.2 in the native conformation versus about 7.3 in the mirror image, so that a measured pKa would report the population of the mirror-image conformation. These acknowledged limitations define a well-posed scientific question that subsequent literature has addressed only in part.

Problem Statement

For the B-domain of staphylococcal protein A, determine whether the physical folding free-energy landscape is genuinely multiple-funnelled, and with what consequences. Concretely, with physically consistent treatments - explicit-solvent, temperature-dependent models in which equilibrium weights and rates are well defined, or direct experiment - establish: (i) the equilibrium populations and interconversion kinetics of the native basin relative to competing ordered non-native funnels, including the mirror-image topology and other off-pathway ordered minima reported in the ART/OPEP study; (ii) whether these competing funnels persist, weaken, or disappear across independent modern force fields and solvent/entropy treatments, i.e. whether they are physical features of the landscape or artifacts of coarse-grained implicit-solvent sampling; and (iii) whether the predicted rare off-pathway ordered structures can be detected experimentally in solution. Component (i) is the central target: converged equilibrium populations and interconversion kinetics of the native basin relative to the competing ordered non-native funnels under physically consistent treatments, with a stated and justified criterion for non-negligibility. Components (ii) and (iii) are corroborating lines of evidence.

References

  1. J.-F. St-Pierre, N. Mousseau, P. Derreumaux, 'The complex folding pathways of protein A suggest a multiple-funnelled energy landscape', The Journal of Chemical Physics 128, 045101 (2008). DOI: 10.1063/1.2812562, https://doi.org/10.1063/1.2812562
  2. M. C. Baxa, K. F. Freed, T. R. Sosnick, 'Quantifying the structural requirements of the folding transition state of Protein A and other systems', Journal of Molecular Biology 381, 1362-1381 (2008). DOI: 10.1016/j.jmb.2008.06.067, https://doi.org/10.1016/j.jmb.2008.06.067
  3. H. Lei, C. Wu, Z.-X. Wang, Y. Zhou, Y. Duan, 'Folding processes of the B domain of protein A to the native state observed in all-atom ab initio folding simulations', The Journal of Chemical Physics 128, 235105 (2008). DOI: 10.1063/1.2937135, https://doi.org/10.1063/1.2937135
  4. K. Lindorff-Larsen, S. Piana, R. O. Dror, D. E. Shaw, 'How fast-folding proteins fold', Science 334, 517-520 (2011). DOI: 10.1126/science.1208351, https://doi.org/10.1126/science.1208351
  5. J. K. Noel, A. Schug, A. Verma, W. Wenzel, A. E. Garcia, J. N. Onuchic, 'Mirror Images as Naturally Competing Conformations in Protein Folding', The Journal of Physical Chemistry B 116, 6880-6888 (2012). DOI: 10.1021/jp212623d, https://doi.org/10.1021/jp212623d
  6. N. Mousseau, L. K. Beland, P. Brommer, J.-F. Joly, F. El-Mellouhi, E. Machado-Charry, M.-C. Marinica, P. Pochet, 'The Activation-Relaxation Technique: ART Nouveau and Kinetic ART', Journal of Atomic, Molecular, and Optical Physics 2012, 925278 (2012). DOI: 10.1155/2012/925278, https://doi.org/10.1155/2012/925278
  7. Y. Chebaro, X. Dong, R. Laghaei, P. Derreumaux, N. Mousseau, 'Replica Exchange Molecular Dynamics Simulations of Coarse-grained Proteins in Implicit Solvent', The Journal of Physical Chemistry B 113, 267-274 (2009). DOI: 10.1021/jp805309e, https://doi.org/10.1021/jp805309e
  8. K. Kachlishvili, G. G. Maisuradze, O. A. Martin, A. Liwo, J. A. Vila, H. A. Scheraga, 'Accounting for a mirror-image conformation as a subtle effect in protein folding', Proceedings of the National Academy of Sciences USA 111, 8458-8463 (2014). DOI: 10.1073/pnas.1407837111, https://doi.org/10.1073/pnas.1407837111
  9. F. Sterpone, S. Melchionna, P. Tuffery, S. Pasquali, N. Mousseau, T. Cragnolini, Y. Chebaro, J.-F. St-Pierre, M. Kalimeri, A. Barducci, Y. Laurin, A. Tek, M. Baaden, P. H. Nguyen, P. Derreumaux, 'The OPEP protein model: from single molecules, amyloid formation, crowding and hydrodynamics to DNA/RNA systems', Chemical Society Reviews 43, 4871-4893 (2014). DOI: 10.1039/c4cs00048j, https://doi.org/10.1039/c4cs00048j
  10. H. Oikawa, K. Kamagata, M. Arai, S. Takahashi, 'Complexity of the folding transition of the B domain of protein A revealed by the high-speed tracking of single-molecule fluorescence time series', The Journal of Physical Chemistry B 119, 6081-6091 (2015). DOI: 10.1021/acs.jpcb.5b00414, https://doi.org/10.1021/acs.jpcb.5b00414
  11. T. Otosu, K. Ishii, H. Oikawa, M. Arai, S. Takahashi, T. Tahara, 'Highly Heterogeneous Nature of the Native and Unfolded States of the B Domain of Protein A Revealed by Two-Dimensional Fluorescence Lifetime Correlation Spectroscopy', The Journal of Physical Chemistry B 121, 5463-5473 (2017). DOI: 10.1021/acs.jpcb.7b00546, https://doi.org/10.1021/acs.jpcb.7b00546
  12. O. A. Martin, Y. N. Vorobjev, H. A. Scheraga, J. A. Vila, 'Outline of an experimental design aimed to detect protein A mirror image in solution', PeerJ Physical Chemistry 1, e2 (2019). DOI: 10.7717/peerj-pchem.2, https://doi.org/10.7717/peerj-pchem.2
  13. A. F. Pereira, L. Martinez, 'Helical Content Correlations and Hydration Structures of the Folding Ensemble of the B Domain of Protein A', Journal of Chemical Information and Modeling 64, 3350-3359 (2024). DOI: 10.1021/acs.jcim.3c01822, https://doi.org/10.1021/acs.jcim.3c01822