Physics and Evolution of Knotted Proteins

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Physics and evolution of knotted proteins

Publication . Especial, João N. C.; Faísca, Patrícia

Proteins are a key component of all biological systems, performing crucial functions in essentially all biological processes. Hence, proteins, already of great value in Medicine, have the potential to become of even greater value when fully mastered. Before they can perform their function, proteins must acquire their biologically active conformation, called the native conformation, through the process of protein folding. Understanding the protein folding process is thus a mandatory step towards mastering these molecular nanomachines. Because knotted proteins embed an open knot in their native conformations, understanding their folding process is the most challenging variant of the protein folding problem and this has led to considerable interest in the scientific community. This work focuses on the folding process of knotted proteins and addresses two important questions: 1. Are non-native interactions required to efficiently fold knotted proteins? If so, what is their role in the folding process? 2. Are early prebiotic amino acid alphabets able to encode knotted folds or do such folds require larger amino acid alphabets? Because, with the exception of small proteins with simple topologies, the protein folding process requires time-scales that are currently unattainable by all-atom computer simulations, we addressed these questions using coarse-grained protein models, with different levels of granularity, and Monte Carlo simulation methods. These methods enabled us to simulate the entire folding process and study both thermal equilibrium ensembles and folding kinetics, the latter using non-equilibrium fixed-temperature off-lattice simulations. This dissertation begins with a brief introduction to proteins, the protein folding process and knotted proteins in particular, in the first chapter. The second chapter introduces protein models and describes in detail the models used in this work. The third chapter recapitulates the theoretical foundations of Monte Carlo methods for protein folding simulations as well as the theoretical foundations of the weighted histogram analysis method (WHAM) used for data analysis. Chapters 4 to 7 report the results achieved. Chapters 4 and 6 address the first question and Chapter 7 the second. In Chapter 4 we report that, on-lattice, thermal equilibrium simulations suggest that efficient knotting is driven by a critical set of specific native interactions, which do not backtrack, and contribute to stabilize an intermediate state that decreases the folding free energy barrier. Nevertheless, these simulations also show that specific non-native interactions may play a functional role in the knotting process by acting like a scaffold that temporarily stabilizes the knotting loop, or assists the threading step. This result is consistent with that observed in off-lattice thermal equilibrium simulations, reported in Chapter 6, which show that the non-native interactions that stabilize knotted conformations are non-local and located in the vicinity of native ones. In Chapter 6 we also report that kinetic simulations (i.e., non-equilibrium fixed-temperature offlattice simulations) suggest that native interactions are sufficient to efficiently fold deeply knotted proteins provided the simulation temperature is well below the transition temperature. Non-native interactions, though not necessary to fold, accelerate knotting by approximately one order of magnitude in the knoticity, this being measured as the mean number of first knotting events per million Monte Carlo steps. A relevant methodological finding of our study, reported in Chapter 5, is that off-lattice thermal equilibrium simulations can be considerably accelerated (relaxation to thermal equilibrium requiring between one and two orders of magnitude less Monte Carlo steps) by using a move-set that does not preserve the linear topology of the chain rather than a move-set that does. By using the former in off-lattice thermal equilibrium simulations, we found that knot depth does not per se influence thermal stability as measured by the transition temperature. In Chapter 4 we also found that, on-lattice, efficient knotting only required 12 out of the 40 native interactions present in our protein model (which represents a reduction of 30% of the original amino acid alphabet). This suggests that while energetic heterogeneity is important to ensure a well-defined and correct order of contact formation, a 20 amino acid alphabet may not be necessary to tie a polypeptide chain efficiently. In Chapter 7 we report that by developing a method to create pre-biotic primary sequences, we found - through the use of AlphaFold - that early amino acid alphabets, which involve smaller numbers of amino acids, appear sufficient to encode knotted folds. In addition, off-lattice Monte Carlo simulations that explored the folding and knotting transition of the AlphaFold predicted knotted proteins, indicate that through the introduction of larger amino acid alphabets, evolution tended to increase the number of native contacts in the native structure, thereby increasing their thermal stability, their folding efficiency (this being measured by the foldicity which we define as the mean number of folding transitions per million Monte Carlo steps) and their knotting efficiency, both to the first knotting event and to the last knotting event that occur along the folding process (these being measured by the respective knoticities which are defined as the mean number of first(last) knotting events per million Monte Carlo steps). The dissertation ends with a concluding chapter that describes the work performed, collects the conclusions reached and identifies future conceptual and methodological work.

2024-04-16Tese de doutoramento

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Fundação para a Ciência e a Tecnologia

Número da atribuição

SFRH/BD/144345/2019