08-17 September 2022
Dr Ivan Coluzza
CIC biomaGUNE, San Sebastian (Donostia)
Prof. Achille Giacometti
University Ca’ Foscari of Venice, Venice, Italy
Aim of the mission
During the STSM we have established a strategy to compute the energy landscape of protein-like polymer chains. We will proceed into three steps; WP1) on the one side we will start by defining the set of parameters of the OPLS model  that allow the model to be designed according to the protocol derived in . WP2) With such parameter we will then explore the equilibrium properties and identify the relative designability of the elixir phase and of knotted structure. WP3) measure of the energy landscape of the designable structures for both models and compare them.
Summary of the Results
WP1: The designability of the Caterpillar model  was demonstrated to arise from the backbone H-Bonds. Later we showed that the directionality of such interactions is key for the designability. In parallel the OPLS model developed by T Škrbić et al. showed that by introducing a side chain mediated directionality chain molecules would develop protein-like secondary structures in a specific region of the model parameters called the Elixir phase. In WP1 we will attempt to test if the OPLS model in the ELIXIR phase is designable and compare the folded structure with the known protein structure. If successful we will have a stepping stone between the caterpillar model and traditional C! models. The importance of this step is to obtain a minimal protein model with the correct geometry of secondary and tertiary structures.
WP2: The parameters resulting from WP1 will allow us to explore the relative designability of target structures. This will be done for both the OPLS and the Caterpillar model and we will compare the results among them and with natural protein architectures. We will also explore the relative designability of knotted structures.
WP3: The equilibrium properties from WP2 will then be used in an energy landscape analysis. The models under consideration [1,2] are not directly amenable to energy landscape approaches based on potential energy minima and transition states because the models incorporate both steeply repulsive (even discontinuous) and flat (zero or near-zero gradient) regions of potential energy. Instead, we will adopt an approach based on free energy landscapes, at least initially. We plan to explore two methods . The first involves enhanced sampling in the joint space of several order parameters. Free energy analysis is often restricted to just one or two parameters, but following a larger number of parameters avoids oversimplifying the landscape and the risk of missing important features. It also somewhat mitigates the problem of choosing appropriate order parameters. The global topology of an order parameter space with, say, three to five dimensions can then be characterised by its minima and saddle points and represented on a disconnectivity graph [3,5]. The second possible method avoids the order parameter problem altogether and uses clustering of configurations in (pseudo-)dynamical trajectories. The flux of trajectories in the network of clusters can then by analysed using the max-flow/min-cut method and represented in a different variety of disconnectivity graph . In either case, the resulting disconnectivity graphs provide a comprehensive characterisation of the system’s behaviour in a way that is not achieved by conventional molecular dynamics, Monte Carlo or structural optimisation approaches.
During the short visit we have established an extensive collaboration program and started already to develop the necessary tools. In the coming years we expect the collaboration to grow an result in several publications across the nodes of EUTOPIA. Moreover, the tools that we will develop will be of high significance for the Work Group 2, on “polymeric and fibrous topological materials” and Work Group 3 on “entangled and self-entangled proteins”. In particular, it will create a theoretical bridge between proteins and polymers that is extremely important to join the activities of the WG2 and WG3.