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Proteins with a non-trivial topological structure are currently well recognized, while a knotted protein chain represents a new motif in protein three dimensional folds. Recent comprehensive analysis of the Protein Data Base shows that knotted proteins represent 1.5% of known protein structures. Determination of a free energy landscape of knotted proteins, and its understanding provides a serious challenge for both experimentalists and theoreticians. Moreover the role of a knot for biological activity of protein still remains elusive. In this work we study the smallest knotted proteins (PDB code 2efv) to understand/investigate their free energy landscape, by means of extensive molecular dynamics simulations. We explore the dependence of the thermodynamics, kinetics and protein folding pathways on the native-likes contact maps and on the length of the chain. We analyze two sets of native-like contacts, which differ by a number of long range interactions, and we consider the 2efv protein with two different lengths of its C-terminus end. We identify the subset of native contacts suffiient to explore the entire free energy landscape. Then, we analyze the influence of the remaining set of native contacts – we show that the set of additional contacts may enhance folding kinetics, and that it has an influence on folding pathways.