Abstract
We investigate aspects of topology in protein folding. For this we numerically simulate the temperature driven folding and unfolding of the slipknotted archaeal virus protein AFV3-109. Due to knottiness the (un)folding is a topological process, it engages the entire backbone in a collective fashion. Accordingly we introduce a topological approach to model the process. Our simulations reveal that the (un)folding of AFV3-109 slipknot proceeds through a folding intermediate that has the topology of a trefoil knot. We observe that the final slipknot causes a slight swelling of the folded AFV3-109 structure. We disclose the relative stability of the strands and helices during both the folding and unfolding processes. We confirm results from previous studies that pointed out that it can be very demanding to simulate the formation of knotty self-entanglement, and we explain how the problems are circumvented: The slipknotted AFV3-109 protein is a very slow folder with a topologically demanding pathway, which needs to be properly accounted for in a simulation description. When we either increase the relative stiffness of bending, or when we decrease the speed of ambient cooling, the rate of slipknot formation rapidly increases.
Highlights
The pertinent partial difference equations describe critical points of an energy function, in an effective theory approach that builds on the Cα protein backbone geometry
Topology and in particular self-entanglement play an important role in protein folding and dynamics
Knotty and other kind of self-entanglements are often important to protein stability, and presumably important for the correct biological function
Summary
They are used with great success to analyze numerous problems in Physics, from theories of fundamental interactions to models of condensed matter. We propose to introduce topological techniques to study protein folding and dynamics, where far these techniques have been used only sparsely. As an example we analyze the formation of knots and self-entanglement in protein folding. A knot along a protein backbone is a delocalized structure, with a definite topological character. A knot can not be removed by any small amplitude local motion such as twisting, bending or crumpling of the protein backbone. A knotty self-entanglement persists as long as there is no backbone chain crossing, and provided the C and N terminals of the protein are not circumnavigated
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