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Geometry and topology are the main factors that determine the functionalproperties of proteins. In this work, we show how to use the Gauss linkingintegral (GLN) in the form of a matrix diagram - for a pair of a loop and atail - to study both the geometry and topology of proteins with closed loopse.g. lassos. We show that the GLN method is a significantly faster technique todetect entanglement in lasso proteins in comparison with other methods. Basedon the GLN technique, we conduct comprehensive analysis of all proteinsdeposited in the PDB and compare it to the statistical properties of thepolymers. We found that there are significantly more lassos with negativecrossings than those with positive ones in proteins, the average value ofmaxGLN (maximal GLN between loop and pieces of tail) depends logarithmically onthe length of a tail similarly as in the polymers. Next, we show the how highand low GLN values correlate with the internal exibility of proteins, and howthe GLN in the form of a matrix diagram can be used to study folding andunfolding routes. Finally, we discuss how the GLN method can be applied tostudy entanglement between two structures none of which are closed loops. Sincethis approach is much faster than other linking invariants, the next step willbe evaluation of lassos in much longer molecules such as RNA or loops in asingle chromosome.

GLN -- a method to reveal unique properties of lasso type topology in proteins