Statistical Properties of Lasso-Shape Polymers and Their Implications for Complex Lasso Proteins Function

Dąbrowski-Tumański, Paweł; Greń, Bartosz Ambroży; Sułkowska, Joanna I.

doi:10.3390/polym11040707

Cited by 9 publications

(4 citation statements)

References 90 publications

(117 reference statements)

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“…The Mathematica visualization of surface files obtained for nontrivial lassos are shown in Figure 6 C. The composition of such commands allows for a comprehensive analysis of the lasso type topology—location of the loop and piercings and depth of piercings. Both parameters are important to study kinetics pathways [ 28 , 54 ], stability [ 38 ] and statistical and biological properties [ 15 ].…”

Section: Exemplary Casesmentioning

confidence: 99%

Topoly: Python package to analyze topology of polymers

Dąbrowski-Tumański¹,

Rubach²,

Niemyska³

et al. 2020

Briefings in Bioinformatics

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The increasing role of topology in (bio)physical properties of matter creates a need for an efficient method of detecting the topology of a (bio)polymer. However, the existing tools allow one to classify only the simplest knots and cannot be used in automated sample analysis. To answer this need, we created the Topoly Python package. This package enables the distinguishing of knots, slipknots, links and spatial graphs through the calculation of different topological polynomial invariants. It also enables one to create the minimal spanning surface on a given loop, e.g. to detect a lasso motif or to generate random closed polymers. It is capable of reading various file formats, including PDB. The extensive documentation along with test cases and the simplicity of the Python programming language make it a very simple to use yet powerful tool, suitable even for inexperienced users. Topoly can be obtained from https://topoly.cent.uw.edu.pl.

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Section: Exemplary Casesmentioning

confidence: 99%

Topoly: Python package to analyze topology of polymers

Dąbrowski-Tumański¹,

Rubach²,

Niemyska³

et al. 2020

Briefings in Bioinformatics

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“…From the above definition 𝑆 𝐴 can take values between −1/4 for perfectly oblate objects and 2 for perfectly prolate ones. An alternative but equivalent definition of the prolatness can be found in Ostermeir et al (2010); Dabrowski-Tumanski et al (2019). The asphericity defined in equation ( 8), also known as anisotropy, is a particular case, for a three-dimensional mass distribution, of the more general quantity…”

Section: Shape Descriptorsmentioning

confidence: 99%

The physical and the geometrical properties of simulated cold H i structures

Gazol¹,

Villagran

2020

Monthly Notices of the Royal Astronomical Society

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The objective of this paper is to help shedding some light on the nature and the properties of the cold structures formed via thermal instability in the magnetized atomic interstellar medium. To this end, we searched for clumps formed in forced (magneto)hydrodynamic simulations with an initial magnetic field ranging from 0 to 8.3 μG. We statistically analysed, through the use of Kernel density estimations, the physical and the morphological properties of a sample containing ∼1500 clumps, as well as the relative alignments between the main direction of clumps and the internal velocity and magnetic field. The density (n ∼ 50–200 cm−3), the thermal pressure (Pth/k ∼ 4.9 × 103–104 K cm−3), the mean magnetic field (∼3–11 μG), and the sonic Mach number of the selected clumps have values comparable to those reported in observations. We find, however, that the cloud sample cannot be described by a single regime concerning their pressure balance and their Alfvénic Mach number. We measured the morphological properties of clumps mainly through the asphericity and the prolatness, which appear to be more sensitive than the aspect ratios. From this analysis, we find that the presence of magnetic field, even if it is weak, does qualitatively affect the morphology of the clumps by increasing the probability of having highly aspherical and highly plolate clumps by a factor of two, that is by producing more filamentary clumps. Finally, we find that the angle between the main direction of the clumps and the local magnetic field lies between ∼π/4 and π/2 and shifts to more perpendicular alignments as the intensity of this field increases, while the relative direction between the local density structure and the local magnetic field transits from parallel to perpendicular.

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“…Phantom lassos (polymers deprived of any interactions and volume) were created by connecting phantom loops and phantom tails. Phantom loops were created as equilateral polygons using the dedicated algorithm [48] and tested earlier in the [49].…”

Section: Methodsmentioning

confidence: 99%

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

Niemyska¹,

Millett²,

Sułkowska³

2020

Preprint

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Geometry and topology are the main factors that determine the functional properties of proteins. In this work, we show how to use the Gauss linking integral (GLN) in the form of a matrix diagramfor a pair of a loop and a tail -to study both the geometry and topology of proteins with closed loops e.g. lassos. We show that the GLN method is a significantly faster technique to detect entanglement in lasso proteins in comparison with other methods. Based on the GLN technique, we conduct comprehensive analysis of all proteins deposited in the PDB and compare it to the statistical properties of the polymers. We found that there are significantly more lassos with negative crossings than those with positive ones in proteins, the average value of maxGLN (maximal GLN between loop and pieces of tail) depends logarithmically on the length of a tail similarly as in the polymers. Next, we show the how high and low GLN values correlate with the internal flexibility of proteins, and how the GLN in the form of a matrix diagram can be used to study folding and unfolding routes. Finally, we discuss how the GLN method can be applied to study entanglement between two structures none of which are closed loops. Since this approach is much faster than other linking invariants, the next step will be evaluation of lassos in much longer molecules such as RNA or loops in a single chromosome.

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Statistical Properties of Lasso-Shape Polymers and Their Implications for Complex Lasso Proteins Function

Cited by 9 publications

References 90 publications

Topoly: Python package to analyze topology of polymers

Topoly: Python package to analyze topology of polymers

The physical and the geometrical properties of simulated cold H i structures

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

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