A5079289692- Geometric and Algebraic Topology
- semigroups and automata theory
- DNA and Nucleic Acid Chemistry
- RNA and protein synthesis mechanisms
- Bacteriophages and microbial interactions
- Homotopy and Cohomology in Algebraic Topology
- Advanced Combinatorial Mathematics
- Mathematics and Applications
- Stochastic processes and statistical mechanics
- Genomics and Chromatin Dynamics
- Topological and Geometric Data Analysis
- Advanced biosensing and bioanalysis techniques
- Protein Structure and Dynamics
- Computational Geometry and Mesh Generation
- Advanced Materials and Mechanics
- Microtubule and mitosis dynamics
- Vestibular and auditory disorders
- Monoclonal and Polyclonal Antibodies Research
- Theoretical and Computational Physics
- Medical Image Segmentation Techniques
- Artificial Intelligence in Games
- Ophthalmology and Eye Disorders
- Mathematical Dynamics and Fractals
- Limits and Structures in Graph Theory
- Algebraic Geometry and Number Theory
University of Southern Denmark
2024
University of Trento
2024
Florida State University
2009-2021
Institut de Biologia Molecular de Barcelona
2002-2005
Consejo Superior de Investigaciones Científicas
2002-2005
University of California, Los Angeles
1970-2000
University of California, Berkeley
1995
University of Toronto
1972-1994
York University
1993-1994
University of South Alabama
1981
The last years have witnessed remarkable advances in our understanding of the emergence and consequences topological constraints biological soft matter. Examples are abundant relation to (bio)polymeric systems range from characterization knots single polymers proteins that whole chromosomes polymer melts. At same time, considerable been made description interplay between physical properties complex fluids, with development techniques now allow researchers control formation interaction...
Discusses the existence of knots in random self-avoiding walks on a lattice. Using Kesten's (1963) pattern theorem, it is shown that almost all sufficiently long three-dimensional simple cubic lattice contain knot.
When linear double-stranded DNA is packed inside bacteriophage capsids, it becomes highly compacted. However, the phage believed to be fully effective only if not entangled. Nevertheless, when extracted from a tailless mutant of P4 phage, found cyclic and knotted (probability 0.95). The knot spectrum very complex, most knots have large number crossings. We quantified frequency crossing numbers these concluded that, for mutant, at least half molecules are formed while still viral capsid...
Icosahedral bacteriophages pack their double-stranded DNA genomes to near-crystalline density and achieve one of the highest levels condensation found in nature. Despite numerous studies, some essential properties packaging geometry inside phage capsid are still unknown. We present a different approach problems randomness chirality packed DNA. recently showed that most molecules extracted from bacteriophage P4 highly knotted because cyclization linear molecule confined capsid. Here, we show...
Recent experiments showed that the linear double-stranded DNA in bacteriophage capsids is both highly knotted and neatly structured. What physical basis of this organization? Here we show evidence from stochastic simulation techniques suggests a key element tendency contacting strands to order, as cholesteric liquid crystals. This interaction favors their preferential juxtaposition at small twist angle, thus promoting an approximately nematic (and apolar) local order. The ordering effect...
Significance Bacteriophages are viruses which infect bacteria. Many of these contain double-stranded DNA packed to almost crystalline density and exploit the resulting pressure trigger ejection into infected bacterial cell. We show that kinetics is highly sensitive ordering knotting packaged which, in turn, controlled by self-interactions. The latter favor ordered spools have a lower effective or topological friction than disordered entangled structures. also find torus knots (which can be...
There exist naturally occurring enzymes (topoisomerases and recombinases), which, in order to mediate the vital life processes of replication, transcription, recombination, manipulate cellular DNA topologically interesting non-trivial ways [24, 30]. These enzyme actions include promoting coiling up (supercoiling) molecules, passing one strand through another via a transient enzyme-bridged break strands (a move performed by topoisomerase), breaking pair recombining them different ends...
Abstract Reconnection is a fundamental event in many areas of science, from the interaction vortices classical and quantum fluids magnetic flux tubes magnetohydrodynamics plasma physics, to recombination polymer physics DNA biology. By using results topological fluid mechanics, helicity tube can be calculated terms writhe twist contributions. Here we show that conserved under anti-parallel reconnection. Hence, for pair interacting equal flux, if reconnected sum original twists tubes, then...
A fundamental and interesting question in knot theory is: Question 1. How many prime knots of n crossings are there ? Over time, theorists have answered this for ≤ 13 by the method exhaustion: one writes down a list all possible crossings, then works hard to eliminate duplications from [12]. perhaps easier is following:
Abstract In this paper we are concerned with questions about the knottedness of a closed curve given length embedded in Z 3 . What is probability that such randomly chosen embedding knotted? contains particular knot? expected complexity To what extent can these also be answered for graph homeomorphism type? We use pattern theorem due to Kesten 12 prove almost all embeddings sufficiently long contain any knot. introduce idea good measure knot complexity. This function F which maps set...
In this paper, we consider knotting of Gaussian random polygons in 3-space. A polygon is a piecewise linear circle with n edges which the length follows distribution. We prove continuum version Kesten's Pattern Theorem for these polygons, and use to that probability 3-space knotted tends one exponentially rapidly as infinity. study properties knots, entanglement complexity knots gets arbitrarily large also almost all are chiral.
Abstract Background The genetic code imposes a dilemma for cells. DNA must be long enough to encode the complexity of an organism, yet thin and flexible fit within cell. combination these properties greatly favors collisions, which can knot drive recombination DNA. Despite well-accepted propensity cellular collide react with itself, it has not been established what physiological consequences are. Results Here we analyze effects recombined knotted plasmids in E. coli using Hin site-specific...
The writhe of a self-avoiding walk in three-dimensional space is the average over all projections onto plane sum signed crossings. We compute this number using Monte Carlo simulation. Our results suggest that absolute value walks increases as nalpha , where n length and alpha approximately=0.5. mean crossing also computed found to have power-law dependence on walks. In addition, we consider effects solvent quality
We consider a model of circular polyelectrolyte, such as DNA, in which the molecule is represented by polygon three-dimensional simple cubic lattice. A short-range attractive force between nonbonded monomers included (to account for solvent quality) together with screened Coulomb potential effect added salt). compute probability that ring knotted function number ring, and ionic strength solution. The results show same general behavior recent experimental Shaw Wang [Science 260, 533 (1993)]...
This paper focuses upon the maximization of labor productivity through selection optimal number, duration, and placement rest breaks. It is demonstrated that resolution limited validity associated with previous models leads to a mixed-integer quadratic programming formulation this problem. Efficient analytic procedures are developed which allow solutions be obtained in minutes using hand-held calculator. Then, characteristics, properties, potential effectiveness examined an illustration from...