About

Kenneth C. Millett is a Professor of Mathematics at the University of California, Santa Barbara. He received his Bachelor of Science degree from the Massachusetts Institute of Technology in 1963, followed by a Master of Science and a Doctor of Philosophy from the University of Wisconsin at Madison in 1964 and 1967, respectively. After holding lecturer positions at UCLA and MIT, he joined the UCSB faculty in 1969. Throughout his career, he has been a visiting professor at prestigious institutions including the Institut des Hautes Etudes Scientifiques, Princeton University, Occidental College, UCLA, MSRI, several French research institutes and universities, and the LOMI in Saint Petersburg. Millett has published over 50 scientific papers and edited four research volumes focusing on geometric topology, knot theory, and their applications to mathematics, computer science, physics, chemistry, and molecular biology. He has also contributed to mathematics education and reform by developing materials aimed at increasing public understanding and support for the renewal and reform of mathematics teaching and assessment. Professor Millett has held numerous leadership roles and contributed extensively to educational outreach and minority participation in STEM. He has served as Chair of The Chancellor's Outreach Advisory Board, Regional Director of the NSF-funded California Alliance for Minority Participation, and Director of UCSB's California Mathematics and Science Teaching Program. He was the founding President and Executive Director of the California Coalition for Mathematics and Science and has been active in various initiatives to improve mathematics education, including the California Mathematics Project and the Mathematicians and Educational Reform Forum. His service extends to national organizations such as the American Mathematical Society, the Mathematical Association of America, and the College Board, where he has held leadership and advisory positions. Millett's efforts have been recognized with several awards, including the Carl B. Allendoerfer Award, the Chauvenet Prize, the Award for Distinguished Public Service from the AMS, and fellowships in the American Association for the Advancement of Science and the American Mathematical Society.

Research topics

• Combinatorics
• Computer Science
• Physics
• Mathematics
• Quantum mechanics
• Statistics
• Pure mathematics
• Mathematical analysis
• Chemistry

Selected publications

• HOMFLY-PT polynomials of open links

  Journal of Knot Theory and Its Ramifications · 2023

  1st authorCorresponding
  • Mathematics
  • Pure mathematics
  • Combinatorics

  We numerically estimate the superposition of the HOMFLY-PT polynomial of an open two-component link, define its spread, and describe how this quantity may be employed to quantify the degree of entanglement of confined two component open links.

  PublisherDOI

• Topological linking and entanglement in proteins

  Contemporary mathematics - American Mathematical Society · 2020-01-01 · 1 citations

  other1st authorCorresponding

  This paper provides a mathematical introduction to the application of the integral formulation of the Gauss linking number to the analysis of entanglement in macromolecules. This application is inspired by knots and slipknots recently found in proteins. Entanglement is understood as the linking or self-linking of segments of a linear macromolecule, e.g. a protein or polymers in a gel. The mathematical features of Gauss linking, as inspired by protein knotting, provide a method to identify and quantify important sites of entanglement. It will be applied in several ways to proteins to locate sites with these structures that are similar to those of knotting and slipknotting. As a vehicle to illuminate this discussion, we will describe the application of these methods to the case of an important unknotted protein, the nitrogenase molybdenum-iron protein from Clostridium pasteruianum, an oxidoreductase identified in the Protein Data Base as 4WES. Expanding upon this linking analysis, we will also describe how the presence of cysteine bonds in proteins gives another structure within which one finds examples of intrinsic linking. This creates distinctly different classes of linked structures and the application to other ways to study linking.

  PublisherDOI

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

  arXiv (Cornell University) · 2020 · 3 citations

  • Computer Science
  • Physics
  • Mathematics

  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 diagram-for 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 show how high and low GLN values correlate with the internal exibility 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.

  PublisherOA PDF

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

  arXiv (Cornell University) · 2020-05-11

  preprintOpen access

  Geometry and topology are the main factors that determine the functional\nproperties of proteins. In this work, we show how to use the Gauss linking\nintegral (GLN) in the form of a matrix diagram - for a pair of a loop and a\ntail - to study both the geometry and topology of proteins with closed loops\ne.g. lassos. We show that the GLN method is a significantly faster technique to\ndetect entanglement in lasso proteins in comparison with other methods. Based\non the GLN technique, we conduct comprehensive analysis of all proteins\ndeposited in the PDB and compare it to the statistical properties of the\npolymers. We found that there are significantly more lassos with negative\ncrossings than those with positive ones in proteins, the average value of\nmaxGLN (maximal GLN between loop and pieces of tail) depends logarithmically on\nthe length of a tail similarly as in the polymers. Next, we show the how high\nand low GLN values correlate with the internal exibility of proteins, and how\nthe GLN in the form of a matrix diagram can be used to study folding and\nunfolding routes. Finally, we discuss how the GLN method can be applied to\nstudy entanglement between two structures none of which are closed loops. Since\nthis approach is much faster than other linking invariants, the next step will\nbe evaluation of lassos in much longer molecules such as RNA or loops in a\nsingle chromosome.\n

  PublisherOA PDFDOI

• Knots, Low-Dimensional Topology and Applications

  Springer proceedings in mathematics & statistics · 2019-01-01 · 9 citations

  book
  PublisherDOI

• KnotProt 2.0: a database of proteins with knots and other entangled structures

  Nucleic Acids Research · 2018-12-01 · 128 citations

  articleOpen access

  The KnotProt 2.0 database (the updated version of the KnotProt database) collects information about proteins which form knots and other entangled structures. New features in KnotProt 2.0 include the characterization of both probabilistic and deterministic entanglements which can be formed by disulfide bonds and interactions via ions, a refined characterization of entanglement in terms of knotoids, the identification of the so-called cysteine knots, the possibility to analyze all or a non-redundant set of proteins, and various technical updates. The KnotProt 2.0 database classifies all entangled proteins, represents their complexity in the form of a knotting fingerprint, and presents many biological and geometrical statistics based on these results. Currently the database contains >2000 entangled structures, and it regularly self-updates based on proteins deposited in the Protein Data Bank (PDB).

  PublisherOA PDFDOI

• Knotting and linking in macromolecules

  Reactive and Functional Polymers · 2018-08-02 · 4 citations

  articleOpen access1st authorCorresponding
  PublisherOA PDFDOI

• PyLink: a PyMOL plugin to identify links

  Bioinformatics · 2018-12-22 · 16 citations

  article

  SUMMARY: Links are generalization of knots, that consist of several components. They appear in proteins, peptides and other biopolymers with disulfide bonds or ions interactions giving rise to the exceptional stability. Moreover because of this stability such biopolymers are the target of commercial and medical use (including anti-bacterial and insecticidal activity). Therefore, topological characterization of such biopolymers, not only provides explanation of their thermodynamical or mechanical properties, but paves the way to design templates in pharmaceutical applications. However, distinction between links and trivial topology is not an easy task. Here, we present PyLink-a PyMOL plugin suited to identify three types of links and perform comprehensive topological analysis of proteins rich in disulfide or ion bonds. PyLink can scan for the links automatically, or the user may specify their own components, including closed loops with several bridges and ion interactions. This creates the possibility of designing new biopolymers with desired properties. AVAILABILITY AND IMPLEMENTATION: The PyLink plugin, manual and tutorial videos are available at http://pylink.cent.uw.edu.pl.

  PublisherDOI

• Linking matrices in systems with periodic boundary conditions

  Journal of Physics A Mathematical and Theoretical · 2018-04-11 · 4 citations

  articleOpen accessSenior author

  Abstract We study the linking matrix , a measure of entanglement for a collection of closed or open chains in 3-space based on the Gauss linking number. Periodic boundary conditions (PBC) are often used in the simulation of physical systems of filaments. To measure entanglement of closed or open chains in systems employing PBC we use the periodic linking matrix , based on the periodic linking number, defined in Panagiotou (2015 J. Comput. Phys . 300 533–73). We study the properties of the periodic linking matrix as a function of cell size. We provide analytical results concerning the eigenvalues of the periodic linking matrix and show that some of them are invariant of cell-size.

  PublisherOA PDFDOI

• Linking in Systems with One-Dimensional Periodic Boundaries

  Springer proceedings in mathematics & statistics · 2017-01-01

  book-chapter1st authorCorresponding
  PublisherDOI

Frequent coauthors

• Andrzej Stasiak

  University of Trento

  84 shared

• Eric J. Rawdon

  70 shared

• Akos Dobay

  University of Zurich

  51 shared

• Michael Piatek

  Google (United States)

  51 shared

• Patrick Plunkett

  49 shared

• John C. Kern

  University of Maryland, College Park

  48 shared

• Joanna I. Sułkowska

  University of Warsaw

  17 shared

• W. B. R. Lickorish

  17 shared

Labs

• Kenneth Millett's LabPI

  Not provided