About

Maria-Carme Calderer is a professor in the School of Mathematics at the University of Minnesota. Her research deals with partial differential equations, dynamical systems, and calculus of variations, with applications to soft matter physics and biology. Specific topics of her research include investigating how DNA arranges itself under confinement, such as in cells or laboratory settings, using calculus of variations to determine energy-minimizing configurations and topology to understand knotting structures. She also studies the dynamics of bacterial infection by viruses, the movement of cancer cells in tissue, and the fluid mechanics of non-Newtonian fluids, colloids, and solid-fluid structures, often involving electric charge and coupling of fluid dynamics with models like Boltzmann and Nernst-Planck equations. Calderer collaborates with industry on medical device problems and pharmaceutical industry issues. Her research is funded by programs of the National Science Foundation. She earned her PhD from Heriot-Watt University in Edinburgh, United Kingdom, in 1980. Recently, she was named an Association for Women in Mathematics Fellow.

Research topics

• Computer Science
• Materials science
• Biology
• Geography
• Mechanics
• Composite material
• Genetics
• Nanotechnology
• Biological system
• Thermodynamics
• Archaeology
• Classical mechanics
• Ecology
• Physics
• Virology
• Chemistry
• Crystallography

Selected publications

• Chevron patterns in an active nematic liquid crystal film in contact with smectic A

  Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences · 2025-08-01

  article1st authorCorresponding

  We study a new mechanism of active matter confinement of a thin, active nematic sample consisting of microtubules, activated by adenosine triphosphate (ATP), placed between a slab of passive liquid crystal, the compound 8CB and water. The 8CB slab is kept at a temperature below the phase transition value between the nematic and the smectic A phases. The smectic A molecules are horizontally aligned with an applied magnetic field, with their centres of mass arranged on equally spaced layers perpendicular to the field. The contact with the active nematic prompts flow in the smectic slab, along the direction parallel to the layers. This flow direction is transferred back to the active nematic. We set up a model of such contact flow and make predictions on the experimentally observed pattern, from the point of view of asymptotic, linear and nonlinear analyses. We examine such results within the scope of the principle of minimum energy dissipation of the flow. For analytic convenience, we consider the active nematic confined between two symmetric 8CB slabs and show that the conclusions still hold when replacing the bottom smectic A substrate with water, as in the experimental setting.

  PublisherDOI

• Author response for "CHEVRON PATTERNS IN AN ACTIVE NEMATIC LIQUID CRYSTAL FILM IN CONTACT WITH SMECTIC A"

  2025-01-14

  peer-review1st authorCorresponding
  PublisherDOI

• Experiments and finite element simulations pertinent to hydrogel debonding from a solid substrate

  Polymer · 2025-07-04 · 4 citations

  article1st author
  PublisherDOI

• Twist dominates bending in the liquid crystal organization of bacteriophage DNA

  ArXiv.org · 2025-10-06

  preprintOpen access

  DNA frequently adopts liquid-crystalline conformations in both cells and viruses. The Oseen--Frank framework provides a powerful continuum description of these phases through three elastic moduli: splay ($K_1$), twist or cholesteric ($K_2$), and bending ($K_3$). While $K_1$ is typically assumed to dominate, the relative magnitude of $K_2$ and $K_3$ in confined DNA remains poorly understood. Here, we combine cryo-electron microscopy, liquid-crystal modeling, and knot theory to quantify this relationship in bacteriophage P4, whose genome is partially organized in a spool-like liquid-crystalline phase. We first show experimentally that the ordered DNA occupies three concentric layers within the capsid. We then formulate an Oseen--Frank model for this geometry and use it, together with the measured layer radii, to estimate the elastic ratio $α= K_3/K_2$. We find $α\approx 0.0064$, indicating that twist elasticity overwhelmingly dominates bending. To validate this result, we perform Langevin dynamics simulations of DNA trajectories and classify the resulting knots. The predicted knot distribution agrees with experimental data from P4, demonstrating consistency between elasticity, topology, and observed genome organization.

  PublisherOA PDFDOI

• Knotted DNA Configurations in Bacteriophage Capsids: A Liquid Crystal Theory Approach

  ArXiv.org · 2025-09-12

  preprintOpen access

  Bacteriophages, viruses that infect bacteria, store their micron long DNA inside an icosahedral capsid with a typical diameter of 40 nm to 100 nm. Consistent with experimental observations, such confinement conditions induce an arrangement of DNA that corresponds to a hexagonal chromonic liquid-crystalline phase, and increase the topological complexity of the genome in the form of knots. A mathematical model that implements a chromonic liquid-crystalline phase and that captures the changes in topology has been lacking. We adopt a mathematical model that represents the viral DNA as a pair of a vector field and a line. The vector field is a minimizer of the total Oseen-Frank energy for nematic liquid crystals under chromonic constraints, while the line is identified with the tangent to the field at selected locations, representing the central axis of the DNA molecule. The fact that the Oseen-Frank functional assigns infinite energy to topological defects (point defects in two dimensions and line defects in three dimensions) precludes the presence of singularities and, in particular, of knot structures. To address this issue, we begin with the optimal vector field and helical line, and propose a new algorithm to introduce knots through stochastic perturbations associated with splay and twist deformations, modeled by means of a Langevin system. We conclude by comparing knot distributions generated by the model and by interpreting them in the context of previously published experimental results. Altogether, this work relies on the synergy of modeling, analysis and computation in the study of viral DNA organization in capsids.

  PublisherOA PDFDOI

• Chevron patterns in an active nematic liquid crystal film in contact with Smectic A

  arXiv (Cornell University) · 2024-07-01

  preprintOpen access1st authorCorresponding

  We study a new mechanism of active matter confinement of a thin, active nematic sample consisting of microtubules, activated by Adenosine Triphosphate (ATP), placed between a slab of passive liquid crystal, the compound 8CB, and water. The 8CB slab is kept at a temperature below the phase transition value between the nematic and the smectic A phases. The smectic A molecules are horizontally aligned with an applied magnetic field, with their centers of mass arranged on equally spaced layers perpendicular to the field. The contact with the active nematic prompts flow in the smectic slab, along the direction parallel to the layers. This flow direction is transferred back to the active nematic. We set up a model of such contact flow and make predictions on the experimentally observed pattern, from the point of view of asymptotic, linear and nonlinear analyses. We examine such results within the scope of the principle of minimum energy dissipation of the flow. For analytic convenience, we consider the active nematic confined between two symmetric 8CB slabs, and show that the conclusions still hold when replacing the bottom smectic A substrate with water, as in the experimental setting.

  PublisherOA PDFDOI

• A Numerical Scheme and Validation of the Asymptotic Energy Release Rate Formula for a 2D Gel Thin-Film Debonding Problem

  SIAM Journal on Applied Mathematics · 2024-08-13 · 2 citations

  article1st authorCorresponding
  PublisherDOI

• Gels: Energetics, Singularities, and Cavitation

  Journal of Elasticity · 2023-03-21 · 1 citations

  article1st authorCorresponding
  PublisherDOI

• Aggregation phenomena in lyotropic chromonic liquid crystals

  Communications in Nonlinear Science and Numerical Simulation · 2023-01-30 · 1 citations

  articleSenior author
  PublisherDOI

• Jerry Ericksen (1924-2021)

  Liquid Crystals · 2023-01-26 · 1 citations

  articleSenior authorCorresponding
  PublisherDOI

Recent grants

• GOALI: Modeling, analysis and numerical simulations of gels in the biomedical industry

  NSF · $323k · 2010–2013

• Collaborative Research: DNA Packing of Bacteriophages: Liquid Crystal Modeling through Analysis, Knot Theory and Numerical Simulation

  NSF · $262k · 2018–2023

• Collaborative Research: FRG: Ferroelectric phenomena in soft matter systems

  NSF · $286k · 2005–2008

• DMREF/Collaborative Research: Materials engineering of chromonic and colloidal liquid crystals via mathematical modeling and simulation

  NSF · $335k · 2014–2017

• DMREF: Collaborative Research: Materials Engineering of Columnar and Living Liquid Crystals via Experimental Characterization, Mathematical Modeling, and Simulation

  NSF · $251k · 2017–2020

Frequent coauthors

• Dmitry Golovaty

  University of Akron

  17 shared

• Jackie Taylor

  University of Minnesota

  10 shared

• Miki Hondzo

  University of Minnesota

  10 shared

• Vaughan R. Voller

  10 shared

• Oleg D. Lavrentovich

  University of Warsaw

  9 shared

• Duvan Henao

  University of O'Higgins

  8 shared

• Bagisa Mukherjee

  Pennsylvania State University

  7 shared

• Shawn W. Walker

  Louisiana State University

  6 shared

Education

• Ph.D, Mathematics

  Heriot-Watt University

Awards & honors

• Maria-Carme Calderer named Association for Women in Mathemat…