Special magazine issue honors Murray's contributions to mathematical biology

A special issue of the Bulletin of Mathematical Biology, Dec. 4, celebrates the contributions of J.D. Murray, one of the modern founders of mathematical biology.

The Bulletin's collection of 17 essays honors Murray's 90th birthday and highlights the many diverse areas in biology where he applied mathematics. It features work by scientists carrying on his mission, and is dedicated to Murray's insights in his long and productive career.

James Dickson Murray is a professor emeritus of applied mathematics at University of Washington in Seattle and at Oxford University in England. His early career was in fluid dynamics.

As Murray himself has noted, the field of mathematical biology is relatively new, developing since the mid-1980s. Murray stresses it is an interdisciplinary collaboration between modelers and experimenters.

The introductory essay reviews Murray's work, starting with his proposal in 1983 for "a new model for self-organization in biological pattern formation." The model from Murray and colleagues hypothesized that the forces generated by mesenchymal cells led to cells "aggregating into self-organized patterns." (Mesenchymal cells are adult stem cells present in bone marrow, which can divide and make and repair other types of tissue.)

Murray's modeling made use of nonlinear partial differential equations to produce patterns observed in biology.

Murray's work developed in many diverse areas, including how patterns form in animal coats, epidermal wound healing, the spread of disease and effectiveness of different control plans, wolf pack territory formation, the growth of brain tumors, cancer treatment effectiveness and even intertribal and marital conflict.

The authors of the introductory essay emphasize that Murray "helped to establish a yardstick for genuinely applied mathematics in the life sciences that now permeates the thinking and policymaking in the field." Further, they note his "infectious enthusiasm" as well as his ability to delve into biological problems brought many top people into the field.

A wide range of research in this special collection

• Murray made important contributions to studying tumor growth and cancer therapy. This special collection includes recent research where mathematical modelling is being used to find markers for chemotherapy treatment to optimize dosing and avoid white blood cell depletion (neutropenia).

• Murray's model of glioblastoma is being broadened by new technology. One of the papers selected for inclusion in this special issue is from a team of researchers at the Mayo Clinic and University of Nottingham. They expanded a previous model to include elements that influence tumor recurrence, such as nutrient supply.

• Another selected article extends Murray's work on the control of disease, such as rabies in foxes, to the spread of bacterial disease in olive trees by insects, and methods to control it.

• One of the publications covers the extension of Murray's mathematical modeling work on pattern formation to the geometry of cell development.

• A review of new work in neural crest cell migration shows how Murray's mathematical models can be applied to understanding cancer cell metastasis.

• Updates on Murray's groundbreaking work on HIV AIDS is another area covered in this special issue. Researchers predicted the effect of stigma on the spread of the disease.

• Another of the reports explores how Murray's work is used to understand saliva formation.

• Other selected publications cover the elaboration of Murray's work for disease dynamics, complex biological phenomena, mechanochemical modeling of pattern formation, evolutionary development across different timescales, high intensity focused ultrasound as a cancer treatment, pattern formation in mussel beds, a model for the composition of atherosclerotic plaques that cause heart attacks and strokes, and a method for assessing extinction in foxes.

A remarkable career

The wide range of topics and research inspired by Murray's work in mathematical biology is remarkable, and still continuing to develop and grow, the bulletin notes.

The introductory essay for the commemorative issue concludes: "The articles in this special collection illustrate the synergy between the fields of mathematics and biology [in its broadest sense] that J.D. Murray has demonstrated countless times throughout his amazing career, that biology inspires new mathematics, while mathematics leads to new biology."

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P.K. Maini, "Special Collection: Celebrating J.D. Murray’s Contributions to Mathematical Biology," Bulletin of Mathematical Biology, Dec. 4, 2021. DOI: https://doi.org/10.1007/s11538-021-00955-8