The objective of the proposed collaborative research is to carry out a comprehensive mathematical investigation of the key processes governing biopreservation of cells by vitrification and desiccation. The research will be focused on the formation of a glassy state in biological solutions and the interaction of the propagating glass transition fronts with cell membranes and intracellular organelles. This will be done by formulating the corresponding mathematical models and their investigation and solution by means of asymptotic and numerical methods. The proposed research program is planned as a close collaboration between a theoretical group at Northwestern University and an experimental group at the Harvard Medical School and the Massachusetts General Hospital. The results of theoretical analysis will be compared, analyzed and supported by experiments. The peculiarity of glassy systems is that the diffusion transport there is anomalous in that it is described by subdiffusion equations with fractional derivatives. From fundamental point of view, this research will allow one to understand the mechanisms of biopreservation based on the formation of glass inside the cell. From the biomedical point of view, this understanding will lead to improvement and optimization of biopreservation techniques and protocols to achieve higher cell survival rates. From the applied mathematics point of view, this research will develop new models and methods of solving special classes of non-trivial fractional PDEs (integro-differential equations) and associated free-boundary problems. The planned experimental work will be used as a guide in formulating the mathematical models. Analytical solutions will be sought in several limiting cases where asymptotic and perturbation methods can be applied, while a computational investigation will be done in the more general cases.

National Institute of Health (NIH)
National Institute of General Medical Sciences (NIGMS)
Research Project (R01)
Project #
Application #
Study Section
Special Emphasis Panel (ZGM1-CBCB-5 (BM))
Program Officer
Brazhnik, Paul
Project Start
Project End
Budget Start
Budget End
Support Year
Fiscal Year
Total Cost
Indirect Cost
Northwestern University at Chicago
Engineering (All Types)
Schools of Engineering
United States
Zip Code
Abazari, Alireza; Chakraborty, Nilay; Hand, Steven et al. (2014) A Raman microspectroscopy study of water and trehalose in spin-dried cells. Biophys J 107:2253-62
Vogl, C J; Miksis, M J; Davis, S H et al. (2014) The effect of glass-forming sugars on vesicle morphology and water distribution during drying. J R Soc Interface 11:
Blount, Maurice J; Miksis, Michael J; Davis, Stephen H (2013) The equilibria of vesicles adhered to substrates by short-ranged potentials. Proc Math Phys Eng Sci 469:20120729
Vogl, Christopher J; Miksis, Michael J; Davis, Stephen H (2012) Moving boundary problems governed by anomalous diffusion. Proc Math Phys Eng Sci 468:3348-3369
Chakraborty, Nilay; Menze, Michael A; Elmoazzen, Heidi et al. (2012) Trehalose transporter from African chironomid larvae improves desiccation tolerance of Chinese hamster ovary cells. Cryobiology 64:91-6
Blount, Maurice J; Miksis, Michael J; Davis, Stephen H (2012) Fluid flow beneath a semipermeable membrane during drying processes. Phys Rev E Stat Nonlin Soft Matter Phys 85:016330
Chakraborty, Nilay; Menze, Michael A; Malsam, Jason et al. (2011) Cryopreservation of spin-dried mammalian cells. PLoS One 6:e24916