Mathematics of membraneless organelles - the postsynaptic density

The National Science Foundation Division of Mathematical Sciences awarded the College of William and Mary $250,000 on September 1, 2026, under the Mathematical and Physical Sciences program to develop and test a predictive mathematical framework for the postsynaptic density—a protein-dense structure at neural synapses—as a multicomponent biomolecular condensate.

The research combines mathematical modeling with laboratory experiments to understand how mutations in SYNGAP, a protein essential to synaptic structure, alter the growth and stability of neuronal connections. The investigators will employ Flory-Huggins free-energy models, Cahn-Hilliard phase-field simulations, laboratory reconstitution of SYNGAP/PSD-95 condensates, empirical phase diagrams, tie-line measurements, and fluorescence recovery after photobleaching assays to characterize how SYNGAP isoforms and clinical variants affect postsynaptic density organization. The work addresses SYNGAP1-related disorders, which present with epilepsy, autism, and intellectual disability.

The award funds student training across mathematics, biology, neuroscience, and bioengineering, and mandates delivery of open-access data and computational tools to the scientific community and public through community engagement, educational events, public demonstrations, and outreach focused on rare neurodevelopmental disorders.

Performance occurs in Williamsburg, Virginia over the period September 1, 2026, through August 31, 2029.

Abstract

Cells organize their activities by bringing the right molecules together at the right place and time. This project focuses on how this kind of organization helps nerve cells (neurons) build and adjust the connections that allow the brain to develop, learn, and respond to experience. The research focuses on a small, dense, organized group of proteins found at the communication points between neurons (synapses), known as the postsynaptic density. Changes in an essential protein known as syngap have been linked to SYNGAP1-related disorders, which are characterized by clinical symptoms including epilepsy, autism, and intellectual disability. A combination of mathematics and laboratory experiments will help US understand how changes (mutations) in syngap alter the growth and stability of connections between neurons. This interdisciplinary project will provide training for students across mathematics, biology, neuroscience, and bioengineering and will deliver open-access data and computational tools to the scientific community and to the public through community engagement, educational events, public demonstrations, and outreach that increase awareness of rare neurodevelopmental disorders. This project will develop and test a predictive mathematical framework for the postsynaptic density of dendritic spines as a finite-sized, multicomponent biomolecular condensate governed by stoichiometric syngap – PSD-95 binding, multivalent interactions, biochemical switching, network percolation, finite-size effects, membrane coupling, and exchange of syngap with the dendritic cytosol. The investigators will use flory – huggins free-energy models, cahn – hilliard phase-field simulations, laboratory reconstitution of syngap/PSD-95 condensates, empirical phase diagrams, tie-line measurements, and fluorescence recovery after photobleaching (frap) assays to determine how syngap isoforms, clinical variants (haploinsufficiency), and secondary messenger cascades alter phase boundaries, condensate composition, and exchange kinetics. They will use the xenopus retinotectal system to connect condensate behavior to dendritic arbor development, synaptic remodeling, syngap residence times, synaptic strength, and circuit excitability in vivo. Theoretical work will extend condensate theory by deriving graph-theoretic criteria for percolation and small-system thermodynamic corrections that account for postsynaptic geometry, curvature, surface-to-volume ratio, and cytosolic reservoirs. These studies will generate quantitative links between syngap molecular variation, postsynaptic density stability, dendritic maturation, and neurodevelopmental phenotypes. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the foundation's intellectual merit and broader impacts review criteria.- subawards are not planned for this award.