Biomolecular condensates are viscoelastic materials formed by liquid-liquid phase separations (LLPS) of biopolymers. In this study, we develop a modified graph Laplacian-based collective model to characterize viscoelastic heterogeneity within condensates based on results of lattice-based Metropolis Monte Carlo (MMC) simulations. By integrating random graph models and simulations of A1-LCD, a type of intrinsically disordered protein, we examine how network topology influences storage modulus, loss modulus, crossover frequency, and relaxation time spectra. Our results reveal a strong correlation between topological features and mechanical response, with the condensate interior exhibiting higher stiffness and faster relaxation than the interface. The relaxation spectra provide rich insights into dynamic behavior beyond what moduli alone can capture. This framework offers a scalable, interpretable approach for quantifying spatial viscoelasticity in biomolecular assemblies.
","abstract_html":"<p>Biomolecular condensates are viscoelastic materials formed by liquid-liquid phase separations (LLPS) of biopolymers. In this study, we develop a modified graph Laplacian-based collective model to characterize viscoelastic heterogeneity within condensates based on results of lattice-based Metropolis Monte Carlo (MMC) simulations. By integrating random graph models and simulations of A1-LCD, a type of intrinsically disordered protein, we examine how network topology influences storage modulus, loss modulus, crossover frequency, and relaxation time spectra. Our results reveal a strong correlation between topological features and mechanical response, with the condensate interior exhibiting higher stiffness and faster relaxation than the interface. The relaxation spectra provide rich insights into dynamic behavior beyond what moduli alone can capture. This framework offers a scalable, interpretable approach for quantifying spatial viscoelasticity in biomolecular assemblies.</p>","abstract_has_math":false,"creators":["Gu, Liwen"],"institution":null,"degree_name":"Master of Science (MS)","degree_level":"Thesis","degree_discipline":"Mechanical Engineering & Materials Science","degree_department":null,"school":null,"contributors":["Rohit V. Pappu","Amit Pathak, Guy Genin"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2025,"date_issued":"2025-05-10T07:00:00Z","date_published":"2025-05-10T07:00:00Z","updated_at":"2026-07-24T06:12:58Z","subjects":["biomolecular condensates","viscoelasticity","graph Laplacian","Biological and Chemical Physics","Biomedical Engineering and Bioengineering","Engineering","Materials Science and Engineering"],"languages":["English (en)"],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["https://openscholarship.wustl.edu/eng_etds/1209"],"render_values":[{"text":"https://openscholarship.wustl.edu/eng_etds/1209","href":"https://openscholarship.wustl.edu/eng_etds/1209","code":true}]}]},"links":{"outbound_url":"https://doi.org/10.7936/29qn-vt65","outbound_label":"DOI","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Rohit V. Pappu","Amit Pathak, Guy Genin"]},{"key":"dc:creator","label":"Author","values":["Gu, Liwen"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2025-05-05T07:00:00Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mechanical Engineering & Materials Science","McKelvey School of Engineering"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Thesis"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science (MS)"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["biomolecular condensates","viscoelasticity","graph Laplacian","Biological and Chemical Physics","Biomedical Engineering and Bioengineering","Engineering","Materials Science and Engineering"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["English (en)"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://doi.org/10.7936/29qn-vt65","https://openscholarship.wustl.edu/eng_etds/1209"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Biomolecular condensates are viscoelastic materials formed by liquid-liquid phase separations (LLPS) of biopolymers. In this study, we develop a modified graph Laplacian-based collective model to characterize viscoelastic heterogeneity within condensates based on results of lattice-based Metropolis Monte Carlo (MMC) simulations. By integrating random graph models and simulations of A1-LCD, a type of intrinsically disordered protein, we examine how network topology influences storage modulus, loss modulus, crossover frequency, and relaxation time spectra. Our results reveal a strong correlation between topological features and mechanical response, with the condensate interior exhibiting higher stiffness and faster relaxation than the interface. The relaxation spectra provide rich insights into dynamic behavior beyond what moduli alone can capture. This framework offers a scalable, interpretable approach for quantifying spatial viscoelasticity in biomolecular assemblies.
"]},{"key":"dc:title","label":"Title","values":["Direct Computations of Spatially Resolved Viscoelastic Moduli of Biomolecular Condensates"]}]}],"canonical_facts":{"dc:contributor":["Rohit V. Pappu","Amit Pathak, Guy Genin"],"dc:creator":["Gu, Liwen"],"dc:date.available":["2025-05-05T07:00:00Z"],"dc:description.abstract":["Biomolecular condensates are viscoelastic materials formed by liquid-liquid phase separations (LLPS) of biopolymers. In this study, we develop a modified graph Laplacian-based collective model to characterize viscoelastic heterogeneity within condensates based on results of lattice-based Metropolis Monte Carlo (MMC) simulations. By integrating random graph models and simulations of A1-LCD, a type of intrinsically disordered protein, we examine how network topology influences storage modulus, loss modulus, crossover frequency, and relaxation time spectra. Our results reveal a strong correlation between topological features and mechanical response, with the condensate interior exhibiting higher stiffness and faster relaxation than the interface. The relaxation spectra provide rich insights into dynamic behavior beyond what moduli alone can capture. This framework offers a scalable, interpretable approach for quantifying spatial viscoelasticity in biomolecular assemblies.
"],"dc:identifier":["https://doi.org/10.7936/29qn-vt65","https://openscholarship.wustl.edu/eng_etds/1209"],"dc:language":["English (en)"],"dc:subject":["biomolecular condensates","viscoelasticity","graph Laplacian","Biological and Chemical Physics","Biomedical Engineering and Bioengineering","Engineering","Materials Science and Engineering"],"dc:title":["Direct Computations of Spatially Resolved Viscoelastic Moduli of Biomolecular Condensates"],"thesis:degree_discipline":["Mechanical Engineering & Materials Science","McKelvey School of Engineering"],"thesis:degree_level":["Thesis"],"thesis:degree_name":["Master of Science (MS)"]},"updated_at":"2026-07-24T06:12:58Z"}