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Network dynamics of the cytoskeleton: chains with cross-linking
Thesis (PhD)--Stellenbosch University, 2025.
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| Format: | Thesis |
| Language: | English |
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Stellenbosch : Stellenbosch University
2025
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| _version_ | 1867613935119630336 |
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| access_status_str | Open Access |
| author | Du Toit, Nadine |
| author2 | Muller-Nedebock, K. K. |
| author_browse | Du Toit, Nadine Muller-Nedebock, K. K. |
| author_facet | Muller-Nedebock, K. K. Du Toit, Nadine |
| author_sort | Du Toit, Nadine |
| collection | Thesis |
| dc_rights_str_mv | Stellenbosch University |
| description | Thesis (PhD)--Stellenbosch University, 2025. |
| format | Thesis |
| id | oai:scholar.sun.ac.za:10019.1/134612 |
| institution | Stellenbosch University (South Africa) |
| language | English |
| last_indexed | 2026-06-10T12:44:02.133Z |
| license_str | Other — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from SUNScholar — Stellenbosch University Repository |
| publishDate | 2025 |
| publishDateRange | 2025 |
| publishDateSort | 2025 |
| publisher | Stellenbosch : Stellenbosch University |
| publisherStr | Stellenbosch : Stellenbosch University |
| record_format | dspace |
| source_str | SUNScholar — Stellenbosch University Repository |
| spelling | oai:scholar.sun.ac.za:10019.1/134612 Network dynamics of the cytoskeleton: chains with cross-linking Du Toit, Nadine Muller-Nedebock, K. K. Pellicane, G. Loos, B Stellenbosch University. Faculty of Science. Dept. of Physics. Crosslinking (Polymerization) -- Models Polymers -- Mathematical models Brownian motion processes -- Computer simulation Polymer solutions -- Mathematical models Dynamics UCTD Thesis (PhD)--Stellenbosch University, 2025. Du Toit, N. 2025. Network dynamics of the cytoskeleton: chains with cross-linking. Unpublished doctoral dissertation. Stellenbosch: Stellenbosch University [online]. Available: https://scholar.sun.ac.za/items/7fade6d2-2ab7-440f-9299-3c98ac79bae7 ENGLISH ABSTRACT: Cross-linked polymer networks have attracted significant interest due to their rich mechanical properties, which underpin a wide range of biological functions and technological applications. In biological systems such as the cytoskeleton, cross-linking proteins act as bridges between polymers of the same or different types and may also anchor them to cellular structures. Some of these cross-links are active: motor proteins not only bind filaments but also generate forces, driving relative motion. These complex dynamics and behaviours suggest a need for a deeper understanding of the effects of microscopic spatio-temporal constraints, introduced via cross-linking, on the collective dynamics of polymeric systems. This dissertation presents a novel field theoretical formalism for modelling such microscopic cross-linking constraints and their effects on the collective dynamics of polymer solutions. Building on an existing Gaussian networking theory developed for an equilibrium system, the formalism is extended to dynamically model reversible cross-linking. The Gaussian fields introduce spatio-temporal constraints, while accounting for all possible configurations in which these constraints can be satisfied. To illustrate the formalism, a toy model of Brownian particles is considered, where the networking approach is combined with a Martin–Siggia–Rose (MSR) functional representing overdamped dynamics. This is followed by an application to a two-species polymer solution with reversible cross-linking, where dynamic structure factors are computed analytically. The approach is developed further by considering the dynamics of dedicated cross-linker particles and including this in a two polymer species system wherein both intra- and inter-species cross-linking is implemented via the networking formalism. Limiting cases of strong and weak cross-linking are analysed for both types, and their influence on the dynamic structure factors is explored. Dynamic structure factors are presented for all four combinations of strong and weak intra- and inter-species cross-linking. To complement the analytical results, molecular dynamics simulations of a comparable system are per-formed, incorporating reversible cross-linking and computing dynamic structure factors for direct comparison. Across all scenarios, it is consistently observed that cross-linking leads to a broadening of the diffusive peaks in the dynamic structure factors. The agreement between theoretical predictions and subsequent simulation supports the applicability of the proposed formalism. This work establishes a versatile modelling tool for probing the collective dynamics of reversibly cross-linked polymer systems, with potential relevance to both biological networks and synthetic materials. AFRIKAANSE OPSOMMING: Gekoppelde polimeernetwerke het beduidende belangstelling getrek weens hul ryk meganiese eienskappe, wat ten grondslag lê aan ’n wye reeks biologiese funksies en tegnologiese toepassings. In biologiese stelsels soos die sitoskelet tree koppelingspro-teïene op as brûe tussen polimere van dieselfde of verskillende tipes, en kan hulle ook aan sellulêre strukture heg. Sommige van hierdie koppelaars is aktief: motoriese proteïene heg nie net aan filamente nie, maar genereer ook kragte wat relatiewe be-weging dryf. Hierdie komplekse dinamika en gedrag dui op ’n behoefte aan ’n dieper begrip van die effekte van mikroskopiese ruimtelik-temporale beperkings, wat deur koppeling ingevoer word, op die kollektiewe dinamika van polimeerstelsels. Hier-die proefskrif stel ’n nuwe veldteoretiese formalisme voor vir die modellering van sodanige mikroskopiese koppelingbeperkings en hul invloed op die kollektiewe di-namika van polimeeroplossings. Gebaseer op ’n bestaande Gaussiese netwerkteorie wat vir ’n ewewigstelsel ontwikkel is, word die formalisme uitgebrei om dinamiese, omkeerbare koppeling te modelleer. Die Gaussiese velde stel ruimtelik-temporale be-perkings voor, terwyl alle moontlike konfigurasies waarin hierdie beperkings nage- kom kan word, in ag geneem word. Om die formalisme te illustreer, word ’n speel-dingmodel van Brownse deeltjies oorweeg, waar die netwerkbenadering gekombineer word met ’n Martin–Siggia–Rose (MSR) funksionele voorstelling van oordempte dina-mika. Hierop volg ’n toepassing op ’n twee-spesie polimeeroplossing met omkeerbare koppeling, waarin dinamiese struktuurfaktore analities bereken word. Die benadering word verder ontwikkel deur die dinamika van toegewyde koppelaardeeltjies in ag te neem en dit in ’n stelsel met twee polimeerspesies in te sluit, waarin beide intra- en interspesie-koppeling deur die netwerkformalisme geïmplementeer word. Limietge-valle van sterk en swak koppeling word vir beide tipes ontleed, en hul invloed op die dinamiese struktuurfaktore word ondersoek. Dinamiese struktuurfaktore word vir al vier kombinasies van sterk en swak intra- en interspesie-koppeling voorgestel. Ter aanvulling van die analitiese resultate word molekulêre dinamika-simulasies van ’n vergelykbare stelsel uitgevoer, wat omkeerbare koppeling insluit en dinamiese struk-tuurfaktore bereken vir direkte vergelyking. In alle scenario’s word dit konsekwent waargeneem dat koppeling lei tot ’n verbreding van die diffussie-pieke in die dina-miese struktuurfaktore. Die ooreenstemming tussen teoretiese voorspellings en daar-opvolgende simulasie ondersteun die toepaslikheid van die voorgestelde formalisme. Hierdie werk vestig ’n veelsydige modelleringsinstrument vir die ondersoek van die kollektiewe dinamika van omkeerbaar gekoppelde polimeerstelsels, met potensiële re- levansie vir beide biologiese netwerke en sintetiese materiale. Doctoral 2025-12-18T12:21:24Z 2025-12-18T12:21:24Z 2025-12 Thesis https://scholar.sun.ac.za/handle/10019.1/134612 en Stellenbosch University xv, 178 pages : illustrations application/pdf Stellenbosch : Stellenbosch University |
| spellingShingle | Crosslinking (Polymerization) -- Models Polymers -- Mathematical models Brownian motion processes -- Computer simulation Polymer solutions -- Mathematical models Dynamics UCTD Du Toit, Nadine Network dynamics of the cytoskeleton: chains with cross-linking |
| title | Network dynamics of the cytoskeleton: chains with cross-linking |
| title_full | Network dynamics of the cytoskeleton: chains with cross-linking |
| title_fullStr | Network dynamics of the cytoskeleton: chains with cross-linking |
| title_full_unstemmed | Network dynamics of the cytoskeleton: chains with cross-linking |
| title_short | Network dynamics of the cytoskeleton: chains with cross-linking |
| title_sort | network dynamics of the cytoskeleton chains with cross linking |
| topic | Crosslinking (Polymerization) -- Models Polymers -- Mathematical models Brownian motion processes -- Computer simulation Polymer solutions -- Mathematical models Dynamics UCTD |
| url | https://scholar.sun.ac.za/handle/10019.1/134612 |
| work_keys_str_mv | AT dutoitnadine networkdynamicsofthecytoskeletonchainswithcrosslinking |