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Topology mediates transport of nanoparticles in macromolecular networks.

ABSTRACT: Diffusion transport of nanoparticles in confined environments of macromolecular networks is common in diverse physical systems and regulates many biological responses. Macromolecular networks possess various topologies, featured by different numbers of degrees and genera. Although the network topologies can be manipulated from a molecular level, how the topology impacts the transport of nanoparticles in macromolecular networks remains unexplored. Here, we develop theoretical approaches combined with simulations to study nanoparticle transport in a model system consisting of network cells with defined topologies. We find that the topology of network cells has a profound effect on the free energy landscape experienced by a nanoparticle in the network cells, exhibiting various scaling laws dictated by the topology. Furthermore, the examination of the impact of cell topology on the detailed behavior of nanoparticle dynamics leads to different dynamical regimes that go beyond the particulars regarding the local network loop. The results might alter the conventional picture of the physical origin of transport in networks.

SUBMITTER: Dai X

PROVIDER: S-EPMC9283426 | biostudies-literature | 2022 Jul

REPOSITORIES: biostudies-literature

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Topology mediates transport of nanoparticles in macromolecular networks.

Dai Xiaobin X Zhang Xuanyu X Gao Lijuan L Xu Ziyang Z Yan Li-Tang LT

Nature communications 20220714 1

Diffusion transport of nanoparticles in confined environments of macromolecular networks is common in diverse physical systems and regulates many biological responses. Macromolecular networks possess various topologies, featured by different numbers of degrees and genera. Although the network topologies can be manipulated from a molecular level, how the topology impacts the transport of nanoparticles in macromolecular networks remains unexplored. Here, we develop theoretical approaches combined ...[more]

PMID: 35835763

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Project description:BackgroundMetabolic Flux Analysis (MFA) based on isotope labeling experiments (ILEs) is a widely established tool for determining fluxes in metabolic pathways. Isotope labeling networks (ILNs) contain all essential information required to describe the flow of labeled material in an ILE. Whereas recent experimental progress paves the way for high-throughput MFA, large network investigations and exact statistical methods, these developments are still limited by the poor performance of computational routines used for the evaluation and design of ILEs. In this context, the global analysis of ILN topology turns out to be a clue for realizing large speedup factors in all required computational procedures.ResultsWith a strong focus on the speedup of algorithms the topology of ILNs is investigated using graph theoretic concepts and algorithms. A rigorous determination of all cyclic and isomorphic subnetworks, accompanied by the global analysis of ILN connectivity is performed. Particularly, it is proven that ILNs always brake up into a large number of small strongly connected components (SCCs) and, moreover, there are natural isomorphisms between many of these SCCs. All presented techniques are universal, i.e. they do not require special assumptions on the network structure, bidirectionality of fluxes, measurement configuration, or label input. The general results are exemplified with a practically relevant metabolic network which describes the central metabolism of E. coli comprising 10390 isotopomer pools.ConclusionExploiting the topological features of ILNs leads to a significant speedup of all universal algorithms for ILE evaluation. It is proven in theory and exemplified with the E. coli example that a speedup factor of about 1000 compared to standard algorithms is achieved. This widely opens the door for new high performance algorithms suitable for high throughput applications and large ILNs. Moreover, for the first time the global topological analysis of ILNs allows to comprehensively describe and understand the general patterns of label flow in complex networks. This is an invaluable tool for the structural design of new experiments and the interpretation of measured data.

Project description:The formation of condensed matter typically involves a trade-off between structural order and flexibility. As the extent and directionality of interactions between atomic or molecular components increase, materials generally become more ordered but less compliant, and vice versa. Nevertheless, high levels of structural order and flexibility are not necessarily mutually exclusive; there are many biological (such as microtubules1,2, flagella 3 , viruses4,5) and synthetic assemblies (for example, dynamic molecular crystals6-9 and frameworks10-13) that can undergo considerable structural transformations without losing their crystalline order and that have remarkable mechanical properties8,14,15 that are useful in diverse applications, such as selective sorption 16 , separation 17 , sensing 18 and mechanoactuation 19 . However, the extent of structural changes and the elasticity of such flexible crystals are constrained by the necessity to maintain a continuous network of bonding interactions between the constituents of the lattice. Consequently, even the most dynamic porous materials tend to be brittle and isolated as microcrystalline powders 14 , whereas flexible organic or inorganic molecular crystals cannot expand without fracturing. Owing to their rigidity, crystalline materials rarely display self-healing behaviour 20 . Here we report that macromolecular ferritin crystals with integrated hydrogel polymers can isotropically expand to 180 per cent of their original dimensions and more than 500 per cent of their original volume while retaining periodic order and faceted Wulff morphologies. Even after the separation of neighbouring ferritin molecules by 50 ångströms upon lattice expansion, specific molecular contacts between them can be reformed upon lattice contraction, resulting in the recovery of atomic-level periodicity and the highest-resolution ferritin structure reported so far. Dynamic bonding interactions between the hydrogel network and the ferritin molecules endow the crystals with the ability to resist fragmentation and self-heal efficiently, whereas the chemical tailorability of the ferritin molecules enables the creation of chemically and mechanically differentiated domains within single crystals.

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Topology mediates transport of nanoparticles in macromolecular networks.

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Topology mediates transport of nanoparticles in macromolecular networks.

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