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Baskerville AL, Gray C, Cox H. Correlated energy from radial density-energy relations. R Soc Open Sci 2023; 10:221402. [PMID: 36938537 PMCID: PMC10014244 DOI: 10.1098/rsos.221402] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 10/30/2022] [Accepted: 02/13/2023] [Indexed: 06/18/2023]
Abstract
Here, we demonstrate that the radial distribution function can be mapped into a radial density-energy space and the relationship between the radial density and radial energy is linear for the ground and excited states of helium-like systems; the gradient of the resulting straight line delivers the energy of the state considered. To utilize this finding, a simple analytical expression for the total energy in terms of the density at the most probable nucleus-electron distance of the systems considered is derived using a fitting procedure.
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Affiliation(s)
- Adam L. Baskerville
- Department of Chemistry, School of Life Sciences, University of Sussex, Falmer, Brighton BN1 9QJ, UK
| | - Conor Gray
- Department of Chemistry, School of Life Sciences, University of Sussex, Falmer, Brighton BN1 9QJ, UK
| | - Hazel Cox
- Department of Chemistry, School of Life Sciences, University of Sussex, Falmer, Brighton BN1 9QJ, UK
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Xu Y, Jacquat RPB, Shen Y, Vigolo D, Morse D, Zhang S, Knowles TPJ. Microfluidic Templating of Spatially Inhomogeneous Protein Microgels. Small 2020; 16:e2000432. [PMID: 32529798 DOI: 10.1002/smll.202000432] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/21/2020] [Revised: 04/20/2020] [Accepted: 05/18/2020] [Indexed: 05/20/2023]
Abstract
3D scaffolds in the form of hydrogels and microgels have allowed for more native cell-culture systems to be developed relative to flat substrates. Native biological tissues are, however, usually spatially inhomogeneous and anisotropic, but regulating the spatial density of hydrogels at the microscale to mimic this inhomogeneity has been challenging to achieve. Moreover, the development of biocompatible synthesis approaches for protein-based microgels remains challenging, and typical gelation conditions include UV light, extreme pH, extreme temperature, or organic solvents, factors which can compromise the viability of cells. This study addresses these challenges by demonstrating an approach to fabricate protein microgels with controllable radial density through microfluidic mixing and physical and enzymatic crosslinking of gelatin precursor molecules. Microgels with a higher density in their cores and microgels with a higher density in their shells are demonstrated. The microgels have robust stability at 37 °C and different dissolution rates through enzymolysis, which can be further used for gradient scaffolds for 3D cell culture, enabling controlled degradability, and the release of biomolecules. The design principles of the microgels could also be exploited to generate other soft materials for applications ranging from novel protein-only micro reactors to soft robots.
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Affiliation(s)
- Yufan Xu
- Centre for Misfolding Diseases, Department of Chemistry, University of Cambridge, Cambridge, CB2 1EW, UK
| | - Raphaël P B Jacquat
- Centre for Misfolding Diseases, Department of Chemistry, University of Cambridge, Cambridge, CB2 1EW, UK
- Cavendish Laboratory, University of Cambridge, Cambridge, CB3 0HE, UK
| | - Yi Shen
- Centre for Misfolding Diseases, Department of Chemistry, University of Cambridge, Cambridge, CB2 1EW, UK
| | - Daniele Vigolo
- School of Chemical Engineering, University of Birmingham, Edgbaston, Birmingham, B15 2TT, UK
| | - David Morse
- Centre for Misfolding Diseases, Department of Chemistry, University of Cambridge, Cambridge, CB2 1EW, UK
- Cavendish Laboratory, University of Cambridge, Cambridge, CB3 0HE, UK
- Division of Preclinical Innovation, National Center for Advancing Translational Sciences, National Institutes of Health, Bethesda, MD, 20892, USA
| | - Shuyuan Zhang
- Centre for Misfolding Diseases, Department of Chemistry, University of Cambridge, Cambridge, CB2 1EW, UK
| | - Tuomas P J Knowles
- Centre for Misfolding Diseases, Department of Chemistry, University of Cambridge, Cambridge, CB2 1EW, UK
- Cavendish Laboratory, University of Cambridge, Cambridge, CB3 0HE, UK
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