An official website of the United States government
In this paper, we derive a dynamic surface elasticity model for the two-dimensional midsurface of a thin, three-dimensional, homogeneous, isotropic, nonlinear gradient elastic plate of thickness ℎ. The resulting model is parameterized by five, conceivably measurable, physical properties of the plate, and the stored surface energy reduces to Koiter’s plate energy in a singular limiting case. The model corrects a theoretical issue found in wave propagation in thin sheets and, when combined with the author’s theory of Green elastic bodies possessing gradient elastic material boundary surfaces, removes the singularities present in fracture within traditional/classical models. Our approach diverges from previous research on thin shells and plates, which primarily concentrated on deriving elasticity theories for material surfaces from classical three-dimensional Green elasticity. This work is the first in rigorously developing a surface elasticity model based on a parent nonlinear gradient elasticity theory.
more »
« less
Allosteric interactions in a birod model of DNA
Allosteric interactions between molecules bound to DNA at distant locations have been known for a long time. The phenomenon has been studied via experiments and numerical simulations, but a comprehensive understanding grounded in a theory of DNA elasticity remains a challenge. Here, we quantify allosteric interactions between two entities bound to DNA by using the theory of birods. We recognize that molecules bound to DNA cause local deformations that can be captured in a birod model which consists of two elastic strands interacting via an elastic web representing the basepairs. We show that the displacement field caused by bound entities decays exponentially with distance from the binding site. We compute the interaction energy between two proteins on DNA as a function of distance between them and find that it decays exponentially while oscillating with the periodicity of the double helix, in excellent agreement with experiments. The decay length of the interaction energy can be determined in terms of the mechanical properties of the strands and the webbing in our birod model, and it varies with the GC content of the DNA. Our model provides a framework for viewing allosteric interactions in DNA within the ambit of configurational forces of continuum elasticity.
more »
« less
- Award ID(s):
- 1662101
- PAR ID:
- 10095554
- Date Published:
- Journal Name:
- Proceedings of the Royal Society of London. Series A, Mathematical and physical sciences
- Volume:
- 474
- ISSN:
- 0080-4630
- Page Range / eLocation ID:
- 20180136
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
null (Ed.)Adhesive interactions between elastic structures such as graphene sheets, carbon nanotubes, and microtubules have been shown to exhibit hysteresis due to irrecoverable energy loss associated with bond breakage, even in static (rate-independent) experiments. To understand this phenomenon, we start with a minimal theory for the peeling of a thin sheet from a substrate, coupling the local event of bond breaking to the nonlocal elastic relaxation of the sheet and show that this can drive static adhesion hysteresis over a bonding/debonding cycle. Using this model we quantify hysteresis in terms of the adhesion and elasticity parameters of the system. This allows us to derive a scaling relation that preserves hysteresis at different levels of granularity while resolving a seeming paradox of lattice trapping in the continuum limit of a discrete fracture process. Finally, to verify our theory, we use new experiments to demonstrate and measure adhesion hysteresis in bundled microtubules.more » « less
-
null (Ed.)Crosslinked porous protein crystals are a new biomaterial that can be engineered to encapsulate, stabilize, and organize guest molecules, nanoparticles, and biological moieties. In this study, for the first time, the combined interactions of DNA strands with porous protein crystals are quantitatively measured by high-resolution atomic force microscopy (AFM) and chemical force microscopy. The surface structure of protein crystals with unusually large pores was observed in liquid via high-resolution AFM. Force–distance ( F – D ) curves were also obtained using AFM tips modified to present or capture DNA. The modification of AFM tips allowed the tips to covalently bind DNA that was pre-loaded in the protein crystal nanopores. The modified tips enabled the interactions of DNA molecules with protein crystals to be quantitatively studied while revealing the morphology of the buffer-immersed protein crystal surface in detail, thereby preserving the structure and properties of protein crystals that could be disrupted or destroyed by drying. The hexagonal space group was manifest at the crystal surface, as were the strong interactions between DNA and the porous protein crystals in question. In sum, this study furthered our understanding of how a new protein-based biomaterial can be used to bind guest DNA assemblies.more » « less
-
Network theory analysis has emerged as a powerful approach for investigating the complex behavior of dynamic and interactive systems, including proteomic systems. One key application of these methods is the study of long-range signaling dynamics in proteins, a phenomenon known as allostery. In this study, we applied computational models using network theory analysis to explore long-range electrostatic interactions and allosteric drug rescue mechanisms in the DNA-binding domain (DBD) of the p53 protein, a critical tumor suppressor whose dysfunction, often caused by missense mutations, is implicated in over 50% of human cancers. Using heat kernel and Wasserstein distance-based analyses, we explored the allosteric behavior of p53-DBD constructs with the Y220C mutation in the presence or absence of allosteric effector drugs. Our results demonstrated that these network theory-based protocols effectively detected the differential efficacies of small molecule allosteric effector drug compounds in restoring long-range electrostatic dynamics in the Y220C mutant. Furthermore, our approach identified key long-range electrostatic interactions critical to both the nominal and drug-rescued functionality of the p53-DBD, providing valuable insights into allosteric modulation and its therapeutic potential.more » « less
-
Abstract Allostery is a hallmark of cellular function and important in every biological system. Still, we are only starting to mimic it in the laboratory. Here, we introduce an approach to study aspects of allostery in artificial systems. We use a DNA origami domino array structure which–upon binding of trigger DNA strands–undergoes a stepwise allosteric conformational change. Using two FRET probes placed at specific positions in the DNA origami, we zoom in into single steps of this reaction cascade. Most of the steps are strongly coupled temporally and occur simultaneously. Introduction of activation energy barriers between different intermediate states alters this coupling and induces a time delay. We then apply these approaches to release a cargo DNA strand at a predefined step in the reaction cascade to demonstrate the applicability of this concept in tunable cascades of mechanochemical coupling with both spatial and temporal control.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1098/rspa.2018.0136
