Mathematical and computational models of RNA nanoclusters and their applications in data-driven environments

Badu, Shyam; Melnik, Roderick; Singh, Sundeep

doi:10.1080/08927022.2020.1804564

Cited by 7 publications

(5 citation statements)

References 297 publications

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“…This reveals that it is possible to efficiently manipulate such properties and characteristics for larger size RNA nanotubes, which are practically important for drug delivery and other biomedical applications of these structures. The developed models could be further generalized to account for more complex multiscale interactions, integrating our developed methodology with predictive, dynamic, and stochastic coarse-grained approaches [11,[57][58][59][60][61][62]. This would allow us to better face challenges of a vast separation of spatial and temporal scales between processes happening at the atomic and cellular levels and to provide a route for more efficient integrations of atomistic and molecular information into larger-scale models.…”

Section: Discussionmentioning

confidence: 99%

Coarse-Grained Models of RNA Nanotubes for Large Time Scale Studies in Biomedical Applications

2020

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In order to describe the physical properties of large time scale biological systems, coarse-grained models play an increasingly important role. In this paper we develop Coarse-Grained (CG) models for RNA nanotubes and then, by using Molecular Dynamics (MD) simulation, we study their physical properties. Our exemplifications include RNA nanotubes of 40 nm long, equivalent to 10 RNA nanorings connected in series. The developed methodology is based on a coarse-grained representation of RNA nanotubes, where each coarse bead represents a group of atoms. By decreasing computation cost, this allows us to make computations feasible for realistic structures of interest. In particular, for the developed coarse-grained models with three bead approximations, we calculate the histograms for the bond angles and the dihedral angles. From the dihedral angle histograms, we analyze the characteristics of the links used to build the nanotubes. Furthermore, we also calculate the bead distances along the chains of RNA strands in the nanoclusters. The variations in these features with the size of the nanotube are discussed in detail. Finally, we present the results on the calculation of the root mean square deviations for a developed RNA nanotube to demonstrate the equilibration of the systems for drug delivery and other biomedical applications such as medical imaging and tissue engineering.

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Section: Discussionmentioning

confidence: 99%

Coarse-Grained Models of RNA Nanotubes for Large Time Scale Studies in Biomedical Applications

2020

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“…Finally, we mention efficient coarse-graining models [ 199 , 200 , 201 , 202 , 203 , 204 ] that have been developed for nucleic-acid-based nanostructures discussed in detail in Section 5.2 .…”

Section: Mathematical and Computational Models For Smart Materials An...mentioning

confidence: 99%

“…Moreover, there are also a number of proposals for hybrid nanostructures where various design and screening strategies can lead to a myriad of RNA-DNA hybrid nanostructures that can be used as programmable platforms for applications in sensing, molecular recognition, protein interaction, and catalyst research [ 253 ]. Given the capabilities of nonlinear responses of such nucleic acid biosensors over a wide dynamic range, refined modelling techniques such as those based on MD simulations are required along with the development of efficient coarse-grained procedures [ 199 , 200 , 201 , 202 , 203 , 204 , 254 ]. In this way, properties of associated nucleic acid nanostructures such as RNA nanotubes have been studied in detail, including their behavior in fluids.…”

Section: Further Characteristics and Areas Of Applicationsmentioning

confidence: 99%

Coupled Multiphysics Modelling of Sensors for Chemical, Biomedical, and Environmental Applications with Focus on Smart Materials and Low-Dimensional Nanostructures

Singh

Melnik

2022

Chemosensors

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Low-dimensional nanostructures have many advantages when used in sensors compared to the traditional bulk materials, in particular in their sensitivity and specificity. In such nanostructures, the motion of carriers can be confined from one, two, or all three spatial dimensions, leading to their unique properties. New advancements in nanosensors, based on low-dimensional nanostructures, permit their functioning at scales comparable with biological processes and natural systems, allowing their efficient functionalization with chemical and biological molecules. In this article, we provide details of such sensors, focusing on their several important classes, as well as the issues of their designs based on mathematical and computational models covering a range of scales. Such multiscale models require state-of-the-art techniques for their solutions, and we provide an overview of the associated numerical methodologies and approaches in this context. We emphasize the importance of accounting for coupling between different physical fields such as thermal, electromechanical, and magnetic, as well as of additional nonlinear and nonlocal effects which can be salient features of new applications and sensor designs. Our special attention is given to nanowires and nanotubes which are well suited for nanosensor designs and applications, being able to carry a double functionality, as transducers and the media to transmit the signal. One of the key properties of these nanostructures is an enhancement in sensitivity resulting from their high surface-to-volume ratio, which leads to their geometry-dependant properties. This dependency requires careful consideration at the modelling stage, and we provide further details on this issue. Another important class of sensors analyzed here is pertinent to sensor and actuator technologies based on smart materials. The modelling of such materials in their dynamics-enabled applications represents a significant challenge as we have to deal with strongly nonlinear coupled problems, accounting for dynamic interactions between different physical fields and microstructure evolution. Among other classes, important in novel sensor applications, we have given our special attention to heterostructures and nucleic acid based nanostructures. In terms of the application areas, we have focused on chemical and biomedical fields, as well as on green energy and environmentally-friendly technologies where the efficient designs and opportune deployments of sensors are both urgent and compelling.

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“…Starting from generalized versions of the master equation, one has to construct an efficient procedure for calculating memory kernels, including non-Markovian cases [218]. Nonperturbative approaches [219][220][221][222] can provide here superior efficiency and accuracy improvements, see, e.g., [223] where they were tested on the Fenna-Matthews-Olson (FMO) light-harvesting complexes important in the analysis of photosynthetic systems [224][225][226][227]. The problems of reductions of Mori-Zwanzig theory models (not limited to their quantum-classical versions) have been a topic of discussion which included also relevant computational complexity issues [228].…”

Section: Modelling With Nonlocality In Data-driven Environmentsmentioning

confidence: 99%

Mathematical Models with Nonlocal Initial Conditions: An Exemplification from Quantum Mechanics

Sytnyk

Melnik

2021

MCA

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Nonlocal models are ubiquitous in all branches of science and engineering, with a rapidly expanding range of mathematical and computational applications due to the ability of such models to capture effects and phenomena that traditional models cannot. While spatial nonlocalities have received considerable attention in the research community, the same cannot be said about nonlocality in time, in particular when nonlocal initial conditions are present. This paper aims at filling this gap, providing an overview of the current status of nonlocal models and focusing on the mathematical treatment of such models when nonlocal initial conditions are at the heart of the problem. Specifically, our representative example is given for a nonlocal-in-time problem for the abstract Schrödinger equation. By exploiting the linear nature of nonlocal conditions, we derive an exact representation of the solution operator under assumptions that the spectrum of Hamiltonian is contained in the horizontal strip of the complex plane. The derived representation permits us to establish the necessary and sufficient conditions for the problem’s well-posedness and the existence of its solution under different regularities. Furthermore, we present new sufficient conditions for the existence of the solution that extend the existing results in this field to the case when some nonlocal parameters are unbounded. Two further examples demonstrate the developed methodology and highlight the importance of its computer algebra component in the reduction procedures and parameter estimations for nonlocal models. Finally, a connection of the considered models and developed analysis is discussed in the context of other reduction techniques, concentrating on the most promising from the viewpoint of data-driven modelling environments, and providing directions for further generalizations.

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Mathematical and computational models of RNA nanoclusters and their applications in data-driven environments

Cited by 7 publications

References 297 publications

Coarse-Grained Models of RNA Nanotubes for Large Time Scale Studies in Biomedical Applications

Coarse-Grained Models of RNA Nanotubes for Large Time Scale Studies in Biomedical Applications

Coupled Multiphysics Modelling of Sensors for Chemical, Biomedical, and Environmental Applications with Focus on Smart Materials and Low-Dimensional Nanostructures

Mathematical Models with Nonlocal Initial Conditions: An Exemplification from Quantum Mechanics

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