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Biomolecular surface construction by PDE transform.

ABSTRACT: This work proposes a new framework for the surface generation based on the partial differential equation (PDE) transform. The PDE transform has recently been introduced as a general approach for the mode decomposition of images, signals, and data. It relies on the use of arbitrarily high-order PDEs to achieve the time-frequency localization, control the spectral distribution, and regulate the spatial resolution. The present work provides a new variational derivation of high-order PDE transforms. The fast Fourier transform is utilized to accomplish the PDE transform so as to avoid stringent stability constraints in solving high-order PDEs. As a consequence, the time integration of high-order PDEs can be done efficiently with the fast Fourier transform. The present approach is validated with a variety of test examples in two-dimensional and three-dimensional settings. We explore the impact of the PDE transform parameters, such as the PDE order and propagation time, on the quality of resulting surfaces. Additionally, we utilize a set of 10 proteins to compare the computational efficiency of the present surface generation method and a standard approach in Cartesian meshes. Moreover, we analyze the present method by examining some benchmark indicators of biomolecular surface, that is, surface area, surface-enclosed volume, solvation free energy, and surface electrostatic potential. A test set of 13 protein molecules is used in the present investigation. The electrostatic analysis is carried out via the Poisson-Boltzmann equation model. To further demonstrate the utility of the present PDE transform-based surface method, we solve the Poisson-Nernst-Planck equations with a PDE transform surface of a protein. Second-order convergence is observed for the electrostatic potential and concentrations. Finally, to test the capability and efficiency of the present PDE transform-based surface generation method, we apply it to the construction of an excessively large biomolecule, a virus surface capsid. Virus surface morphologies of different resolutions are attained by adjusting the propagation time. Therefore, the present PDE transform provides a multiresolution analysis in the surface visualization. Extensive numerical experiment and comparison with an established surface model indicate that the present PDE transform is a robust, stable, and efficient approach for biomolecular surface generation in Cartesian meshes.

SUBMITTER: Zheng Q

PROVIDER: S-EPMC3347862 | biostudies-literature | 2012 Mar

REPOSITORIES: biostudies-literature

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Biomolecular surface construction by PDE transform.

Zheng Qiong Q Yang Siyang S Wei Guo-Wei GW

International journal for numerical methods in biomedical engineering 20110926 3

This work proposes a new framework for the surface generation based on the partial differential equation (PDE) transform. The PDE transform has recently been introduced as a general approach for the mode decomposition of images, signals, and data. It relies on the use of arbitrarily high-order PDEs to achieve the time-frequency localization, control the spectral distribution, and regulate the spatial resolution. The present work provides a new variational derivation of high-order PDE transforms. ...[more]

PMID: 22582140

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Project description:Fractional derivative or fractional calculus plays a significant role in theoretical modeling of scientific and engineering problems. However, only relatively low order fractional derivatives are used at present. In general, it is not obvious what role a high fractional derivative can play and how to make use of arbitrarily high-order fractional derivatives. This work introduces arbitrarily high-order fractional partial differential equations (PDEs) to describe fractional hyperdiffusions. The fractional PDEs are constructed via fractional variational principle. A fast fractional Fourier transform (FFFT) is proposed to numerically integrate the high-order fractional PDEs so as to avoid stringent stability constraints in solving high-order evolution PDEs. The proposed high-order fractional PDEs are applied to the surface generation of proteins. We first validate the proposed method with a variety of test examples in two and three-dimensional settings. The impact of high-order fractional derivatives to surface analysis is examined. We also construct fractional PDE transform based on arbitrarily high-order fractional PDEs. We demonstrate that the use of arbitrarily high-order derivatives gives rise to time-frequency localization, the control of the spectral distribution, and the regulation of the spatial resolution in the fractional PDE transform. Consequently, the fractional PDE transform enables the mode decomposition of images, signals, and surfaces. The effect of the propagation time on the quality of resulting molecular surfaces is also studied. Computational efficiency of the present surface generation method is compared with the MSMS approach in Cartesian representation. We further validate the present method by examining some benchmark indicators of macromolecular surfaces, i.e., surface area, surface enclosed volume, surface electrostatic potential and solvation free energy. Extensive numerical experiments and comparison with an established surface model indicate that the proposed high-order fractional PDEs are robust, stable and efficient for biomolecular surface generation.

Project description:Biomolecular condensates are cellular compartments that concentrate biomolecules without an encapsulating membrane. In recent years, significant advances have been made in the understanding of condensates through biochemical reconstitution and microscopic detection of these structures. Quantitative visualization and biochemical assays of biomolecular condensates rely on surface passivation to minimize background and artifacts due to condensate adhesion. However, the challenge of undesired interactions between condensates and glass surfaces, which can alter material properties and impair observational accuracy, remains a critical hurdle. Here, we introduce an efficient, generically applicable, and simple passivation method employing self-assembly of the surfactant Pluronic F127 (PF127). The method greatly reduces nonspecific binding across a range of condensates systems for both phase-separated droplets and biomolecules in dilute phase. Additionally, by integrating PF127 passivation with the Biotin-NeutrAvidin system, we achieve controlled multi-point attachment of condensates to surfaces. This not only preserves condensate properties but also facilitates long-time FRAP imaging and high-precision single-molecule analyses. Using this method, we have explored the dynamics of polySIM molecules within polySUMO/polySIM condensates at the single-molecule level. Our observations suggest a potential heterogeneity in the distribution of available polySIM-binding sites within the condensates.Significance statementThe understanding of biomolecular condensates has significantly benefited from biochemical reconstitution with microscopy detection. Here, we present a novel surface passivation method utilizing self-assembly of Pluronic F127 on hydrophobic surfaces. This approach not only effectively minimizes non-specific binding without altering the physical properties of the condensates but also offers universal passivation across a variety of condensate systems. It demonstrates high resistance to different treatments and enables condensate immobilization through controlled anchor points. This allows for highly sensitive analytical techniques, including single-molecule imaging. The simplicity and high-performance of this method, coupled with time and cost efficiencies, could facilitate robustness and throughput of experiments, and could broaden the accessibility of biochemical phase separation studies to a wider scientific community.

Project description:BACKGROUND: From the 1950s computer based renderings of molecules have been produced to aid researchers in their understanding of biomolecular structure and function. A major consideration for any molecular graphics software is the ability to visualise the three dimensional structure of the molecule. Traditionally, this was accomplished via stereoscopic pairs of images and later realised with three dimensional display technologies. Using a haptic feedback device in combination with molecular graphics has the potential to enhance three dimensional visualisation. Although haptic feedback devices have been used to feel the interaction forces during molecular docking they have not been used explicitly as an aid to visualisation. RESULTS: A haptic rendering application for biomolecular visualisation has been developed that allows the user to gain three-dimensional awareness of the shape of a biomolecule. By using a water molecule as the probe, modelled as an oxygen atom having hard-sphere interactions with the biomolecule, the process of exploration has the further benefit of being able to determine regions on the molecular surface that are accessible to the solvent. This gives insight into how awkward it is for a water molecule to gain access to or escape from channels and cavities, indicating possible entropic bottlenecks. In the case of liver alcohol dehydrogenase bound to the inhibitor SAD, it was found that there is a channel just wide enough for a single water molecule to pass through. Placing the probe coincident with crystallographic water molecules suggests that they are sometimes located within small pockets that provide a sterically stable environment irrespective of hydrogen bonding considerations. CONCLUSION: By using the software, named HaptiMol ISAS (available from http://www.haptimol.co.uk), one can explore the accessible surface of biomolecules using a three-dimensional input device to gain insights into the shape and water accessibility of the biomolecular surface that cannot be so easily attained using conventional molecular graphics software.

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Biomolecular surface construction by PDE transform.

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Biomolecular surface construction by PDE transform.

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