Department of Mechanical & Aerospace Engineering, The George Washington University, Washington, DC 20052, USA.
Department of Mechanical Engineering and Centro Científico Tecnológico de Valparaíso, Universidad Técnica Federico Santa María, Valparaíso, Chile.
Phys Rev E. 2019 Dec;100(6-1):063305. doi: 10.1103/PhysRevE.100.063305.
The phenomenon of localized surface plasmon resonance (LSPR) provides high sensitivity in detecting biomolecules through shifts in resonance frequency when a target is present. Computational studies in this field have used the full Maxwell equations with simplified models of a sensor-analyte system, or they neglected the analyte altogether. In the long-wavelength limit, one can simplify the theory via an electrostatics approximation while adding geometrical detail in the sensor and analytes (at moderate computational cost). This work uses the latter approach, expanding the open-source PyGBe code to compute the extinction cross section of metallic nanoparticles in the presence of any target for sensing. The target molecule is represented by a surface mesh, based on its crystal structure. PyGBe is research software for continuum electrostatics, written in python with computationally expensive parts accelerated on GPU hardware, via PyCUDA. It is also accelerated algorithmically via a treecode that offers O(NlogN) computational complexity. These features allow PyGBe to handle problems with half a million boundary elements or more. In this work, we demonstrate the suitability of PyGBe, extended to compute LSPR response in the electrostatic limit, for biosensing applications. Using a model problem consisting of an isolated silver nanosphere in an electric field, our results show grid convergence as 1/N, and accurate computation of the extinction cross section as a function of wavelength (compared with an analytical solution). For a model of a sensor-analyte system, consisting of a spherical silver nanoparticle and a set of bovine serum albumin (BSA) proteins, our results again obtain grid convergence as 1/N (with respect to the Richardson extrapolated value). Computing the LSPR response as a function of wavelength in the presence of BSA proteins captures a redshift of 0.5 nm in the resonance frequency due to the presence of the analytes at 1-nm distance. The final result is a sensitivity study of the biosensor model, obtaining the shift in resonance frequency for various distances between the proteins and the nanoparticle. All results in this paper are fully reproducible, and we have deposited in archival data repositories all the materials needed to run the computations again and recreate the figures. PyGBe is open source under a permissive license and openly developed. Documentation is available at http://pygbe.github.io/pygbe/docs/.
局部表面等离子体共振（LSPR）现象通过在存在目标时共振频率的位移提供了对生物分子的高灵敏度检测。该领域的计算研究使用了全麦克斯韦方程和传感器-分析物系统的简化模型，或者完全忽略了分析物。在长波长极限下，可以通过静电近似简化理论，同时在传感器和分析物中添加几何细节（以适度的计算成本）。这项工作采用了后一种方法，扩展了开源的 PyGBe 代码，以计算存在任何目标用于传感时金属纳米粒子的消光截面。目标分子由基于其晶体结构的表面网格表示。PyGBe 是用于连续静电的研究软件，用 Python 编写，通过 PyCUDA 在 GPU 硬件上加速计算昂贵的部分，它还通过提供 O(NlogN)计算复杂度的树码算法进行加速。这些功能使 PyGBe 能够处理具有五十万个边界元素或更多边界元素的问题。在这项工作中，我们展示了扩展到静电极限下计算 LSPR 响应的 PyGBe 的适用性，适用于生物传感应用。使用由电场中的孤立银纳米球组成的模型问题，我们的结果表明网格收敛为 1/N，并且作为波长函数准确计算消光截面（与解析解相比）。对于由球形银纳米粒子和一组牛血清白蛋白（BSA）蛋白组成的传感器-分析物系统模型，我们的结果再次获得了 1/N 的网格收敛（相对于 Richardson 外推值）。在存在 BSA 蛋白的情况下，作为波长函数计算 LSPR 响应捕获了由于分析物在 1nm 距离处存在而导致的共振频率的 0.5nm 红移。最终结果是对生物传感器模型的灵敏度研究，获得了各种蛋白与纳米粒子之间距离的共振频率偏移。本文中的所有结果都是完全可重现的，我们已经将再次运行计算并重新创建图所需的所有材料存储在档案数据存储库中。PyGBe 是在宽松许可证下开源的，并公开开发。文档可在 http://pygbe.github.io/pygbe/docs/ 获得。
