A detailed study of ion transport through the SARS-CoV-2 E protein ion channel.

The envelope (E) protein encoded in the genome of an RNA virus is crucial for the replication, budding and pathophysiology of the virus. In the light of the ongoing pandemic, we explored similarities/differences between SARS-CoV-1 and SARS-CoV-2 E protein ion channels in terms of their selectivity. Further, we also examined the impact of variation of the bath concentration and introduction of potential and concentration gradients across the channel on the binding ratios of sodium and chloride ions for the SARS-CoV-2 E protein. Ion transport is described through the fourth-order Poisson-Nernst-Planck-Bikerman (4PNPBik) model which generalizes the traditional model by including ionic interactions between ions and their surrounding medium and non-ionic interactions between particles due to their finite size. Governing equations are solved numerically using the immersed boundary-lattice Boltzmann method (IB-LBM). The mathematical model has been validated by comparing analytical and experimental ion activity. The SARS-CoV-1 E protein ion channel is found to be more permeable to cationic ions, while the SARS-CoV-2 E protein has similar selectivity for both cationic and anionic species. For SARS-CoV-2, an increase in the bath concentration results in an increase in the binding ratio for sodium ions. Furthermore, the chloride binding ratio increases as the concentration gradient increases. A potential gradient has a minimal effect on the binding ratio. The SARS-CoV-2 E protein was found to support higher ionic currents than the SARS-CoV-1 E protein. Furthermore, the ionic current increased with increasing bath concentrations.

Investigation of the Efficiency of Mask Wearing, Contact Tracing, and Case Isolation during the COVID-19 Outbreak.

Case isolation and contact tracing are two essential parts of control measures to prevent the spread of COVID-19, however, additional interventions, such as mask wearing, are required. Taiwan successfully contained local COVID-19 transmission after the initial imported cases in the country in early 2020 after applying the above-mentioned interventions. In order to explain the containment of the disease spread in Taiwan and understand the efficiency of different non-pharmaceutical interventions, a mathematical model has been developed. A stochastic model was implemented in order to estimate the effectiveness of mask wearing together with case isolation and contact tracing. We investigated different approaches towards mask usage, estimated the effect of the interventions on the basic reproduction number (R0), and simulated the possibility of controlling the outbreak. With the assumption that non-medical and medical masks have 20% and 50% efficiency, respectively, case isolation works on 100%, 70% of all people wear medical masks, and R0 = 2.5, there is almost 80% probability of outbreak control with 60% contact tracing, whereas for non-medical masks the highest probability is only about 20%. With a large proportion of infectiousness before the onset of symptoms (40%) and the presence of asymptomatic cases, the investigated interventions (isolation of cases, contact tracing, and mask wearing by all people), implemented on a high level, can help to control the disease spread. Superspreading events have also been included in our model in order to estimate their impact on the outbreak and to understand how restrictions on gathering and social distancing can help to control the outbreak. The obtained quantitative results are in agreement with the empirical COVID-19 data in Taiwan.

Investigating ion transport inside the pentameric ion channel encoded in COVID-19 E protein.

Ion flow inside an ion channel can be described through continuum based Born-Poisson-Nernst-Planck (BPNP) equations in conjunction with the Lennard-Jones potential. Keeping in mind the ongoing pandemic, in this study, an attempt has been made to understand the selectivity and the current voltage relation of the COVID-19 E protein pentameric ion channel. Two ionic species, namely Na^{+} and Cl^{-}, have been considered here. E protein is one of the smallest structural protein which is embedded in the outer membrane of the virus. Once the virus is inside the host cell, this protein is expressed abundantly and is responsible for activities such as replication and budding of the virus. In the literature, we can find a few experimental studies focusing on understanding the activity of the channel formed by E proteins of different viruses. Here, we attempt the same study for the COVID-19 E protein ion channel through mathematical modeling. The channel geometry is calculated from the protein data bank file which was provided by NARLabs, Taiwan, using the hole program. Further, it was used to obtain the charge distribution using the pdbtopqr online program. The immersed boundary-lattice Boltzmann method (IB-LBM) has been implemented to numerically solve the system of equations in the channel generated by the protein data bank file. Further, an in-house code which operates on multiple GPUs and uses the cuda platform has been developed to achieve the goal of performing the current investigation.

Solution of Ion Channel Flow Using Immersed Boundary-Lattice Boltzmann Methods.

Poisson-Nernst-Planck (PNP) model has been extensively used for the study of channel flow under the influence of electrochemical gradients. PNP theory is a continuum description of ion flow where ionic distributions are described in terms of concentrations. Nonionic interparticle interactions are not considered in this theory as in continuum framework, their impact on the solution is minimal. This theory holds true for dilute flows or flows where channel radius is significantly larger than ion radius. However, for ion channel flows, where channel dimensions and ionic radius are of similar magnitude, nonionic interactions, particularly related to the size of the ions (steric effect), play an important role in defining the selectivity of the channel, concentration distribution of ionic species, and current across the channel, etc. To account for the effect of size of ions, several modifications to PNP equations have been proposed. One such approach is the introduction of Lennard-Jones potential to the energy variational formulation of PNP system. This study focuses on understanding the role of steric effect on flow properties. To discretize the system, Lattice Boltzmann method has been used. The system is defined by modified PNP equations where the steric effect is described by Lennard-Jones potential. In addition, boundary conditions for the complex channel geometry have been treated using immersed boundary method.

Effects of exchange correlation functional on optical permittivity of gold and electromagnetic responses.

Understanding the optical properties of nanometer-scale noble metals is important for the nanoplasmonic devices. The bulk gold and thin film are calculated by density functional theory (DFT) with LDA, PBE, and GLLBSC functionals, respectively. The GLLBSC results for bulk gold are closer to the experimental data because the GLLBSC functional has better descriptions of transition energy. The Im(ε) of thin film calculated by LDA and PBE are overestimated. The effects of DFT-based optical properties are performed by conducting electromagnetic simulations. The transmission for the gold thin film by GLLBSC is blue-shifted. The gold grating structure with the GLLBSC-based optical permittivity has strong localized streamlines of Poynting vector in the corner edges at the resonance condition.

Modulation of optical focusing by using optimized zone plate structures.

The focusing properties of the optimized zone plate structures which have upper and lower zones with different thicknesses are studied by the three-dimensional finite-difference time-domain method. Two kinds of materials are chosen, including silver representing metal and BK7 glass representing dielectric. An optimization algorithm is applied to tune the parameters of zone plate structures. Several optimized zone plate structures with smaller circular-shape focus are presented. By using the angular spectrum representation method, we found that the cases with smaller focal sizes have larger high-k components; however, the intensities of side lobes also become larger in comparison with the main beam. It is also found that the phase differences between different spatial field components can have the influences on focusing properties. A special case with two focuses is shown by changing the cost function of the same optimization algorithm. Our findings suggest that the optimized zone plate structures can reconstruct the light intensity distribution and have a great potential for the applications in imaging, lithography, and data storage.

Simulation of portal hemodynamic changes in a donor after right hepatectomy.

Remnant livers will be regenerated in live donors after a large volume resection for transplantation. How the structures and hemodynamics of portal vein will evolve with liver regeneration remains unknown. This prompts the present hemodynamic simulation for a 25 year-old man who received a right donor lobectomy. According to the magnetic resonance imaging/computed tomography images taken prior to the operation and one month after the operation, three sequential models of portal veins (pre-op, immediately after the operation, and one-month post-op) were constructed by AMIRA and HYPERMESH, while the immediately after the operation model was generated by removing the right branch in the pre-op model. Hemodynamic equations were solved subject to the sonographically measured inlet velocity. The simulated branch velocities were compared with the measured ones. The predicted overall pressure in the portal vein after resection was found to increase to a magnitude that has not reached to an extent possibly leading to portal hypertension. As expected, blood pressure has a large change only in the vicinity of the resection region. The branches grew considerably different from the original one as the liver is regenerated. Results provide useful evidence to justify the current computer simulation.

Computer simulation of hemodynamic changes after right lobectomy in a liver with intrahepatic portal vein aneurysm.

BACKGROUND/PURPOSE: Intrahepatic portal vein aneurysm is rare and its natural history is unknown. A 22-year-old healthy man, who wished to donate part of his liver to his diseased father, was incidentally diagnosed to have an intrahepatic portal vein aneurysm. The surgical decision of performing live donor hepatectomy for such a patient is normally difficult. We combined modern imaging reconstruction technologies with scientific computing as a new modality to foresee the risks of surgical complications. METHODS: Cross-sectional computed tomography images were used to reconstruct the three-dimensional image of portal vein distribution using the 3D-Doctor v3.5 software. The reconstructed images were further employed to generate surface and interior meshes with CFX software. Simulated hemodynamic changes in velocity, pressure, and wall stress were determined for the right lobectomy case pre- and postoperatively. RESULTS: The simulation results indicated that aneurismal pressure would be elevated significantly to 12.03 mmHg after operation. The left segmental portal venous blood flow would increase from 2.95- to 4.25-fold. The area near the branch point of one left segmental portal vein, which supplies blood to liver segment 4, and the portal vein aneurysm would endure high shear stress gradient. The resulting elevated aneurismal pressure may cause the thin wall to enlarge and rupture, while the high shear stress gradient would lead to vascular endothelial cell injury. Living donor surgery was not recommended hemodynamically based on the simulated results. CONCLUSION: Scientific computing and modern imaging technologies can be applied together to aid surgeons to make the best decision in difficult clinical situations.