Calculations of protein-protein interactions with the fast multipole method

I present a physical model to calculate protein-protein interactions. General formulations to calculate the electrostatic and the van der Waals free energies are brought by the boundary element method of solving linearized Poission-Boltzmann equation in an electrolyte solution, then further expanded to the application of the Fast Multipole Method(FMM). We built an efficient solver to investigate how the mutations on the active site of the protein-protein interface affect changes in binding affinities of protein complexes. Calculated results in addition to the structural analysis help us to understand the protein-protein interaction energy and provide a model to the important applications such as protein crystallization. The osmotic second virial coefficient B2 is directly related to the solubility of protein molecule in electrolyte solution and determined by molecular interactions involving both solvent and solute molecules. Calculations of interaction energies account for the electrostatic and the van der Waals interactions with the structural anisotropic properties of protein molecules. The orientation dependence of interaction energies between two proteins is determined by the crystal space operations and small number of protein-protein pair configurations according to the anisotropic patch model are required to calculate B2. With the extended FMMs, double-tree and single-tree algorithms, the boundary element formulations of interaction energies can be applied with low computational cost to the proteins. B2 Calculations of Bovine Pancreatic Trypsin Inhibitor are firstly performed to validate our model and the results of lysozyme protein under different salts, concentrations, pH and temperatures are correlated to the experimental B2. The reduced number of pair interaction energies between two proteins are interpolated to predict all pair interaction energies in the patch model as a precursor of the protein phase diagram calculation

Reconstructing primary production in a changing estuary: A mass balance modeling approach

Estuarine primary production (PP) is a critical rate process for understanding ecosystem function and response to environmental change. PP is fundamentally linked to estuarine eutrophication, and as such should respond to ongoing efforts to reduce nutrient inputs to estuaries globally. However, concurrent changes including warming, altered hydrology, reduced input of sediments, and emergence of harmful algal blooms (HABs) could interact with nutrient management to produce unexpected changes in PP. Despite its fundamental importance, estuarine PP is rarely measured. We reconstructed PP in the York River Estuary with a novel mass balance model based on dissolved inorganic nitrogen (DIN) for the period 1994–2018. Modeled PP compared well to previous estimates and demonstrated a long-term increase and down-estuary shift over the study period. This increase occurred despite reductions in discharge, flushing time, DIN loading, and DIN standing stock over the same period. Increased PP corresponded to increased water temperature, decreased turbidity and light attenuation, and increased photic depth and assimilation ratio, suggesting that phytoplankton in the York River Estuary have become more efficient at converting nutrients into biomass primarily due to a release from light limitation. The increase in PP also coincided with the increasing occurrence of late summer HABs in the lower York River Estuary, including the emergence of a second bloom-forming dinoflagellate in 2007. Results demonstrate how changes concurrent with nutrient management could alter expected system responses and illustrate the utility of the mass balance approach for estimating critical rate processes like PP in the absence of observations

Contrasting controls on seasonal and spatial distribution of marine cable bacteria (Candidatus Electrothrix) and Beggiatoaceae in seasonally hypoxic Chesapeake Bay

Marine cable bacteria (Candidatus Electrothrix) and large colorless sulfur-oxidizing bacteria (e.g., Beggiatoaceae) are widespread thiotrophs in coastal environments but may exert different influences on biogeochemical cycling. Yet, the factors governing their niche partitioning remain poorly understood. To map their distribution and evaluate their growth constraints in a natural setting, we examined surface sediments across seasons at two sites with contrasting levels of seasonal oxygen depletion in Chesapeake Bay using microscopy coupled with 16S rRNA gene amplicon sequencing and biogeochemical characterization. We found that cable bacteria, dominated by a single phylotype closely affiliated to Candidatus Electrothrix communis, flourished during winter and spring at a central channel site which experiences summer anoxia. Here, cable bacteria density was positively correlated with surface sediment chlorophyll, a proxy of phytodetritus sedimentation. Cable bacteria were also present with a lower areal density at an adjacent shoal site which supports bioturbating macrofauna. Beggiatoaceae were more abundant at this site, where their biomass was positively correlated with sediment respiration, but additionally potentially inhibited by sulfide accumulation which was evident during one summer. A springtime phytodetritus sedimentation event was associated with a proliferation of Beggiatoaceae and multiple Candidatus Electrothrix phylotypes, with cable bacteria reaching 1000 m length cm−2. These observations indicate the potential impact of a spring bloom in driving a hot moment of cryptic sulfur cycling. Our results suggest complex interactions between benthic thiotroph populations, with bioturbation and seasonal oscillations in bottom water dissolved oxygen, sediment sulfide, and organic matter influx as important drivers of their distribution

Calculations of the binding affinities of protein-protein complexes with the fast multipole method

In this paper, we used a coarse-grained model at the residue level to calculate the binding free energies of three protein-protein complexes. General formulations to calculate the electrostatic binding free energy and the van der Waals free energy are presented by solving linearized Poisson-Boltzmann equations using the boundary element method in combination with the fast multipole method. The residue level model with the fast multipole method allows us to efficiently investigate how the mutations on the active site of the protein-protein interface affect the changes in binding affinities of protein complexes. Good correlations between the calculated results and the experimental ones indicate that our model can capture the dominant contributions to the protein-protein interactions. At the same time, additional effects on protein binding due to atomic details are also discussed in the context of the limitations of such a coarse-grained model

Calculations of protein-protein interactions with the fast multipole method

I present a physical model to calculate protein-protein interactions. General formulations to calculate the electrostatic and the van der Waals free energies are brought by the boundary element method of solving linearized Poission-Boltzmann equation in an electrolyte solution, then further expanded to the application of the Fast Multipole Method(FMM). We built an efficient solver to investigate how the mutations on the active site of the protein-protein interface affect changes in binding affinities of protein complexes. Calculated results in addition to the structural analysis help us to understand the protein-protein interaction energy and provide a model to the important applications such as protein crystallization. The osmotic second virial coefficient B2 is directly related to the solubility of protein molecule in electrolyte solution and determined by molecular interactions involving both solvent and solute molecules. Calculations of interaction energies account for the electrostatic and the van der Waals interactions with the structural anisotropic properties of protein molecules. The orientation dependence of interaction energies between two proteins is determined by the crystal space operations and small number of protein-protein pair configurations according to the anisotropic patch model are required to calculate B2. With the extended FMMs, double-tree and single-tree algorithms, the boundary element formulations of interaction energies can be applied with low computational cost to the proteins. B2 Calculations of Bovine Pancreatic Trypsin Inhibitor are firstly performed to validate our model and the results of lysozyme protein under different salts, concentrations, pH and temperatures are correlated to the experimental B2. The reduced number of pair interaction energies between two proteins are interpolated to predict all pair interaction energies in the patch model as a precursor of the protein phase diagram calculation.</p

Calculations of the Second Virial Coefficients of Protein Solutions with an Extended Fast Multipole Method

The osmotic second virial coefficients B2 are directly related to the solubility of protein molecules in electrolyte solutions and can be useful to narrow down the search parameter space of protein crystallization conditions. Using a residue level model of protein-protein interaction in electrolyte solutions B2 of bovine pancreatic trypsin inhibitor and lysozyme in various solution conditions such as salt concentration, pH and temperature are calculated using an extended fast multipole method in combination with the boundary element formulation. Overall, the calculated B2 are well correlated with the experimental observations for various solution conditions. In combination with our previous work on the binding affinity calculations it is reasonable to expect that our residue level model can be used as a reliable model to describe protein-protein interaction in solutions.This article is from Physical Review E 83 (2011): 011915, doi:10.1103/PhysRevE.83.011915. Posted with permission.</p