Modeling of a single nanoparticle interaction with the human blood plasma proteins

When nanoparticles are introduced into a physiological environment, proteins and lipids immediately cover their surface, forming a protein “corona”. It is well recognized that the corona structure influences the biological response of the body. Two deterministic models for corona formation of the human blood serum proteins around a single nanoparticle are presented and studied numerically in this paper. One of them is based on a coupled system of PDEs and involves diffusion of proteins toward the nanoparticle surface. The other one is described by ODEs and is a limit version of the first model as the protein diffusivity tends to infinity. The protein diffusivity influence on the temporal corona structure is studied in detail. Results are presented using figures and discussion.     

Modeling of toxin–antibody interaction and toxin transport toward the endoplasmic reticulum

A model for toxin–antibody interaction and toxin trafficking towards the endoplasmic-reticulum is presented. Antibody and toxin (ricin) initially are delivered outside the cell. The model involves: the pinocytotic (cellular drinking) and receptor-mediated toxin internalization modes from the extracellular into the intracellular domain, its exocytotic excretion from the cytosol back to the extracellular medium, the intact toxin retrograde transport to the endoplasmic reticulum, the anterograde toxin movement outward from the cell across the plasma membrane, the lysosomal toxin degradation, and the toxin clearance (removal from the system) flux. The model consists of a set of coupled PDEs. Using an averaging procedure, the model is reduced to a system of coupled ODEs. Both PDEs and ODEs systems are solved numerically. Numerical results are illustrated by figures and discussed.     

Nonlinear annihilation of excitations in photosynthetic systems.

The theory of the singlet-singlet annihilation in quasi-homogeneous photosynthetic antenna systems is developed further. In the new model, the following important contributions are taken into account: 1) the finite excitation pulse duration, 2) the occupation of higher excited states during the annihilation, 3) excitation correlation effects, and 4) the effect of local heating. The main emphasis is concentrated on the analysis of pump-probe kinetic measurements demonstrating the first two above possible contributions. The difference with the results obtained from low-intensity fluorescence kinetic measurements is highlighted. The experimental data with picosecond time resolution obtained for the photosynthetic bacterium Rhodospirillum rubrum at room temperature are discussed on the basis of this theory.     

Modeling neutralization of Shiga 2 toxin by A-and B-subunit-specific human monoclonal antibodies

A mathematical model for Shiga 2 toxin neutralization by A-and B-subunit-specific human monoclonal antibodies initially delivered in the extracellular domain is presented, taking into account toxin and antibodies interaction in the extracellular domain, diffusion of toxin, antibodies, and their reaction products toward the cell, the receptor-mediated toxin and complex composed of toxin and antibody to A-subunit internalization from the extracellular into the intracellular medium and excretion of this complex back to the extracellular environment via recycling endosomal carriers. The retrograde transport of the intact toxin to the endoplasmic reticulum and its anterograde movement back to the vicinity of the plasma membrane with its subsequent exocytotic removal to the extracellular space via the secretory vesicle pathway is also taken into account. The model is composed of a set of coupled PDEs. A mathematical model based on a system of ODEs for Shiga 2 toxin neutralization by antibodies in the absence of cell is also studied. Both PDE and ODE systems are solved numerically. Numerical results are illustrated by figures and discussed.