Study: A mathematical model for the movement of nanoparticles and viruses in cells

The steady-state density distribution functions ns(x) at different I(x) and ν (numbers at the curves). Credit: Crystals (2022). DOI: 10.3390/cryst12081159
The steady-state density distribution functions ns(x) at different I(x) and ν (numbers at the curves). Credit: Crystals (2022). DOI: 10.3390/cryst12081159

Ural Federal University (UrFU) physicists and mathematicians have developed a complicated mathematical model that analyzes the dispersion of nanoparticles (particularly viruses) in live cells. The mathematical model aids in determining how nanoparticles cluster (merge into a single particle) inside cells, namely in cellular endosomes, which are important for protein and lipid sorting and transport. These calculations will be valuable in medicine because they reveal how viruses behave when they enter cells and attempt to multiply. The model also allows for the precise calculation of the amount of medicine required for therapy, ensuring that the treatment is as successful as feasible while causing as little adverse effects as possible. The model description and calculation results were published in the journal Crystals.

The processes in cells are exceedingly complicated, according to Dmitri Alexandrov, Head of the Laboratory of Multiscale Mathematical Modeling at UrFU, but in basic terms, viruses employ different types to replicate. Some of them directly carry genetic material to the cytoplasm. Others employ the endocytosis process, which involves releasing the viral DNA from endosomes. When viruses remain in the endosomes, the acidity rises and they die in the lysosomes. So, using our model, we were able to determine when and which viruses 'escape' from endosomes in order to live. Some influenza viruses, for example, are low pH-dependent viruses that fuse with the endosome membrane and release their DNA into the cytoplasm. Second, we discovered that viruses are more likely to survive in endosomes during clustering, which occurs when two particles mix and tend to create a single particle.

According to the researchers, the mathematical model will also be beneficial in tumor targeted therapy: many cancer treatments rely on when and how medication nanoparticles saturate cancer cells. And the model will aid in the calculation of this parameter. Furthermore, knowing viral activity in cells is critical for the creation of vaccinations and medications, as well as gene therapy, which addresses disorders that traditional medicine cannot treat. To treat the condition, for example, different adenovirus-based vectors and lipid particles are utilized as a platform for gene delivery. However, their inability to "slip out" of endosomes restricts their use as deliverers.

According to Eugenya Makoveeva, head of the Laboratory of Stochastic Transport of Nanoparticles in Living Systems (UrFU), nanoparticles smaller than 100 nanometers are becoming more significant instruments in modern medicine. Its uses span from nanodiagnostics to cancer radiation treatment. pH-sensitive nanoparticles that imitate viruses, for example, are employed for anticancer medication delivery. Drugs are carried from complete organs to individual cells in this manner.

Journal Information: Eugenya V. Makoveeva et al, Analysis of Smoluchowski's Coagulation Equation with Injection, Crystals (2022). DOI: 10.3390/cryst12081159v
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