As we do our best to map out natural phenomena, math gives us the precision we need to explore and understand them. It’s like a compass and a map.

 

Whether we’re calculating the orbits of planets, deciphering the code of DNA, or predicting the next big technological breakthrough, math is at the core of it.

 

Genetics and cosmology: How math unveils hidden truths

Gregor Mendel’s work with pea plants is a perfect example. By crossbreeding plants, he observed traits like flower color and seed shape, recording their occurrence in ratios. His mathematical analysis revealed predictable 3:1 ratios in dominant and recessive traits, uncovering the fundamental laws of inheritance. Without math, these genetic principles would have remained hidden.

 

Einstein’s theory of relativity mathematically predicted regions where gravity is so intense that nothing, not even light, could escape. These predictions came long before astronomical observations confirmed the presence of black holes, validating the mathematical forecasts.

 

The crucial role of mathematics in virology and molecular biology

In the lab, mathematics plays a crucial role. From calculating molarity (concentration of a solution) to determining an EC50 (the concentration of a drug that gives half-maximal response) using a four-parameter regression method (a statistical technique to fit a curve), math helps us perform experiments and translate their outcomes into something understandable, communicable, and comparable.

 

While it may not be practical to remember the rationale behind every formula at the moment of use, revisiting (or discovering!) the origins of these formulas can provide a deeper understanding of our processes and data.

 

Exploring virology through numbers: A new blog series

Why do we multiply by 0.7 when converting TCID50/ml (tissue culture infectious dose, the amount of virus required to kill 50% of cells in culture) to PFU/ml (plaque-forming units, a measure of viable virus particles)? Why do we typically stop PCR (polymerase chain reaction) at around 40 cycles? What is the best way to compare EC50 values (drug potency)? What is a Z’ score (a statistical measure of assay quality) really telling us?

 

In this new blog series, we will explore the mathematics of virology, sharing our insights gained at the bench.

 

Counting infectious virus

We start this series with the first fundamental operation in virology: determining the number of infectious particles in a virus stock or experimental sample. The two main techniques to quantify infectious virus are the plaque assay and the TCID50 assay.

 

Calculations for the plaque assay

The plaque assay is the most direct way to count infectious virus: this is because, as a first and sensible approximation, each plaque is the product of one single infectious unit.

In a plaque assay, a series of virus dilutions is prepared, most typically 10-fold dilutions. These dilutions are then used to inoculate cell monolayers, which are then overlayed with a solid (e.g., agarose) or semisolid (e.g., carboxymethyl cellulose) overlay to prevent the cell-free spread of the newly released virus (limiting the infection to cell-to-cell spread). This is what gives shape to plaques (or foci, if the infection is visualised by immunostaining).