Cell biology formulas

Cell structure, cell cycle, protein trafficking and cell death. 5 formulas for GATE BT Genetics, Cell and Molecular Biology, each with when to use it. Each is explained in the topic notes.

All 5 Cell biology formulas

EXPONENTIAL GROWTH OF A CELL POPULATION

N = N_{0} \cdot 2^{t / t_{d}}

Here $N_{0}$ is the initial cell count, $N$ the count after time $t$ , and $t_{d}$ the doubling time. It holds only while every cell is cycling with the same doubling time, with no cell death and outside any lag or stationary phase.

NUMBER OF GENERATIONS (DOUBLINGS) IN TIME T

n = \frac{t}{t _{d}} = \frac{lo g _{10} N - lo g _{10} N _{0}}{lo g _{10} 2} \approx 3.32 (lo g_{10} N - lo g_{10} N_{0})

This follows directly from the exponential-growth formula under the same conditions.

SPECIFIC GROWTH RATE

μ = \frac{ln 2}{t _{d}}, N = N_{0} e^{μ t}

This is the same exponential law written with base $e$ . $μ$ has units of reciprocal time.

PHASE DURATION FROM THE FRACTION OF CELLS IN THAT PHASE (E.G., MITOTIC INDEX)

t_{phase} \approx \frac{n _{phase}}{n _{total}} \times T

$T$ is the total cell-cycle time and $n_{phase} / n_{total}$ is the fraction of cells observed in the phase; for M phase this fraction is the mitotic index. This is an approximation for an asynchronous culture that treats cells as evenly spread across cycle ages. In an exponentially growing culture young cells slightly outnumber old ones, so the estimate is not exact.

INDEPENDENT ASSORTMENT

number of possible chromosome combinations = 2^{n}

Here $n$ is the haploid chromosome number. The count ignores crossing over, which adds further variation. For humans ( $n = 23$ ), $2^{23} = 8, 388, 608$ .

Where this was asked: 2019 (2), 2020 (4), 2022 (2), 2023 (1), 2024 (3), 2025 (1), 2026 (2). See the 15 previous-year questions on Cell biology. This shows what was asked, not what will be asked.

KEEP GOING

Cell biology: the notes and 15 solved previous-year questions