# Binary fission

Prokaryotes use binary fission. Two cells arise from one. Cells elongate to twice their original length, and the cytoplasmic membrane forms a septum which separates the cells. A generation is when1cells divides to form two. Polymerizations reactions are macromolecules from monomers (most common reaction). Fts proteins are essential for growth, prokaryotic, interact to form division apparatus called divisome. FtsI is bound to penicillin and the divisome orchestrates synthesis of new cytoplasmic membrane. Actin is a eukaryotic protein.

Peptidoglycan is synthesized before cell division. Transpeptidation is the formation of peptide crosslinks. Peptidoglycan is right outside the cytoplasmic membrane. It is inhibited by penicllin. Generationt time is the doubling time. Population doubles in 2 hours. t=2, n=1. g=t/n. N=N_{0}2^{n} where N is final cell #, N_{0} initial cell #, n is number of generations, g is t/n where t is duration. Lag phase, exponential phase, stationary phase and death phase. Batch culture versus chemostat.

If it takes 30 minutes for *E. coli* to replicate it's genome, then why does it only take 20 minutes to reproduce? It is because the daughter cells already have some of their genome replicated. Therefore, each generation has already begun replication before it is generated.

## Population dynamics

In binary fission, a parent cell divides to form two daughter cells. Thus, bacterial population increase exponentially. Note the table below, demonstrating how quickly a population of bacteria can explode from just a single cell. The generation (first, second, third, etc) is denoted *n* and the number of cells at a given time is *N* (or *N _{0}* at time zero).

Generation (n) | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | n |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Formula | 2^{0} | 2^{1} | 2^{2} | 2^{3} | 2^{4} | 2^{5} | 2^{6} | 2^{7} | 2^{8} | 2^{9} | 2^{10} | 2^{11} | 2^{n-1} |

# of Cells (N) | 1 | 2 | 4 | 8 | 16 | 32 | 64 | 128 | 256 | 512 | 1024 | 2048 | N |

The table below describes important formulas regarding population dynamics. They are valid for any value of *x*, as long as it is kept constant throughout the problem. Also, *t* is elapsed time and *t _{d}* is the time require for one complete cell division (for a cell to double).

###### Important formulas

- N = N
_{0}2^{n} - log
_{x}N = log_{x}N_{0}+ n (log_{x}2) - log
_{x}(N / N_{0}) = n (log_{x}2) - n = [ log
_{x}(N/N_{0}) ] / [ log_{x}2 ] - N = N
_{0}antilog_{10}(.301n) - n = t / t
_{d}