TABLE 1.

Predicted number of input phage sufficient for infection of 99.99% of cells according to cell density^a

C	M13		P1
	Theoretical MOIinput for MOIactual of 10	Theoretical Po needed for MOIactual of 10	Theoretical MOIinput for MOIactual of 10	Theoretical Po needed for MOIactual of 10
1010	10.0	100,000,000,000	10.0	100,000,000,000
109	10.0	10,001,234,250	10.0	10,000,000,000
108	16.9	1,685,117,750	10.0	1,001,008,802
107	116.2	1,161,861,009	20.1	200,632,421
106	1,116.1	1,116,118,611	150.1	149,985,032
105	11,116.1	1,111,611,186	1,454.3	145,428,111
104	111,116.1	1,111,161,112	14,497.8	144,977,542
103	1,111,116.1	1,111,116,111	144,932.5	144,932,536
102	11,111,116.1	1,111,111,611	1,449,280.4	144,928,036
10	111,111,116.1	1,111,111,161	14,492,758.6	144,927,586
1	1,111,111,116.1	1,111,111,116	144,927,541.2	144,927,541
Limiting value		1,111,111,111		144,927,536

^aThe theoretical MOI_input needed to realize an MOI_actual of 10 for phages M13 and P1 was calculated for cell densities of 1 to 10¹⁰ cells per cm³ and an adsorption time of 30 min by using equation 2. The theoretical minimum number of phage necessary to attain an MOI_actual of 10 in 30 min at each cell density in a volume of 1 cm³ was calculated by using equation 4 for P_min. Notice that the theoretical minimums slowly approach but never reach the limiting value, or lower bound, of P_min (from equation 5). In addition, note that P_min changes very little for any cell concentration at or below 10⁶/cm³ for M13 or 10⁵/cm³ for P1.