Table 4. Open in new tab Population...

Parameter	Symbol	Unit	Estimate (SE)
Growth parameters
log₁₀ initial inoculum	log_cfu0	log₁₀ cfu/mL	7.14 (0.3%)
mean generation time	k₁₂⁻¹	min	42.6 (0.6%)
replication rate constant	k₂₁	h⁻¹	50 (fixed)
log₁₀ (maximum population size)	log_cfumax	log₁₀ cfu/mL
for untreated control arms			10.2 (1.2%)
for piperacillin-treated arms			9.48 (0.8%)
Log₁₀ (mutant frequencies)
for intermediate population	logMF_I	—	−3.53 (0.9%)
for resistant population	logMF_R	—	−6.33 (0.7%)
Inhibition of growth rate by piperacillin
maximum inhibition
for susceptible population	Imax_k12,S	—	0.760 (2.9%)
for intermediate population	Imax_k12,I		0.970 (2.8%)
for resistant population	Imax_k12,R	—	0.285 (28.4%)
concentration causing 50% of maximum inhibition
for susceptible population	IC50_k12,S	mg/L	0.877 (20.9%)
for intermediate population	IC50_k12,I	mg/L	5.96 (5.6%)
for resistant population	IC50_k12,R	mg/L	23.7 (2.2%)
Hill coefficient	hill_k12	—	4.67 (10.9%)
Inhibition of probability of successful replication by piperacillin
maximum inhibition	Imax_Rep	—	1.0 (fixed)^a
concentration causing 50% of maximum inhibition
for susceptible population	IC50_Rep,S	mg/L	0.831 (21.9%)
for intermediate and resistant population	IC50_Rep,IR	mg/L	45.8 (0.5%)
Hill coefficient	hill_Rep	—	2.43 (3%)
Standard deviation of additive residual error on log₁₀ scale	SD_cfu	log₁₀ cfu/mL	0.259

Parameter

Symbol

Unit

Estimate (SE)

Growth parameters

log₁₀ initial inoculum

log_cfu0

log₁₀ cfu/mL

7.14 (0.3%)

mean generation time

k₁₂⁻¹

min

42.6 (0.6%)

replication rate constant

k₂₁

h⁻¹

50 (fixed)

log₁₀ (maximum population size)

log_cfumax

log₁₀ cfu/mL

for untreated control arms

10.2 (1.2%)

for piperacillin-treated arms

9.48 (0.8%)

Log₁₀ (mutant frequencies)

for intermediate population

logMF_I

—

−3.53 (0.9%)

for resistant population

logMF_R

—

−6.33 (0.7%)

Inhibition of growth rate by piperacillin

maximum inhibition

for susceptible population

Imax_k12,S

—

0.760 (2.9%)

for intermediate population

Imax_k12,I

0.970 (2.8%)

for resistant population

Imax_k12,R

—

0.285 (28.4%)

concentration causing 50% of maximum inhibition

for susceptible population

IC50_k12,S

mg/L

0.877 (20.9%)

for intermediate population

IC50_k12,I

mg/L

5.96 (5.6%)

for resistant population

IC50_k12,R

mg/L

23.7 (2.2%)

Hill coefficient

hill_k12

—

4.67 (10.9%)

Inhibition of probability of successful replication by piperacillin

maximum inhibition

Imax_Rep

—

1.0 (fixed)^a

concentration causing 50% of maximum inhibition

for susceptible population

IC50_Rep,S

mg/L

0.831 (21.9%)

for intermediate and resistant population

IC50_Rep,IR

mg/L

45.8 (0.5%)

Hill coefficient

hill_Rep

—

2.43 (3%)

Standard deviation of additive residual error on log₁₀ scale

SD_cfu

log₁₀ cfu/mL

0.259

Parameter	Symbol	Unit	Estimate (SE)
Growth parameters
log₁₀ initial inoculum	log_cfu0	log₁₀ cfu/mL	7.14 (0.3%)
mean generation time	k₁₂⁻¹	min	42.6 (0.6%)
replication rate constant	k₂₁	h⁻¹	50 (fixed)
log₁₀ (maximum population size)	log_cfumax	log₁₀ cfu/mL
for untreated control arms			10.2 (1.2%)
for piperacillin-treated arms			9.48 (0.8%)
Log₁₀ (mutant frequencies)
for intermediate population	logMF_I	—	−3.53 (0.9%)
for resistant population	logMF_R	—	−6.33 (0.7%)
Inhibition of growth rate by piperacillin
maximum inhibition
for susceptible population	Imax_k12,S	—	0.760 (2.9%)
for intermediate population	Imax_k12,I		0.970 (2.8%)
for resistant population	Imax_k12,R	—	0.285 (28.4%)
concentration causing 50% of maximum inhibition
for susceptible population	IC50_k12,S	mg/L	0.877 (20.9%)
for intermediate population	IC50_k12,I	mg/L	5.96 (5.6%)
for resistant population	IC50_k12,R	mg/L	23.7 (2.2%)
Hill coefficient	hill_k12	—	4.67 (10.9%)
Inhibition of probability of successful replication by piperacillin
maximum inhibition	Imax_Rep	—	1.0 (fixed)^a
concentration causing 50% of maximum inhibition
for susceptible population	IC50_Rep,S	mg/L	0.831 (21.9%)
for intermediate and resistant population	IC50_Rep,IR	mg/L	45.8 (0.5%)
Hill coefficient	hill_Rep	—	2.43 (3%)
Standard deviation of additive residual error on log₁₀ scale	SD_cfu	log₁₀ cfu/mL	0.259

Table 4.

Open in new tab

Population parameter estimates for piperacillin against P. aeruginosa 1280

Parameter	Symbol	Unit	Estimate (SE)
Growth parameters
log₁₀ initial inoculum	log_cfu0	log₁₀ cfu/mL	7.14 (0.3%)
mean generation time	k₁₂⁻¹	min	42.6 (0.6%)
replication rate constant	k₂₁	h⁻¹	50 (fixed)
log₁₀ (maximum population size)	log_cfumax	log₁₀ cfu/mL
for untreated control arms			10.2 (1.2%)
for piperacillin-treated arms			9.48 (0.8%)
Log₁₀ (mutant frequencies)
for intermediate population	logMF_I	—	−3.53 (0.9%)
for resistant population	logMF_R	—	−6.33 (0.7%)
Inhibition of growth rate by piperacillin
maximum inhibition
for susceptible population	Imax_k12,S	—	0.760 (2.9%)
for intermediate population	Imax_k12,I		0.970 (2.8%)
for resistant population	Imax_k12,R	—	0.285 (28.4%)
concentration causing 50% of maximum inhibition
for susceptible population	IC50_k12,S	mg/L	0.877 (20.9%)
for intermediate population	IC50_k12,I	mg/L	5.96 (5.6%)
for resistant population	IC50_k12,R	mg/L	23.7 (2.2%)
Hill coefficient	hill_k12	—	4.67 (10.9%)
Inhibition of probability of successful replication by piperacillin
maximum inhibition	Imax_Rep	—	1.0 (fixed)^a
concentration causing 50% of maximum inhibition
for susceptible population	IC50_Rep,S	mg/L	0.831 (21.9%)
for intermediate and resistant population	IC50_Rep,IR	mg/L	45.8 (0.5%)
Hill coefficient	hill_Rep	—	2.43 (3%)
Standard deviation of additive residual error on log₁₀ scale	SD_cfu	log₁₀ cfu/mL	0.259

Parameter	Symbol	Unit	Estimate (SE)
Growth parameters
log₁₀ initial inoculum	log_cfu0	log₁₀ cfu/mL	7.14 (0.3%)
mean generation time	k₁₂⁻¹	min	42.6 (0.6%)
replication rate constant	k₂₁	h⁻¹	50 (fixed)
log₁₀ (maximum population size)	log_cfumax	log₁₀ cfu/mL
for untreated control arms			10.2 (1.2%)
for piperacillin-treated arms			9.48 (0.8%)
Log₁₀ (mutant frequencies)
for intermediate population	logMF_I	—	−3.53 (0.9%)
for resistant population	logMF_R	—	−6.33 (0.7%)
Inhibition of growth rate by piperacillin
maximum inhibition
for susceptible population	Imax_k12,S	—	0.760 (2.9%)
for intermediate population	Imax_k12,I		0.970 (2.8%)
for resistant population	Imax_k12,R	—	0.285 (28.4%)
concentration causing 50% of maximum inhibition
for susceptible population	IC50_k12,S	mg/L	0.877 (20.9%)
for intermediate population	IC50_k12,I	mg/L	5.96 (5.6%)
for resistant population	IC50_k12,R	mg/L	23.7 (2.2%)
Hill coefficient	hill_k12	—	4.67 (10.9%)
Inhibition of probability of successful replication by piperacillin
maximum inhibition	Imax_Rep	—	1.0 (fixed)^a
concentration causing 50% of maximum inhibition
for susceptible population	IC50_Rep,S	mg/L	0.831 (21.9%)
for intermediate and resistant population	IC50_Rep,IR	mg/L	45.8 (0.5%)
Hill coefficient	hill_Rep	—	2.43 (3%)
Standard deviation of additive residual error on log₁₀ scale	SD_cfu	log₁₀ cfu/mL	0.259

^aImax_Rep was estimated at 0.994 and therefore eventually was fixed to 1.0.

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