Presentation on theme: "Chapter 3 Objectives The fastest known doubling time for a bacterium and under what conditions this occurs The slowest estimated doubling time for a bacterium."— Presentation transcript:
1Chapter 3 ObjectivesThe fastest known doubling time for a bacterium and under what conditions this occursThe slowest estimated doubling time for a bacterium and under what conditions this occursCalculate a growth rate, u, from the slope of a growth curveCompare and contrast growth in pure culture with growth in the environmentThe growth curve and the parts of the curveA mathematical equation for each part of the curve as well as the Monod equationAt least two electron acceptors that can be used under anaerobic conditions in place of oxygenWhether aerobic or anaerobic metabolism yields more energy and whyThe mass balance equation for aerobic metabolism
2Lecture 3 – GrowthWhat are the differences between growth in a flask in pure culture and growth in the environment (e.g. soil, water, skin surfaces, leaf surfaces)?
4Lag phase Three causes for lag: physiological lag low initial numbers appropriate gene(s) absentgrowth approx. = (dX/dt = 0)
5Exponential phaseNutrients and conditions are not limitinggrowth = 2n or X = 2nX0Where X0 = initial number of cellsX = final number of cellsn = number of generations20212223242n20212223242n20212223242n20212223242n20212223242n20212223242n
6This is an increase is 5 orders of magnitude!! Example: An experiment was performed in a lab flask growing cells on 0.1% salicylate and starting with 2.2 x 104 cells. As the experiment below shows, at the end there were 3.8 x 109 cells.This is an increase is 5 orders of magnitude!!How many doublings or generations occurred?Cells grown on salicylate, 0.1%X = 2nX03.8 x 109 = 2n(2.2 x 104)1.73 x 105 = 2nlog(1.73 x 105) = nlog217.4 = n
7How does this compare to growth in the soil? Response of culturable microbial community to addition of a carbon source.SoilUnamendedCFU/g soil1% GlucoseLog IncreasePimaBrazitoClover SpringsMt. Lemmon5.6 x 1051.1 x 1061.4 x 1071.4 x 1064.6 x 1071.1 x 1081.9 x 1088.3 x 1071.92.01.11.7Only a 1 to 2 order of increase!!
8Now compare how environmental conditions can impact metabolism in soil Degradation of straw under different conditionsResidueHalf-lifeDaysuDays-1Relative rateWheat straw, laboratoryRye straw, NigeriaRye straw, EnglandWheat straw, Saskatoon917751600.0080.040.010.00310.50.1250.05Nigeria hot all year round with a rainy season and a dry seasonEngland is a warm summer and cold winter and plenty of rainfallSaskatoon cold winters and summers in the high 60s. Plenty of rainfall
9Calculating growth rate during exponential growth dX/dt = uXwhere u = specific growth rate (h-1)Calculating growth rate during exponential growthdX/dt = uX where u = specific growth rate (h-1)Rearrange: dX/X = udtIntegrate: lnX = ut + C, where C = lnX0lnX = ut + ln X0 or X = X0euty = mx + b (equation for a straight line)Note that u, the growth rate, is the slope of this straight line
10Calculating growth rate during exponential growth dX/dt = uX where u = specific growth rate (h-1)Rearrange: dX/X = udtIntegrate: lnX = ut + C, where C = lnX0lnX = ut + ln X0 or X = X0euty = mx + b (equation for a straight line)Note that u, the growth rate, is the slope of this straight line
11Find the slope of this growth curve lnX = ut + ln X0 or u = lnX – lnX0t – t0u = ln 5.5 x 108 – ln 1.7 x 105= 2 hr-1
12What is fastest known doubling time? Slowest? Now calculate the doubling timeIf you know the growth rate, u, you can calculate the doubling time for the culture.lnX = ut + ln X0For X to be doubled: X/X0 = 2or: 2 = eutFrom the previous problem, u = 2 hr-1,2 = e2(t)t = hr = minWhat is fastest known doubling time? Slowest?
13How can you change the growth rate??? When under ideal, nonlimiting conditions, the growth rate can only be changed by changing the temperature (growth increases with increasing temp.). Otherwise to change the growth rate, you must obtain a different microbe or use a different substrate.In the environment (non-ideal conditions), the growth rate can be changed by figuring out what the limiting condition in that environment is.Question: Is exponential growth a frequent occurrence in the environment?
15Stationary phase Death phase nutrients become limiting and/or toxic waste products accumulategrowth = death (dX/dt = 0)death > growth (dX/dt = -kdX)Death phase
16Monod EquationThe exponential growth equation describes only a part of the growth curve as shown in the graph below.The Monod equation describes the dependence of the growth rate on the substrate concentration:u = um SKs + S.u = specific growth rate (h-1)um = maximal growth rate (h-1)S = substrate concentration (mg L-1)Ks = half saturation constant (mg L-1)
17Combining the Monod equation and the exponential growth equation allows expression of an equation that describes the increase in cell mass through the lag, exponential, and stationary phases of growth:dX/dt = uXu = dX/Xdtu = um SKs + S.Monod equationExponential growth equationdX/dt = um S XKs + S.Does not describe death phase!
18Ks . There are two special cases for the Monod growth equation At high substrate concentration when S>>Ks, the Monod equationsimplifies to:dX/dt = umXgrowth will occur at the maximal growth rate.Ks2. At low substrate concentrationwhen S<< Ks, the Monod equationsimplifies to:dX/dt = um S XKs.growth will have a first order dependence on substrate concentration (growth rate is very sensitive to S).Which of the above two cases is the norm for environmental samples?
19Growth in terms of substrate loss In this case the growth equation must be expressed in terms of substrate concentration. The equations for cell increase and substrate loss can be related by the cell yield:dS/dt = -1/Y (dX/dt) where Y = cell yieldY = g cell mass producedg substrate consumedGlucose (C6H12O6) Pentachlorophenol (C6Cl5OH) Octadecane (C18H38)0.40.051.49
20Growth in terms of substrate loss dS/dt = -1/Y (dX/dt)dS/dt = -1/Y (dX/dt)Combine with: dX/dt = um S XKs + S.Combine with: dX/dt = um S XKs + S..dS/dt = - um (S X)Y (Ks + S)Which parts of this curve does the equation describe?
22Examples of when this knowledge is important?? Aerobic metabolismGeneral equation:(C6H12O6) + 6(O2) (CO2) + 6(H2O)Mass balance equation:a(C6H12O6) + b(NH3) + c(O2) d(C5H7 NO2) + e(CO2) + f(H2O)cell massThe mass balance equation illustrates that some of the carbon in the substrate is used to build new cell mass and some is oxidized completely to CO2 to provide energy for the cell.Using the mass balance equation and the cell yield, one can calculate the % of the substrate carbon that is used to build new cell mass and the % that is evolved as CO2Examples of when this knowledge is important??
23Anaerobic metabolismUnder anaerobic conditions, the substrate undergoes disproportionation, whereby some of the carbon is oxidized completely to CO2 and some is reduced to CH4 (because CO2) acts as a terminal electron acceptor.General equation:C6H12O6 + alternate TEA CO2 + CH4 + H2OSome Typical Terminal Electron Acceptors