Microbial Growth Kinetics http://users.rowan.edu/~jahan/sophclinic/.../8%20JC

%20MicrobialGrowth.ppt

http://www.montana.edu/wwwmb/coursehome/mb433/Lectures/Lecture3.ppt

AJE Lecture Note

Growth of Microbes •  Increase in

number of cells, not cell size

•  One cell becomes colony of millions of cells

Growth of Microbes •  Control of growth is important for

–  infection control – growth of industrial and biotech organisms – Biodegradation process

Factors Regulating Growth

•  Nutrients •  Environmental

conditions: temperature, pH, osmotic pressure

•  Generation time

Chemical Requirements •  #1 = water! •  Elements

– C (50% of cell’s dry weight) HONPS – Trace elements

•  Organic – Source of energy (glucose) – Vitamins (coenzymes) – Some amino acids, purines and

pyrimidines

Nutritional Categories

•  Carbon sources –  CO2 = autotroph –  organic = heterotroph

•  Energy sources –  sunlight = phototroph –  organic = chemotroph

Chemoautotrophs

Inorganic C Organic carbon

Electron donor Carbon source

Electron acceptor O2 aerobic respiration H2O NO3, Fe(III), Mn(IV), SO4, CO2 anaerobic respiration

NH4+, Fe(II), Mn(II), H2S

Carbon dioxide

N2O, Fe(II), Mn(II), H2S, CH4

Energy source (electron donor):inorganic carbon Carbon source: inorganic carbon

Chemoheterotrophs

Organic C Carbon dioxide

Electron donor Carbon source

Electron acceptor O2 aerobic respiration

H2O

NO3, Fe(III), Mn(IV), SO4, CO2 anaerobic respiration

Energy source (electron donor):organic carbon Carbon source: organic carbon

Photoautotrophs

Inorganic C (CO2) Organic carbon Carbon source, electron acceptor

H2O O2

Light (λ)

Carbon dioxide

Electron donor

Electron donor

Energy source Water

Energy source: light Electron donor: water Carbon source: inorganic carbon

Photoheterotrophs

Organic C CO2 Carbon source

Fe-S clusters in Photo System 1

Light (λ)

Organic C

Energy source

Terminal electron acceptor

Electron donor Water

Energy source: light Electron donor: water Carbon source: organic carbon

Environmental Factors Influencing Growth

•  Temperature •  O2 •  pH •  Osmotic Pressure •  Others: radiation, atmospheric pressure

Temperature Optima

•  Psychrophiles: cold-loving •  Mesophiles: moderate temperature-loving •  Thermophiles: heat-loving •  Each has a minimum, optimum, and

maximum growth temperature

Fig. 7.8

Temperature Optima

•  Optimum growth temperature is usually near the top of the growth range

•  Death above the maximum temp. comes from enzyme inactivation

•  Mesophiles most common group of organisms

•  40ºF (5°C) slows or stops growth of most microbes

Oxygen Requirements

•  Obligate aerobes – require O2

•  Facultative anaerobes – can use O2 but also grow without it

•  Obligate anaerobes – die in the presence of O2

pH •  Most bacteria grow between pH 6.5 and

7.5 •  Acid (below pH 4) good preservative for

pickles, sauerkraut, cheeses •  Acidophiles can live at low pH

Measuring Bacterial Growth

Bacterial Division

•  Bacteria divide by binary fission •  Alternative means

– Budding – Conidiospores (filamentous bacteria) – Fragmentation

Fig. 7.13

Generation Time

•  Time required for cell to divide/for population to double

•  Average for bacteria is 1-3 hours •  E. coli generation time = 20 min

– 20 generations (7 hours), 1 cell becomes 1 million cells!

Fig. 7.14a

Plotting growth on graphs

Standard Growth Curve

Phases of Growth

•  Lag phase – making new enzymes in response to new medium

•  Log phase – exponential growth – Desired for production of products – Most sensitive to drugs and radiation during

this period

Phases of Growth

•  Stationary phase – – nutrients becoming limiting or waste products

becoming toxic –  death rate = division rate

•  Death phase – death exceeds division

Measuring Growth

•  Direct methods – count individual cells •  Indirect Methods – measure effects of

bacterial growth

Fig. i7.6

Fig. 7.17

Turbidity

Metabolic Activity

Dry Weight

Energy Yield In a chemical reaction, only part of the energy is used to do work.

Energy available for work is called “free energy” or ΔG. The rest of the energy is lost to entrophy. ΔG = -RT log Keq where Keq = [C] [D] / [A] [B] from rxn:

A + B C + D

If logKeq is a negative value, this means the reaction can only proceed if energy is added (endothermic rxn).

When logKeq is a negative value, ΔG is positive. If logKeq is a positive value, this means the reaction is favored and, in fact, gives off energy (exothermic rxn).

When logKeq is a positive value, ΔG is negative.

Energy yield from electron acceptor

•  6O2 6H2O aerobic respiration -686 •  24 NO3 12N2 anaerobic respiration -36

•  SO4 H2S anaerobic respiration -40 •  CO2 CH2O photosynthesis +115

ΔG (kcal/mol)Terminal electron acceptor

e-

Reduction Potential vo

lts

+0.85

+0.75

0.00

-0.22 -0.47 CH2O/CO2

SO4/H2S

NO3/ N2

O2/H2O

1.28 1.22

0.25

Energy yield relationship between electron acceptor and electron donor Electron Reduction Electron Reduction Difference Acceptor Potential (V) Donor Potential (V) (V) O2 H2O +0.81 CH2O CO2 -0.47 -1.28 NO3 N2 +0.75 -1.22 SO4 H2S -0.22 -0.25

The sign and magnitude of the difference represents how much free energy is available to the cell.

Growth Kinetics

Pertumbuhan Bakteri

lag log stasioner Endogenous

Concentration

Waktu

bakteri

Makanan/substrat

Pertumbuhan bakteri

•  Pers matematis pertumbuhan bakteri : Persamaan Monod (1920)

µ = µmaksS/(Ks + S) dimana:

µ = laju pertumbuhan spesifik, 1/waktu S = konsentrasi substrat, mg/L Ks = half saturation konstant

Pertumbuhan Bakteri

µmaks

µmaks/2

S, mg/L Ks

Pertumbuhan Bakteri

•  Rumus umum (heterotroph bacteria): –  µmaks <, Ks > : less biodegradable –  µmaks >, Ks < : biodegradable –  Contoh:

•  Glukosa: µmaks = 0,37 – 0,77 dan Ks = 11 – 108 mg/L •  Skim milk: µmaks = 0,10 – 0,12 dan Ks = 100 – 110 mg/L

•  Autotroph bacteria dalam nitrifikasi: –  µmaks << : lambat –  Ks <<: independent

•  Penentuan laju pertumbuhan dilakukan pada fase log: dX/dt = kX, Xt = X0ekt sehingga k = ln Xt – ln X0/(t – t0) Dimana:

X = biomassa t = waktu k = laju pertumbuhan

Persamaan Monod

•  Mencari harga k: y = a + bx, dimana:

y = ln (A600) x = waktu a = intial ln (A600) pd t = 0 b = gradien, k

•  Mencari harga Ks dan µmaks: persamaan Monod diubah menjadi

persamaan double reciprocal: 1/µ = (Ks/µmaks) (1/S) + 1/µmaks, sehingga:

–  Pada saat 1/S = 0, maka 1/µ = 1/µmaks

–  Pada saat 1/µ = 0, maka (Ks/ µmaksS) = - 1/µ -1/S = 1/Ks

Persamaan Monod 1/µ

1/S

1/µmaks

1/Ks

Persamaan Monod

•  Jumlah biomass dalam reaktor menerus: dX/dt = kX – kdX, kd = koefisien decay dX/dt = ((µmaksSX)/(Ks + S)) – kdX

•  Makanan: Food consumption ≅ biomass production dX/dt = rx = - y dS/dt, dimana y = decimal fraction yg menunjukkan perbandingan berat

biomass per kg substrate: - Aerobik: 0,4 – 0,8 - Anerobik: 0,08 – 0,2 dS/dt = -rx/y = (µmaksSX)/y(Ks + S)

Cell Yield (Y)

•  Not all of the carbon added as the carbon source is converted to cell biomass

•  A fraction is respired as CO2 during the transformation of the carbon to energy (ATP)

•  Cell yield coefficient is defined as the amount of biomass produced per unit substrate consumed

Cell Yield

Carbon source Yield coefficient

glucose 0.4

Pentachlorophenol (PCP) 0.05

octadecane 1.49

Activated Sludge

•  Kondisi steady-state, neraca massa: –  Biomassa: biomass in + biomass growth = biomass out –  Food: food in – food consumed = food out

•  Biomassa: Q0X0 + (((µmaksSX)/(Ks + S)) – kdX) V = (Q0 – Qw)Xe + QwXu

•  Food: Q0S0 – ((µmaksSX)/y(Ks + S))V = (Q0 – Qw)S + QwS

Reaktor Secondary Clarifier

Effluent Q0, S0, X0

V, S, X Q0 + Qr X, S

Qu, Xu Qr, Xu

Qw, Xu Sludge treatment

Q0 – Qw, Xe, S

Activated Sludge

•  X0 dan Xe sgt kecil dibandingkan di reaktor, X0 dan Xe ≅ 0, sehingga persamaan neraca massa biomass menjadi:

V (((µmaksSX)/(Ks + S)) – kdX) = QwXu (µmaksS)/(Ks + S) = ((QwXu)/VX) + kd

•  Penyederhanaan neraca massa food: (µmaksS)/(Ks + S) = ((Q0/V)(y/X)(S0 – S)) – kd note: V/Q0 = hydraulic retention time = θ (VX)/(QwXu) = θc = sludge age (umur lumpur)

•  Susbtitusi persamaan neraca massa biomass dan food: 1/θc = (y(S0-S)/θX) – kd X = (θcy(S0-S))/(θ (1+kdθc)) θ < X besar: tdk mungkin, sehingga apabila θ terlalu singkat: wash out dan tdk ada pertumbuhan (X turun) So mendekati S: tdk ada pengolahan

Ensimologi - 1

•  Ensimologi: ilmu yang mempelajari karakteristik dan perilaku ensim •  Ensim: katalis organik (biokatalis) yang dibentuk dari protein dan

dihasilkan oleh sel makhluk hidup yang sensitif terhadap perubahan temperatur

•  Keberadaannya: –  Extra selular: bekerja diluar sel dengan tujuan untuk mereduksi senyawa2

kompleks sehingga mudah di dialisis oleh dinding sel –  Intra selular: untuk melangsungkan reaksi biokimia di dalam sel

•  Berdasarkan cara diproduksinya: –  Konstitutif: diproduksi secara kontinu –  Indusif: diproduksi karena respon thd stimulus yang diaplikasikan dari

luar •  Nomenclature: diakhiri dengan “ase”, contoh dehalogenase atau

sucrase yang merubah sucrosa menjadi glukosa dan fructosa

Ensimologi - 2

•  Aktivitas ensim tgt dari: –  Kofaktor: struktur tambahan yang diperlukan oleh ensim

•  Logam •  Molekul organik

–  Temperatur: terlalu rendah inactive, terlalu tinggi denaturasi –  pH –  Mikro + makro nutrien –  Inhibitor dan inducer

•  Bidang TL: –  Immobilisasi ensim –  Reaksi akan jauh lebih cepat –  Target: mineralisasi bukan biotransformasi

Ensimologi - 3

•  Kinetika ensim: Persamaan Michaelis-Menten Vx = Vmax Sx/(Sx + Km) Vmax = maksismum specific activity Km = Michaelis-Menten konstan Sx = Substrat

•  Enzim Specificity: kemampuan ensim untuk mendegradasi senyawa yang serupa dengan substrat utamanya

•  Enzim purifikasi: Proses pemurnian ensim dalam kaitannya dengan karakterisasi ensim

Understanding Km •  Km is a constant •  Km is a constant derived from rate constants •  Km is, under true Michaelis-Menten conditions,

an estimate of the dissociation constant of E from S

•  Small Km means tight binding; high Km means weak binding

Enzyme Substrate Km (mM) Glutamate dehydrogenase NH4

+ 57 Glutamate 0.12

Carbonic anhydrase CO2 12

Understanding Vmax

The theoretical maximal velocity •  Vmax is a constant •  Vmax is the theoretical maximal rate of the

reaction - but it is NEVER achieved in reality •  To reach Vmax would require that ALL enzyme

molecules are tightly bound with substrate •  Vmax is asymptotically approached as

substrate is increased

Double-Reciprocal or Lineweaver-Burk Plot

1 KM 1 ______ = _______ + ______

Vo Vmax[S] Vmax

From Lehninger Principles of Biochemistry

Use linear plot and intercepts to determine Km and Vmax

Enzyme Inhibitors

Reversible versus Irreversible •  Reversible inhibitors interact with an

enzyme via noncovalent associations •  Irreversible inhibitors interact with an

enzyme via covalent associations

Classes of Inhibition Two real, one hypothetical

•  Competitive inhibition - inhibitor (I) binds only to E, not to ES

•  Uncompetitive inhibition - inhibitor (I) binds only to ES, not to E. This is a hypothetical case that has never been documented for a real enzyme, but which makes a useful contrast to competitive inhibition

•  Noncompetitive (mixed) inhibition - inhibitor (I) binds to E and to ES

Inhibitor (I) binds only to E, not to ES

Inhibitor (I) binds only to ES, not to E.

This is a hypothetical case that has never been documented for a real enzyme, but which makes a useful contrast to competitive inhibition

Inhibitor (I) binds to E and to ES.Enzyme Inhibition

From Lehninger Principles of Biochemistry

Competitive Uncompetitive Noncompetitive Inhibition Inhibition (Mixed) Inhibition

Kmchanges while Vmax does not

Km and Vmax both change

Km and Vmax both change

From Lehninger Principles of Biochemistry