1. Cell Division or Reproduction
Binary Fission Mitosis Meiosis
Cell Growth
Bacterial Cell Growth (Division) Cell Growth and Division
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2. Yeast Cell Growth Cell size regulation
Budding
Polarized growth of the budding yeast S. cerevisiae Yeast mutant lost
cell size control
Cell Cycle Mammalian Cell Growth Regulation
G0 phase is a period in the cell cycle
where cells exist in a quiescent state.
G1 phase is the first growth phase.
S phase, during which the DNA is
replicated, where S stands for the
synthesis of DNA.
G2 phase is the second growth phase,
also the preparation phase for the cell.
M phase or mitosis and cytokinesis,
the actual division of the cell into two
daughter cells
For mammalian cells, there are many factors impacting the protein complex (Raptor,
The cell cycle, or cell division cycle, is the cycle of events in a eukaryotic
mTOR and GßL) that orchestrates cell growth. The protein mTOR is a serine/threonine
cell from one cell division to the next. It consists of interface (I), mitosis (M),
kinase that regulates translation and cell division. Nutrient availability influences mTOR
and usually cell division.
so that when cells are not able to grow to normal size they will not undergo cell
division.
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3. Mycelial Growth Bacterial Growth Kinetics
log (cell number or density)
Time
Pellet Bacterial growth can be modeled with four different phases: lag phase (A),
Elongation and Branching exponential or log phase (B), stationary phase (C), and death phase (D).
Measuring bacterial growth Plate count
• Cell number
– Direct microbial count (Petroff-Housser slide or Serial dilution
hemocytometer)
– Plate count - colony forming unit (CFU), 24 hrs
– Slide culture – miniature culture dish, 3 hrs
– Coulter counter – cell number and size
– Nepholometery – light scattering by particle
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4. Coulter counter Measuring bacterial growth
• Cell mass
– Cell dry weight (105oC overnight), volume
– Turbidity (optical density)
– Indirect measurements of cell components
• Protein – biuret, Lowery
• DNA
• ATP (~ 1 mg ATP/g cell dry weight)
• NAD(P)H – culture florescence
• GFP (green fluorescent protein)
Optical density Measuring bacterial growth
• Indirect methods
– Nutrient uptake (carbon substrate, oxygen)
– Product formation (CO2)
– Heat evolution
– Broth viscosity
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5. Specific Growth Rate Specific growth rate
dN
= μN N = N0 eμ t dN
dt =μN ⇒ N = N 0e μ t
dt
dX
= μX X = X 0 eμ t
dt
X N = N 0 2t / t d td : doubling time or generation time
ln = μt
X0
ln 2 0.693
Specific growth rate: μ= =
td td
dX
μ= /X
dt
Cell Growth
• Stoichiometrically limiting compound
• Growth rate limiting compound
Stoichiometry of Cell Growth
Cell growth yield factor: Y x = ΔX
s ΔS
ΔS = (ΔS )a + (ΔS )eg + (ΔS )em
where: (∆S)a = ∆S for cell assimilation (growth)
(∆S)eg = ∆S for growth energy
(∆S)em = ∆S for growth maintenance
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6. Cell growth Aerobic growth
• without product formation
1 (ΔS )a (ΔS )eg (ΔS )em
= + + CH x O y + a ' O 2 + b' N l H m O n → c' CH α O β N δ + d ' H 2 O + e' CO 2
Yx (ΔX ) (ΔX ) (ΔX )
s
substrate N source cell
• where:
(∆S)a / (∆X) is constant
• Material balance on C, H, N, and O
• Respiratory Quotient (RO):
but (∆S)eg / (∆X) and (∆S)em / (∆X) varies depending on
Mole of CO2 formed / mole of O2 consumed
the environment, cell physiology, and growth phase
Can solve for a’, b’, c’, d’, and e’
Anaerobic Growth Product Formation
• With ATP generation • Growth associated
• Energy equation: ATP, NAD • Non-Growth associated
• Assume steady state on ATP and NAD • Secondary metabolites
• YATP = cell mass formed / mole ATP consumed Substrate + O2 + N − source → Cells + H 2O + CO2 + Product
– ~10.7 g cells / mol ATP for anaerobic growth
• YP/S = product formed / substrate consumed
– variable for aerobic bacteria
– Proportional to YX/S for growth associated
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7. Metabolic Heat Generation Theoretical Yields
• For aerobic fermentation with complete oxidation
• Y∆ = gram cell formed / kcal heat generated • Product Yield
YX – YP/S
YΔ = S
ΔH s − Y X ΔH c – Calculated from stoichiometry
S
– e.g. C6H12O6 2 C2H5OH + 2 CO2
ΔH S = (ΔH g ) + (ΔH c ⋅ Y X S ) + (ΔH p ⋅ YP S )
YP/S = 2 mol EtOH / mol glucose
where ∆HS = heat of substrate combustion (116 Kcal/O2 for carbohydrate) or 0.51 gram EtOH / gram glucose
∆HC = heat of cell combustion (104 Kcal per mole of O2 used)
∆Hg = heat generated
More reduced substrate greater heat removal demands
Theoretical Yields (Cont’d) Theoretical Yields (Cont’d)
• Cell Yield YX/S can be calculated based on • Constant ATP Yield
available electrons or constant yield of ATP – Many organisms derive ATP from catabolism
• Available electrons with the same efficiency
– 4 x (moles of O2 required to completely oxidize the – YATP = 10.5 g cells / mol of ATP produced
organic carbon to CO2 and H2O)
under anaerobic conditions
C6H12O6 + 6 O2 6 CO2 + 6 H2O
– Aerobic: 6 – 29 g cells / mole ATP
available electrons: 4 x 6 = 24
cell yield per available electron = 3.14 ± 0.11 g when
ammonia is used as the nitrogen source
YX/S = 24 x 3.14 = 75.36 g cell / mol glucose = 0.42 g
cell / g glucose
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