2. Growth: linear 2
N = No10kt

3. N=No10kt N/No = 10kt log(N/No) = kt
Growth: semilog 3
A semi-log plot N
logN 8 7 6 5 4 3 2 1
log(N/No) = kt
N=No10kt N/No = 10kt log(N/No) = kt
Note: just used k here not k’, k defined in context in general

4. Growth phases 4
Real life
(linear on a semi-log plot)

5. Use calculus if you know it, it’s more natural: dN/dt = kN 5
Use calculus if you know it, it’s more natural:
dN/dt = kN
Separating variables: dN/N = kdt
Integrating between time zero when N = No and time t, when N = N,
dN/N = kdt, we get:
lnN - ln No = kt - 0, or ln(N/No) = kt, or N = Noekt,
which is exactly what we derived above.
But is this k the same k as before?
We can now calculate this constant k by considering the case of the time interval over which No has exactly doubled; in that case:
N/No = 2 and t = tD, so: N = Noekt  2 = ektD
To solve for k, take the natural logarithm of both sides: ln2=ktD, or k=ln2/tD,
so the constant comes out exactly as before as well. See exponential growth handout

6. Our first “functional group”:6
E. coli molecule #1
water
H2O
HOH
Our first “functional group”:
hydroxyl, -OH O H
105o
Covalent bond
(strength = ~100
kcal/mole)

7. δ+ = partial charge, not quantified Not “ + ” , a full unit charge,
Waterdeltas 7
δ+ = partial charge, not quantified
Not “ + ” , a full unit charge,
as in the formation of ions by NaCl in solution:
NaCl  Na+ + Cl-
Water is a POLAR molecule (partial charge separation)
Negative pole
Positive pole

8. waterHbonds 8

9. (strength = ~ 3 kcal/mole)
waterHbonds 9
Hydrogen bond
“H-bond”
(strength = ~ 3 kcal/mole)

10. 10
Ethanol and Water
hydroxyl group again 3 2 3 2

11. O is more electronegative than C
amide3 11
R= any group of atoms
O is more electronegative than C
R-CONH2 is an “amide”, CONH2 is an amide group
(another functional group - the whole –CONH2 together)

12. Hydrogen bonds between 2 organic molecules12
ethanol, an alcohol
an amide
Hydrogen bonds between 2 organic molecules
Water often out-competes this interaction (but not always)

13. The chemical structures of the functional groups used in this 13
The chemical structures of the functional groups used in this
course must be memorized.
See the Functional Groups handout.
This is one of very few memorizations required. O ||
-C -- OH
“carboxyl” Me
You

14. Water is a POLAR molecule, a dipole
Waterdeltas
Water is a POLAR molecule, a dipole
Negative
pole
Positive
pole

15. waterHbonds
Hydrogen bond

16. Ethanol and Water 16 3 2 3 2

17. (the rest of the molecule)
amide3
R= any group of atoms
(the rest of the molecule)
Note: carbon atoms always make 4 bonds
R-CONH2 is an “amide”, CONH2 is an amide group
(another functional group)
Note: Don’t break down the amide into a C=O and an –NH2; the whole thing is one functional group, the amide. It is highly polar but with no full charges

18. They face formidable competition from water
Hydrogen bonds between 2 organic molecules
ethanol, an alcohol
an amide
They face formidable competition from water

19. X Not all molecules are polar; e.g. octane, a non-polar, or apolar
CH3-CH2-CH2-CH2-CH2-CH2-CH2-CH3
H H H H H H H H
| | | | | | | |
H-C-C-C-C-C-C-C-C-H Note the absence of δ’s X

20. Chemical Bonds
Bond:
Energy needed to break:
Comments:
Strength class-ification:
Covalent
~100
kcal/mole
Electrons
shared
strong

21. 1 calorie = amount of energy needed to raise the temperature of 1 gram of water (1 cc or ml. of water) one degree C
1 Calorie = dietary calorie = 1000 calories
1 kilocalorie (kcal) = 1000 calories

22. Energy needed to break:
Chemical Bonds
Bond:
Energy needed to break:
Comments:
Strength class-ification:
Covalent
~100
kcal/mole
Electrons
shared
strong
Hydrogen ~3
Water-water;
Organic-water;
Organic-organic (having polar functional groups)
weak

23. Ionic bonds Full loss or capture of an electron Full charge separation
Full positive charge, or full negative charge (= charge of one electron)
E.g. NaCl = Na+:::Cl Strong bond between the ions in a crystal (e.g., rock salt)
But: weak in aqueous solution
So the ionic bond of NaCl becomes weak in water
Is the bond between an Na+ ion and water ionic or an H-bond? Some characteristics of each:
a “polar interaction” or an “ion-dipole interaction”

24. Organic IONS = acids and bases
ACIDS= carboxylic acids
Lose a proton
O O || ||
R-C-OH  R-C-O H+
(net charge ≈ -1 at pH 7)
Example: acetic acid:
CH3-COOH
BASES = amines
Gain a proton
R-NH2 + H R-NH3+
(net charge ≈ +1 at pH 7)
Example: ethyl amine: CH3-CH2-NH2
Carboxyl group = -COOH
Amine group = -NH2
Where does the base get the proton? Are there any protons around in water at pH7?

25. Under the right conditions (to be seen later), two oppositely charged organic ions can form an ionic bond:
O ||
R-C-O H3N-R
Weak, ~ 5 kcal/mole.
But these weak bonds are VERY important for biological molecules …….

26. Energy needed to break:
Chemical Bonds
Bond:
Energy needed to break:
Comments:
Strength class-ification:
Covalent
~100
kcal/mole
Electrons
shared
strong
Hydrogen ~3
Water-water;
Organic-water;
Organic-organic
weak;
orientation dependent
Ionic ~5
Full charge transfer;
Can attract H-bond;
Strong in crystal
weak

27. Van der Waals bonds
Can form between ANY two atoms that approach each other
“Fluctuating induced dipole”
Very weak (~ 1 kcal/m)
Effective ONLY at very close range (1A) (0.1 nm)
First molecule “

28. Energy needed to break:
Chemical Bonds
Bond:
Energy needed to break:
Comments:
Strength
Class-
ification:
Covalent
~100
kcal/mole
Electrons
shared
strong
Hydrogen ~3
Water-water;
Organic-water;
Organic-organic
weak
Ionic ~5
Full charge transfer;
Can attract H-bond;
Strong in crystal
weak
Van der Waals ~1
Fluctuating
induced
dipole;
Close range
only
weak
Why are we doing all this now?

29. Energy needed to break:
Chemical Bonds
Bond:
Energy needed to break:
Comments:
Strength class-ification:
Covalent
~100
kcal/mole
Electrons
shared
strong
Hydrogen ~3
Water-water;
Organic-water;
Organic-organic
weak
Ionic ~5
Full charge transfer;
Can attract H-bond;
Strong in crystal
weak
Van der Waals ~1
Fluctuating
induced
dipole;
Very close range only
weak
Hydro-phobic forces ~3
Not a bond per se;
entropy driven;
only works in water
weak

30. Consider octane, C8H18, or: CH3-CH2-CH2-CH2-CH2-CH2-CH2-CH3
Electro-negativities of C and H are ~ equal
No partial charge separation
Non-polar, cannot H-bond to water, = “hydrophobic”
Contrast: polar compounds = “hydrophilic”

31. Octane in water
(These numbers are made up.)

32. (These numbers are made up.)

33. ENTROPY: related to the number of different states possible
The water molecules around the non-polar molecule have a LOWER entropy (less choices, more ordered).
Systems tend to change to maximize entropy (different states possible to occupy).
Aggregation of the non-polar molecules with each other minimizes the number of water molecules that are on their surface, thus maximizing the entropy of the system

34. Admittedly, the non-polar octane molecules lose entropy when they coalesce. That is, they are more disordered when they are separate.
However, this loss of entropy apparently cannot counteract the gain in entropy of the system brought about by the freeing up of water molecule from the “cage” around the non-polar molecules.

35. Hydrophobic “bonds” (forces)
Affects NON-polar molecules that find themselves in an aqueous environment (i.e., must be in water)
They cannot H-bond with water molecules
The water molecules around the non-polar molecule are not able to constantly switch partners for H-bonding
The water molecules around the non-polar molecule are in a MORE ordered state.
Hydrophobic “forces”, not really “bonds” per se

36. Water cages around methane: CH4
3 artists’ depictions

37. End of bonds, and water, our molecule #1 Now for the next 4999 types of molecules found in an E. coli cell: First let’s categorize: Small vs. large molecules
LARGE
>= ~5000 daltons
Called macromolecules
Examples: proteins, polysaccharides, DNA
SMALL
<= ~500 daltons (~ 50 atoms)
Called small molecules
Size differences are rough, there are gray areas
Examples: water, ethanol, glucose, acetamide, methane, octane

38. Propylene CH3-CH=CH2
Polypropylene, a polymer, a large molecule

39. Large molecules are built up from small molecules
One possibility:
Poly ?

40. Or from many different small molecules?No

41. A great simplification:
Large molecules are linear polymers of
small molecules.
O-O-O-O-O-O-O-………

42. Nomenclature for polymers
monomer
O-O
dimer
O-O-O
trimer
O-O-O-O
tetramer
oligomer
O-O-O-O-O-O-O
O-O-O-O-O-O-O-O-O-O-O
oligomer
a monomer of the polymer
polymer

43. The large molecules, or macromolecules, of all cells can be grouped into 4 categories:
polysaccharides,
lipids,
 nucleic acids, and
proteins.
Many of the important small molecules of the cell are the monomers of these polymers.
There are only about 50 of these monomers, a very manageable number to learn about.
There are about another dozen small molecules in an E. coli cell that are important but are not monomers of polymers (Most of these are related to vitamins).

44. Monomers and polymers Macromolecule: polysaccharide
A monomer of many polysaccharides is glucose:
Present in our minimal medium ) .

45. CH3 C H2N COOH H Getting the monomers For example: Polymer: protein
Monomer: amino acids
Example at right = alanine
Looks nothing like glucose
Where does E. coli get alanine?
CH3 C
H2N
COOH H

46. E. coli makes all the monomers by biochemical transformations starting from glucose
glucose →A → B→C →D →E →alanine →protein
A, B, C, D, E, are “intermediates”:
i.e., intermediate chemical structures (molecules) between glucose and alanine.

48. Very rough estimate of the total number of different small molecules in an E. coli cell:
50 monomers
15 non-monomer important small molecules (e.g., like vitamins)
65 total “end products”
Average pathways to monomers and important small molecules starting from glucose: =~ 10 steps, so 9 intermediates per pathway
65 such pathways  65 x 9 = 585 intermediates
65 end-products intermediates = 650 total types of small molecules per E. coli cell
A manageable number, and we ~ know them all

49. Macromolecule class #1: Polysaccharides
Monomer = sugars
Sugars = small carbohydrate molecules
Carbohydrates ~= CnH2nOn
Contain one C=O group and many –OH’s
Can contain other functional groups as well (carboxyls, amines)
Most common sugar and monomer is glucose

50. Glucose, straight chain depictions
Abbreviated C
Remember, always 4 bonds to carbon; Often even if not depicted
With numbering

51. anomeric
carbon
Fisher
view
Chair view
Haworth view
Handout 2-7

52. 11 9 10 5 6 7 8 3 4 2 1

53. 9 6 5 8 7 3 4 2 1

54. Physical model ball and stick model of glucose ring closure/opening

55. beta-glucose
alpha-glucose

56. Ball and stick models of glucose

57. Glucose
Gray = C
White = H
Red = O
Ring oxygen
C6 (-CH2OH) C5 C1
hydroxyl

58. Alpha glucose
All the hydroxyls and the –CH2OH are sticking out equatorial
Except for the hydroxyl on the anomeric carbon 1

59. 2 5 3
From Handout 2-7

60. 5 3 4 1
From Handout 2-7

61. Relationship between Haworth (flat ring) depiction and chair-form
Flat ring (Haworth projection) just gives the relative positions of the H and OH at each carbon, one is “above” the other. But it does not tell the positions of the groups relative to the plane of the ring (up, down or out)
Handout 2-8

62. Alpha or beta?
You try it later.
Glucose
Gray = C
White = H
Red = O
Ring oxygen
C6 (-CH2OH) C5 C1
hydroxyl