Growth: linear 2 N = No10kt

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

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

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

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)

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

waterHbonds 8

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

10 Ethanol and Water hydroxyl group again 3 2 3 2

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)

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

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

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

waterHbonds Hydrogen bond

Ethanol and Water 16 3 2 3 2

(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

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

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

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

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

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

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”

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?

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 …….

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

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 “

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?

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

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”

Octane in water (These numbers are made up.)

(These numbers are made up.)

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

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.

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

Water cages around methane: CH4 3 artists’ depictions

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

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

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

Or from many different small molecules? No

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

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

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).

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

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

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.

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 + 585 intermediates = 650 total types of small molecules per E. coli cell A manageable number, and we ~ know them all

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

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

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

11 9 10 5 6 7 8 3 4 2 1

9 6 5 8 7 3 4 2 1

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

beta-glucose alpha-glucose

Ball and stick models of glucose

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

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

2 5 3 From Handout 2-7

5 3 4 1 From Handout 2-7

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

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