Scientific Notation and Units

Shorthand dealing with large and small numbers e.g. 10^2, 10^-1

• 10 = Decimal Place
• ^x = Number of zeros (orders of magnitude)

e.g. 

10^6 = 1,000,000

10^1 = 10

10^-2 = 0.01

10^-9 = 0.000000001

Convert large numbers to small numbers and a wide range to a small range. They are very useful for formatting graphs - they can turn curves into straight lines.

Log^x = x 

• Log 10^0 = 0
• Log 10^7 = 7
• Log 10^-5 = -5

They have no units

e.g. pH scale

10^12     Tera     Tm

10^9       Giga    Gm

10^6       Mega   Mm

10^3       Kilo      km

10^0       Metre   m

10^-3      Mili      mm

10^-6      Micro    um

10^-9      Nano    nm

10^-12     Pico    pm

New unit every 1000-fold change in value

To go up you divide by 1000 to go down you times by 1000

Largest

• 50s ribosome subunit
• 30s ribosome subunit
• Antibody
• Nucleosome
• Haemoglobin
• Cell membrane
• Insulin
• DNA
• Glucose

Mass

• Solids are measured by weight/mass
• Units: g
• g -> mg -> ug -> ng
• Individual moleculea have a Molecular weight (Mw)
• Relative molecular mass (RMM) - the weight of 6.02x10^23 molecules

Moles

• Mole is a quantity -> 6.02x10^23 molecules or atoms
• Units: mol
• mol -> mmol -> umol -> nmol
• RMM is the mass of 1 mole of a molecule - mass per mole (g/mol)

Volume (l)

• Measurement of liquids, solutions or gases
• l -> ml -> ul -> nl

Concentration (various unit combinations)

• Mass of a dissolved solid per unit of volume
• g/l -> mg/ml -> ug/ul -> ng/nl
• The % concentratuib of a solution is per 100ml/g of a unit

Molarity (M)

• Moles per litre
• M -> mM -> uM -> nM
• In the pH scale the concentration of H+ ions must be Molar

Caculations

When doing calculations units must match:

• When changing both units the number stays the same e.g 80mg/ml = 80g/l
• When changing one unit the number changes e.g. 80mg/l = 0.08g/ml

Dilutions

Adding water can reduce concentration

C1 x V1 = C2 x V2

V1 = (C2/C1) x V2

• C1 = Concentration of stock
• C2 - Desired final concentration after dilution
• V1 = Volume of added stock
• V2 = Final Volume

e.g. Absorbance and concentration 

A = εcl

• A = absobance
• ε = molar excitation coefficient (M-1cm-1)
• c = concentration (M)
• l = light path (cm)

As ε and l are usually constant, doubling A doubles c

Equilibrium - a state of balance between different components of a system

Defined by a constant k

• If K>1 = more of the upper quantity
• If K<1 = more of the lower quantity

Strong acid:

pH = -log[H+]

Weak acid: 

pH = pKa + log [A-]/[HA]

pKA = -logKa = pH when [uncharged]=[charged] = indicates the strength of an acid

Ka = [H+][A-]/[HA] = ratio of uncharged to charge molecules

Exponential Curves - a change in growth/decay and the change in how much it it growing or decaying

Fibonacci series - all flowers have a number of petals found in the Fibonacci series

If theres is a mathematical equation that describes a biological system then it can be modelled in silico (computers):

• Equation for a system known
• Implement in a spreadsheet and generate data
• Visulalise trends graphically 
• Interpret and evaluate