The whole General Biology formula sheet, to print

Ratio of deprotonated (A-) to protonated (HA) form of one ionisable group, with pKa = -log10 Ka. At pH = pKa the two forms are equal, and a group buffers best within about 1 pH unit of its pKa.

pK1 is the alpha-COOH and pK2 the alpha-NH3+. For any amino acid, pI is the average of the two pKa values that lie on either side of the neutral (net charge zero) form.

Right-handed alpha helix: 3.6 residues per turn, 0.15 nm rise per residue, i to i+4 hydrogen bonds.

n is the number of chiral carbons in the open-chain form (valid when there are no meso forms). Aldohexoses have n = 4, giving 16 (8 D and 8 L); ketohexoses have n = 3, giving 8. Cyclisation adds one more chiral centre, the anomeric carbon.

Idealised B-form: 0.34 nm rise per base pair, 10 bp per turn, so pitch 3.4 nm; diameter about 2 nm; right-handed. B-DNA in solution has about 10.5 bp per turn; use 10 unless a question states otherwise.

Same form as Michaelis-Menten kinetics: flux saturates at Jmax, and Kt is the solute concentration giving half-maximal flux. Simple diffusion has no such limit; its flux rises linearly with the concentration difference.

R = 8.314 J mol${}^{-1}$ K${}^{-1}$, T in kelvin, F = 96,485 C mol${}^{-1}$, z the signed charge of the solute, and $\Delta \psi ={\psi }_2-{\psi }_1$ in volts; $\Delta G$ is in J mol${}^{-1}$. For an uncharged solute z = 0 and only the concentration term remains. A negative value means the movement is spontaneous (passive); a positive value means it needs an energy input.

i is the number of particles each formula unit gives in solution (1 for glucose, about 2 for NaCl), C the molar concentration, R the gas constant (0.0821 L atm mol${}^{-1}$ K${}^{-1}$ gives $\pi$ in atm) and T in kelvin; iC is the osmolarity. Valid for ideal dilute solutions. Water moves by osmosis from lower to higher osmolarity, often through aquaporins; a cell swells in a hypotonic medium and shrinks in a hypertonic one (tonicity also depends on whether the solute can cross the membrane).

One permeant ion at equilibrium; z is its signed charge (+1 for K+ and Na+, -1 for Cl-, +2 for Ca2+). 2.303RT/F = 61.5 mV at 37 degrees C (about 59 mV at 25 degrees C).

Steady-state potential (no net current) with several monovalent permeant ions, assuming a constant electric field across the membrane. P is each ion's permeability; only ratios matter. The Cl- terms are inverted because it is an anion. The result lies between the ions' Nernst potentials, closest to that of the most permeable ion; with only one permeant ion it reduces to the Nernst equation.

R = 8.315 J/(mol·K); RT ≈ 2.48 kJ/mol at 25 °C. Q is the mass-action ratio [products]/[reactants]; at equilibrium Q = K'eq and ΔG = 0.

K'eq is the equilibrium constant at pH 7. Each tenfold change in K'eq changes ΔG°' by about 5.7 kJ/mol at 25 °C (this is RT ln 10).

n = electrons transferred per mole of the reaction as written, F = 96.5 kJ/(V·mol), ΔE°' = E°'(electron acceptor) minus E°'(electron donor), both at pH 7.

Ranges from 0 (all AMP) to 1 (all ATP); cells usually hold it at about 0.8–0.95. ATP-generating pathways are inhibited and ATP-using pathways stimulated as it rises. Adenylate kinase (2 ADP ⇌ ATP + AMP) makes [AMP] change far more, in proportion, than [ATP], which is why AMP is a sensitive low-energy signal.

Terms: glycolysis ATP, cytosolic NADH (2.5 each via the malate-aspartate shuttle, 1.5 each via the glycerol-3-phosphate shuttle), PDH NADH, TCA GTP (counted as ATP), TCA NADH, TCA FADH2. Gives 32 with the malate-aspartate shuttle and 30 with the glycerol-3-phosphate shuttle.

Carbohydrate 1.0 (C6H12O6 + 6 O2 → 6 CO2 + 6 H2O). Fat about 0.7 (palmitic acid: C16H32O2 + 23 O2 → 16 CO2 + 16 H2O, RQ = 16/23 ≈ 0.70). Protein about 0.8. Above 1 for oxygen-rich substrates such as organic acids (malate 4/3), when fat is being made from carbohydrate, or with fermentation.

Uses 2.5 per NADH and 1.5 per FADH2, so 4 per β-oxidation round and 10 per acetyl-CoA, and 2 spent on activation. For palmitate (C = 16): 7 rounds give 28, 8 acetyl-CoA give 80, gross 108, net 106. Stearate (C = 18) gives 120. With the older ratios (3 and 2) palmitate gives 129.

Per CO2 fixed: 3 ATP and 2 NADPH. Three CO2 give one net G3P using 9 ATP and 6 NADPH.

Initial velocity of a single-substrate enzyme under steady state with $[S]\gg [E{]}_T$. $K_m$ is in concentration units (mM or $\mu$M), $V_{max}$ in concentration per time (for example $\mu$M/min).

For $E+S\underset{k_{-1}}{\stackrel{k_1}{\rightleftharpoons }}ES\stackrel{k_2}{\to }E+P$. $K_m$ equals the substrate concentration at which $v=V_{max}/2$. It equals the dissociation constant $K_d=k_{-1}/k_1$ of ES only if $k_2\ll k_{-1}$.

$k_{cat}$ (units s${}^{-1}$) is the number of substrate molecules converted per active site per second at saturation. For the simple mechanism above $k_{cat}=k_2$.

Units M${}^{-1}$s${}^{-1}$. It is the apparent second-order rate constant at $[S]\ll K_m$, where $v\approx (k_{cat}/K_m)[E{]}_T[S]$. Its upper limit is set by diffusion, about $10^8$ to $10^9$ M${}^{-1}$s${}^{-1}$.

For example $f=0.5$ gives $[S]=K_m$, and $f=0.9$ gives $[S]=9K_m$.

Plot $1/v$ against $1/[S]$: slope $=K_m/V_{max}$, y-intercept $=1/V_{max}$, x-intercept $=-1/K_m$.

Plot $v$ against $v/[S]$: slope $=-K_m$, y-intercept $=V_{max}$, x-intercept $=V_{max}/K_m$.

Plot $[S]/v$ against $[S]$: slope $=1/V_{max}$, y-intercept $=K_m/V_{max}$, x-intercept $=-K_m$.

General mixed case. Competitive: ${\alpha }^{\prime }=1$. Uncompetitive: $\alpha =1$. Pure non-competitive: $\alpha ={\alpha }^{\prime }$ ($K_i=K_i^{\prime }$), so $K_m$ is unchanged.

Here $K^{\prime }=(K_{0.5}{)}^{n_H}$. A plot of the left side against $\log [S]$ has slope $n_H$, the Hill coefficient. $n_H>1$ means positive cooperativity, $n_H=1$ no cooperativity, $n_H<1$ negative cooperativity. $n_H$ cannot exceed the number of substrate-binding sites.

$N_0$ is the initial count and $N_t$ the survivors after time $t$ at one fixed temperature; $D$ is in the same unit as $t$. Valid while the death curve is a straight line on a log scale.

$D_{T_1}$ and $D_{T_2}$ are the D-values at temperatures $T_1$ and $T_2$ ($T_2>T_1$); $z$ is in the same temperature unit.

$d$ is the smallest resolvable distance, $\lambda$ the wavelength, $n$ the refractive index between specimen and objective and $\theta$ half the angle of the cone of light entering the objective. This is the Rayleigh form; some texts use $d=0.5\lambda /\text{NA}$. A smaller $d$ means better resolution.

Here the dilution factor is the fraction left after all dilutions, for example $10^{-6}$ after six tenfold steps. Equivalently, CFU/mL = colonies × reciprocal of the dilution ÷ volume plated.

Use only for the exponential phase. $N_0$ and $N$ are the cell counts at the start and end of the interval.

$t$ is the elapsed exponential time; $k$ is generations per unit time.

Per unit time (for example per hour). It uses the natural log, so $\mu =0.693k$.

$S$ is the limiting nutrient concentration; $K_s$ is the value of $S$ at which $\mu ={\mu }_{\max }/2$ (units of concentration). It applies when one nutrient is limiting.

$\bar{S}$ and $\bar{X}$ are the steady-state substrate and biomass concentrations, and $Y_{X/S}$ is the biomass yield (mass of cells formed per mass of substrate used). This assumes Monod kinetics with no cell death and no maintenance consumption.

Convention: 2 ATP hydrolysed per electron transferred; 8 electrons per N₂ (6 to make 2 NH₃ and 2 for the obligatory H₂), so 16 ATP per N₂. In cells the cost is often higher because extra H₂ is made.

Use a plate with a countable number of plaques (conventionally 30 to 300). The dilution is the fraction of the original stock in the plated sample (such as $10^{-6}$).

m is the multiplicity of infection (phage added per bacterium), assuming random adsorption. P(k) is the fraction of cells infected by exactly k phages.

Each cleaves C3 into C3a (anaphylatoxin) and C3b (opsonin); C3b joining the convertase makes the C5 convertase.

Common to all pathways. The MAC is a pore that lyses Gram-negative bacteria and other susceptible cells.

Applies when each monomer has two sites: IgG, IgE, IgD = 2; secretory IgA dimer = 4; IgM pentamer = 10.

Counts of functional segments. Total combinations are N_H x N_L (assuming any heavy chain pairs with any light chain), before junctional diversity and somatic hypermutation are added.

Applies when the two parents carry four different haplotypes between them and there is no recombination within the MHC. Each child receives one of two maternal and one of two paternal haplotypes, each with probability 1/2.

$R_0$ is the basic reproduction number and $E$ is vaccine efficacy (fraction, 0 to 1). $1-1/R_0$ is the herd immunity threshold, the coverage needed when $E=1$. Assumes homogeneous mixing, and applies when $E$ is high enough that $p_c$ does not exceed 1.