Bench Science and Laboratory Math

Tools in this group

• Molarity and Dilution (C1V1=C2V2) - Solve for the missing fourth from any three of stock concentration, stock volume, final concentration, final volume.
• Serial Dilution Planner - Per-tube transfer volume, per-tube diluent volume, and resulting concentration at each step.
• Molecular Weight from Formula - Client-side parser handling parentheses and subscripts. IUPAC standard atomic weights bundled.
• Mass-to-Moles and Moles-to-Mass - Solve for the missing third from mass, moles, and molecular weight.
• Centrifuge RPM and RCF - RCF (g) = 1.118e-5 * r(cm) * RPM^2. Both directions. Bundled rotor radii.
• Resuspension Volume - Diluent volume to add given lyophilized mass and target concentration.
• PCR Master Mix - Per-component master-mix volume for N reactions with a pipetting fudge factor.
• Beer-Lambert Concentration - Concentration from absorbance, path length, and molar extinction coefficient.
• Henderson-Hasselbalch Buffer - Conjugate-base / acid ratio and moles for a target pH. Bundled pKa for common laboratory buffers.
• Hemocytometer Cell Count - Cells per mL from squares counted; optional trypan blue viability percent.
• OD600 to Cell Density - Cells/mL = OD600 x conversion factor x dilution, with a linear-range flag above OD ~0.8. Conversion factor is strain- and instrument-specific (user-supplied). Lab SOP governs.
• Agarose Gel Percent - Recommended agarose percent for a fragment-size range and grams of agarose for the buffer volume (percent/100 x mL). Per Sambrook & Russell resolution tables; lab SOP governs.
• Primer Melting Temperature - PCR primer melting temperature (Tm), length, and GC content by the Wallace short-oligo rule (<=14 nt) or the basic GC% formula.
• CFU/mL Viable Plate Count - Colony-forming units per mL of the original sample from colonies counted, dilution factor, and volume plated, with a countable-range validity flag.
• Molarity from Concentrated Reagent - Stock molarity of a concentrated liquid reagent from its assay percent, density, and molecular weight (M = 10 x %w/w x density / MW), plus the volume of concentrate to draw for a target working solution. Add acid to water.
• Nucleic Acid Concentration (A260) - DNA/RNA concentration from a 260 nm read using the mass extinction factor (50 dsDNA, 33 ssDNA/oligo, 40 RNA) and dilution, plus the 260/280 purity ratio that flags protein or phenol carryover. Off every NanoDrop or cuvette read.
• Ligation Insert:Vector Molar Ratio - Insert mass to add for a target insert:vector molar ratio (insert_ng = ratio x insert_len/vector_len x vector_ng), plus each in picomoles at 650 g/mol per bp. A short insert needs less mass, not equal mass; equal masses over-represent small fragments.
• Cell Culture Doubling Time - Doubling time, specific growth rate, and number of doublings from two counts (or ODs) and the elapsed time (Td = t x ln2 / ln(N/N0)). Valid only in log phase; a span across lag or stationary phase is meaningless.
• Michaelis-Menten Enzyme Kinetics - Reaction velocity and percent of Vmax from Vmax, Km, and substrate concentration (v = Vmax[S]/(Km+[S])). Km is the substrate at half Vmax -- an affinity proxy (low Km = high affinity), not a rate; the hyperbola never reaches Vmax.
• Substrate for a Target Fraction of Vmax (Michaelis-Menten Inverse) - The assay-design inverse of Michaelis-Menten: enter Km and the fraction of Vmax you want, get the substrate concentration to use. [S] = Km x f/(1 - f). Half of Vmax takes exactly one Km (the definition of Km), but 90% takes 9 x Km and 99% takes 99 x Km -- the runaway excess that shows why an enzyme approaches Vmax but never reaches it. Feeds straight back into the forward tile. Steady state, substrate in excess of enzyme; the assay conditions govern.