Comprehensive Guide to Pipetting, Solutions, and Serial Dilutions

Precision and Accuracy in Experimental Science

• Performing biological laboratory procedures requires the same rigor as baking: precise measurements and accurate execution ensure repeatable, high-quality results.

• Accuracy: Refers to how close a measured or calculated value is to the true, target, or officially reported value.

• Precision: Refers to how close repeated measurements or experimental data points are to one another, regardless of whether they hit the true target.

• Experimental outcomes can fall into distinct accuracy and precision categories:

  • Low Accuracy, Low Precision: Data points are widely scattered and far from the target value.

  • Low Accuracy, High Precision: Data points are tightly clustered together, but consistently off-target from the true value.

  • High Accuracy, High Precision: Data points are tightly clustered together directly on top of the target value.

Measurement Unit Conversions and Basic Rules

• Metric conversions rely on power-of-ten adjustments between units:

  • Converting to a smaller unit (moving right): Multiply by $1000$ or shift the decimal point $3$ digits to the right.

  • Converting to a larger unit (moving left): Divide by $1000$ or shift the decimal point $3$ digits to the left.

• Volume Conversions:

  • $1\,\text{Liter (L)} = 1000\,\text{milliliters (mL)}$

  • $1\,\text{mL} = 1000\,\text{microliters } (\mu\text{L})$

  • $0.5\,\text{L} = 500\,\text{mL}$

  • $0.05\,\text{L} = 50\,\text{mL}$

  • $0.5\,\text{mL} = 500\,\mu\text{L}$

  • $0.05\,\text{mL} = 50\,\mu\text{L}$

  • A volume of $100\,\text{mL}$ is $1000\times$ larger than $100\,\mu\text{L}$.

• Mass Conversions:

  • $1\,\text{kilogram (kg)} = 1000\,\text{grams (g)}$

  • $1\,\text{g} = 1000\,\text{milligrams (mg)}$

  • $1\,\text{mg} = 1000\,\text{micrograms } (\mu\text{g}\text{ or mcg})$

Micropipette Components, Sizes, and Volume Ranges

• Micropipettes are high-precision volumetric instruments designed to transfer liquid volumes in the microliter range.

• Key structural components include:

  1. Volume adjustment dial: Rotated clockwise or counterclockwise to adjust the volume setting up or down digit by digit.

  2. Tip ejector button: Depressed to push off and discard used tips.

  3. Plunger button: Operates aspirating and dispensing functions using tactile stops.

  4. Volume indicator: Digital readout window displaying current set volume.

  5. Stainless steel ejector arm: Lever arm transferring force to eject tips.

  6. Plastic shaft: Lower body attaching to disposable tips.

  7. Disposable tip: Replaceable plastic tip holding the fluid sample.

• Micropipette Models and Operating Limits:

  • Desired pipetting volume must fall completely within the specified operational range of the instrument.

  • Standard laboratory micropipette sizes include:

    • P20: Designed for volumes from $0.5\,\mu\text{L}$ to $20\,\mu\text{L}$.

    • P200: Designed for volumes from $20\,\mu\text{L}$ to $200\,\mu\text{L}$.

    • P1000: Designed for volumes from $200\,\mu\text{L}$ to $1000\,\mu\text{L}$.

  • Note: There is no "P100" micropipette standard; select either P200 or P20 as appropriate for volumes near $100\,\mu\text{L}$.

Reading and Adjusting Micropipette Volume Displays

• Each micropipette model features a three-digit display window where digits represent different place values depending on the tool's volume capacity.

• P20 Volume Reading (Max $20\,\mu\text{L}$):

  • Top digit = Tens ($10\,\mu\text{L}$)

  • Middle digit = Ones ($1\,\mu\text{L}$)

  • Bottom digit (red) = Tenths ($0.1\,\mu\text{L}$)

  • Display [1, 7, 4] represents $17.4\,\mu\text{L}$.

  • Display [0, 1, 5] (with red $5$) represents $1.5\,\mu\text{L}$.

  • Display [1, 5, 0] (with red $0$) represents $15.0\,\mu\text{L}$.

• P200 Volume Reading (Max $200\,\mu\text{L}$):

  • Top digit = Hundreds ($100\,\mu\text{L}$)

  • Middle digit = Tens ($10\,\mu\text{L}$)

  • Bottom digit = Ones ($1\,\mu\text{L}$)

  • Display [0, 5, 7] represents $57\,\mu\text{L}$.

  • Display [0, 2, 0] represents $20\,\mu\text{L}$.

  • Display [2, 0, 0] represents $200\,\mu\text{L}$.

• P1000 Volume Reading (Max $1000\,\mu\text{L}$):

  • Top digit (red) = Thousands ($1000\,\mu\text{L}$)

  • Middle digit = Hundreds ($100\,\mu\text{L}$)

  • Bottom digit = Tens ($10\,\mu\text{L}$)

  • Display [0, 9, 7] represents $970\,\mu\text{L}$.

  • Display [0, 2, 0] represents $200\,\mu\text{L}$.

  • Display [1, 0, 0] (with red $1$) represents $1000\,\mu\text{L}$.

Proper Micropipetting Technique and Operation

• Step-by-Step Liquid Handling Sequence:

  1. Attach Tip: Press shaft firmly into a fresh tip inside the tip box and tap lightly to ensure an airtight seal.

  2. Set First Stop: Press the plunger button down to the first stop prior to inserting tip into the liquid sample.

  3. Aspirate Sample: Submerge tip vertically below liquid surface. Slowly release plunger button to draw fluid smoothly into tip without introducing bubbles.

  4. Dispense Sample: Place tip against receiving container wall. Depress plunger past the first stop all the way down to the second stop to force out residual droplets.

  5. Withdraw Instrument: Pull tip clear of container before slowly releasing plunger back to rest.

  6. Eject Tip: Press ejector button to eject contaminated tip into biohazard waste.

Solution Preparation and Molarity Calculations

• Solution Terminology:

  • Solution: Homogeneous mixture created by dissolving one or more solutes into a solvent.

  • Aqueous Solution: Any solution where water is the solvent.

  • Concentration Units: Expressed as Molarity ($\text{M}$), mass/volume concentration ($\text{mg/mL}$), or percentage ($\%$).

• Molarity Definition and Formulas:

  • $\text{Molarity (M)} = \frac{\text{Moles of Solute}}{\text{Liters of Solution}}$

  • Because balances measure mass rather than moles:         $\text{Moles} = \frac{\text{Mass of Solute (g)}}{\text{Molecular Weight (g/mol)}}$

  • Direct mass calculation formula:         $\text{Mass of Solute (g)} = \text{Molarity (mol/L)} \times \text{Volume (L)} \times \text{Molecular Weight (g/mol)}$

• Worked Example: Preparing $250\,\text{mL}$ of a $2\,\text{M}\,\text{NaCl}$ Solution

  • Given Data:

    • Desired Molarity ($\text{M}$) = $2\,\text{M} = 2\,\text{mol/L}$

    • Total Volume ($\text{V}$) = $250\,\text{mL} = 0.25\,\text{L}$

    • Molecular Weight ($\text{MW}$) of $\text{NaCl}$ = $58.44\,\text{g/mol}$

  • Calculation:         $\text{Mass of NaCl} = 2\,\text{mol/L} \times 0.25\,\text{L} \times 58.44\,\text{g/mol} = 29.22\,\text{g}$

  • Proper Preparation Protocol:

    • Weigh out exactly $29.22\,\text{g}$ of solid $\text{NaCl}$.

    • Dissolve the solid in a volume of water less than $250\,\text{mL}$ (e.g., $150\text{--}200\,\text{mL}$).

    • Transfer to a volumetric container and bring total volume up to the $250\,\text{mL}$ line (do not add $250\,\text{mL}$ of water directly to dry salt, as dissolved solute expands total volume). Read volume at the bottom of the meniscus at eye level.

Liquid-to-Liquid Stock Dilutions ($C_sV_s = C_dV_d$)

• Dilution Equation Principles:

  • Used to dilute a concentrated stock solution ($s$) to a lower target concentration ($d$).

  • $C_s V_s = C_d V_d$

    • $C_s$ = Concentration of stock solution

    • $V_s$ = Volume of stock solution required

    • $C_d$ = Concentration of diluted solution

    • $V_d$ = Volume of diluted solution desired

  • Units for concentration must match on both sides ($\text{M}$ to $\text{M}$), and volume units must match ($\text{mL}$ to $\text{mL}$).

• Worked Example: Preparing $500\,\text{mL}$ of $2.5\,\text{M}\,\text{NaCl}$ from a $10\,\text{M}$ Stock Solution

  • Given Data: $C_s = 10\,\text{M}$, $C_d = 2.5\,\text{M}$, $V_d = 500\,\text{mL}$, $V_s = x$

  • Step 1: Solve for stock volume ($V_s$):         $10\,\text{M} \times x = 2.5\,\text{M} \times 500\,\text{mL}$         $10x = 1250$         $x = \frac{1250}{10} = 125\,\text{mL of stock solution}$

  • Step 2: Calculate diluent (water) volume:         $\text{Diluent Volume} = V_d - V_s = 500\,\text{mL} - 125\,\text{mL} = 375\,\text{mL}$

  • Final Recipe: Mix $125\,\text{mL}$ of $10\,\text{M}\,\text{NaCl}$ stock with $375\,\text{mL}$ distilled water.

Dilution Factors and Terminology

• Essential Terms:

  • Aliquot: Sub-volume sample taken from the original stock solution.

  • Diluent: Fluid (e.g., water or buffer) used to dilute the sample.

  • Dilution Factor (DF): Unitless ratio of total final volume to aliquot volume.

• Dilution Factor Formula:

  • $\text{DF} = \frac{\text{Final Volume}}{\text{Aliquot Volume}} = \frac{\text{Aliquot Volume} + \text{Diluent Volume}}{\text{Aliquot Volume}}$

• Standard Examples:

  • Diluting $1\,\text{mL}$ sample (aliquot) into $9\,\text{mL}$ $\text{H}_2\text{O}$ (diluent):         $\text{Final Volume} = 1\,\text{mL} + 9\,\text{mL} = 10\,\text{mL}$         $\text{DF} = \frac{10\,\text{mL}}{1\,\text{mL}} = 10 \quad (1:10 \text{ dilution or } 10^1)$

  • Diluting $1\text{ part}$ sample into $19\text{ parts}$ diluent:         $\text{DF} = \frac{1 + 19}{1} = 20 \quad (1:20 \text{ dilution}, \text{concentration is } \frac{1}{20}\text{th} \text{ of stock})$

Serial Dilutions Procedure and Mathematical Analysis

• Applications:

  • Used in microbiology to estimate viable microbial concentrations ($\text{cells/mL}$) in high-density cultures.

  • Used to achieve extremely high dilution ratios without needing impossibly small pipetting volumes or gigantic solvent containers.

• Operational Definition:

  • A series of step-by-step dilutions maintaining a constant dilution factor and total volume at each step.

  • Initial stock is drawn only once for Step 1; each subsequent diluted tube serves as the stock for the next transfer step.

• Worked Example: Serial Dilution from $10^9\,\text{cells/mL}$ ($1\text{ billion}$) to $10^5\,\text{cells/mL}$ ($100,000$) in $1000\,\mu\text{L}$ Total Volume:

  • Intermediate Steps: $10^9 \rightarrow 10^7 \rightarrow 10^5$

  • Step Dilution Factor Calculation:         $\text{Step DF} = \frac{10^9}{10^7} = 100 \quad (1:100 \text{ or } 10^2)$

  • Step Aliquot Volume Calculation:         $\text{Aliquot Volume} = \frac{\text{Total Volume}}{\text{Step DF}} = \frac{1000\,\mu\text{L}}{100} = 10\,\mu\text{L}$

  • Step Diluent Volume Calculation:         $\text{Diluent Volume} = 1000\,\mu\text{L} - 10\,\mu\text{L} = 990\,\mu\text{L}$

• Step-by-Step Serial Scheme:

  • Tube A (Stock): $10^9\,\text{cells/mL}$

  • Tube B ($10^7\,\text{cells/mL}$): Add $10\,\mu\text{L}$ of Tube A to $990\,\mu\text{L}$ diluent ($1000\,\mu\text{L}$ total volume, mix).

  • Tube C ($10^5\,\text{cells/mL}$): Add $10\,\mu\text{L}$ of Tube B to $990\,\mu\text{L}$ diluent ($1000\,\mu\text{L}$ total volume, mix).

• Method Comparison Analysis:

  • $10\times$ Step Strategy: Would require $4\text{ steps}$ ($10^9 \rightarrow 10^8 \rightarrow 10^7 \rightarrow 10^6 \rightarrow 10^5$), using $100\,\mu\text{L}$ sample into $900\,\mu\text{L}$ diluent per step.

  • Single-Step Direct Dilution: Requires transferring $0.01\,\mu\text{L}$ into $1000\,\mu\text{L}$, which is far below standard micropipette accuracy limits.

Course Schedule and Upcoming Deliverables

• Next Week Schedule:

  • No in-person laboratory meeting next week; in-person sessions resume the following week.

• Assigned Online Tasks:

  • Simbio Activities: Download Simbio software onto a laptop (tablets are unsupported) and complete assigned activities in the Simbio Folder.

  • SDP Post-Lecture Online Quiz: Complete timed online quiz on Blackboard.

  • Academic Integrity Quiz: Mandatory deadline by $11:59\,\text{PM}$ on Friday.

• Two Weeks Ahead:

  • New Module: "Beer Me Week 1" (requires prelab quiz completion).

• Virtual Office Hours:

  • Held Sunday at $8:00\,\text{PM}$ (access link on Blackboard).