Terminologies, principles, and hemocytometer-based calculations for cell viability and concentration.
Flowchart: Sample → Dilution → Counting → Calculation → Interpretation
1.1 Terminologies and principles
Key terminologies:
- Hemocytometer/Neubauer Chamber: Gridded glass slide for manual cell counting with defined volumes per square.
- Trypan Blue Exclusion: Dye exclusion method where viable cells with intact membranes exclude the dye, while dead cells with compromised membranes take up the blue color.
- Cell Viability: Percentage of living cells in a population calculated as: (Viable cells/Total cells) × 100.
- Dilution Factor: Ratio of final volume to original volume of a diluted sample.
- Serial Dilution: Stepwise dilution where each step uses a portion of the previous dilution.
- C1V1 = C2V2: Fundamental dilution formula where concentration1 × volume1 = concentration2 × volume2.
Principles:
- Volume-to-Concentration Relationship: Cell concentration is expressed as cells/mL, requiring conversion from counted volume to standard milliliter volume.
- Dye Exclusion Principle: Only cells with intact plasma membranes can exclude certain dyes; this forms the basis of viability assessment.
- Accurate Dilution Design: Critical for achieving precise experimental conditions while maintaining solvent concentrations below cytotoxic levels.
1.2 Cell Counting and Viability
Hemocytometer Basics:
Each of the 4 large corner squares: 1 mm × 1 mm × 0.1 mm = 0.1 mm³ = 1 × 10⁻⁴ mL
Total viable cells/mL = (Average count per square) × (Dilution Factor) × (10⁴).
Dilution Principles and Common Errors
A 1:5 dilution means 1 part sample + 4 parts diluent.
Original concentration = Count × Dilution Factor × 10⁴.
Common error: forgetting the 10⁴ conversion factor
Trypan Blue Exclusion Principle:
Viable cells exclude the dye and remain clear/unstained.
Non-viable cells take up the dye and appear blue.
% Viability = [Viable / (Viable + Non-viable)] × 100.
Worked example:
A cultured cell suspension was mixed with Trypan Blue for viability assessment. A volume of 20 µL of the cell suspension was mixed with 80 µL of Trypan Blue and loaded onto a haemocytometer. After counting four large squares, a total of 120 unstained (viable) cells and 30 stained (non-viable) cells were observed.
a) Calculate the dilution factor of the cell suspension.
b) Calculate the total number of cells counted.
c) Determine the percentage viability of the cell population.
Step-by-step calculations
a) Dilution Factor (DF)
Given:
- Volume of cell suspension = 20 µL
- Volume of Trypan Blue = 80 µL
Total volume mixed:
Total volume = 20 µL + 80 µL = 100 µL
Dilution Factor is calculated as:
DF = Total volume / Volume of cells
DF = 100 µL / 20 µL
DF = 5 (Dilution factor has no unit)
b) Total number of cells counted
Given:
- Viable (unstained) cells = 120
- Non-viable (stained) cells = 30
Total cells counted:
Total cells = Viable cells + Non-viable cells
Total cells = 120 + 30
Total cells = 150 cells
c) Percentage cell viability
Formula:
% Viability = (Number of viable cells / Total number of cells) × 100
Substitute values:
% Viability = (120 / 150) × 100
% Viability = 0.8 × 100
% Viability = 80%
1.3 Designing Drug Dilution Schemes
Use C1V1 = C2V2.
Intermediate dilutions are required to limit solvent toxicity (e.g., DMSO ≤ 0.1%).
Worked example:
A small-molecule drug is supplied as a 10 mM stock solution prepared in 100% DMSO. The drug will be tested on cultured cells in a final well volume of 2.0 mL. The required final drug concentration is 10 µM, and the final DMSO concentration must not exceed 0.1% (v/v) to avoid solvent toxicity.
a) Calculate the maximum volume of the 10 mM stock that can be added directly to one well without exceeding the 0.1% DMSO limit.
b) Determine whether the target concentration of 10 µM can be achieved by direct dilution from the stock. Show your calculation.
c) Design an appropriate intermediate dilution of the drug using culture medium such that the final concentration of 10 µM can be achieved in the well while maintaining DMSO ≤ 0.1%.
d) Calculate the volume of the intermediate dilution required to prepare one well at the final concentration.
Step-by-step calculations
Given
- Stock drug concentration (C₁, stock) = 10 mM
- Stock solvent = 100% DMSO
- Final desired drug concentration (C₂, final) = 10 µM
- Final well volume (V₂, final) = 2.0 mL
- Maximum allowable DMSO concentration = 0.1% (v/v)
a) Maximum volume of stock allowed by DMSO limit
0.1% (v/v) means:
0.1 mL DMSO per 100 mL solution
For a 2.0 mL well:
Maximum DMSO volume = (0.1 / 100) × 2.0 mL
Maximum DMSO volume = 0.002 mL
Convert to microlitres:
0.002 mL × 1000 µL/mL = 2 µL
Maximum volume of 10 mM stock allowed = 2 µL
b) Can 10 µM be achieved by direct dilution from stock?
Using C₁V₁ = C₂V₂
C₁ = 10 mM
C₂ = 10 µM = 0.01 mM
V₂ = 2.0 mL
Solve for V₁:
V₁ = (C₂ × V₂) / C₁
V₁ = (0.01 mM × 2.0 mL) / 10 mM
V₁ = 0.002 mL
Convert to microlitres:
0.002 mL × 1000 µL/mL = 2 µL
This volume equals the maximum allowable DMSO volume.
Conclusion:
Yes, the target concentration can be achieved, but it is at the upper safety limit for DMSO. To minimize solvent toxicity, an intermediate dilution is recommended.
c) Design of an intermediate dilution
Choose an intermediate concentration that reduces the volume of DMSO added to the final well.
A common choice is a 1 mM intermediate solution.
Preparation of 1 mM intermediate from 10 mM stock
Using C₁V₁ = C₂V₂
C₁ = 10 mM
C₂ = 1 mM
Assume V₂ = 1.0 mL
V₁ = (C₂ × V₂) / C₁
V₁ = (1 mM × 1.0 mL) / 10 mM
V₁ = 0.1 mL = 100 µL
Add:
- 100 µL of 10 mM stock (100% DMSO)
- 900 µL of culture medium
This intermediate contains 10% DMSO.
d) Volume of intermediate needed for final well
Using C₁V₁ = C₂V₂
C₁ = 1 mM
C₂ = 10 µM = 0.01 mM
V₂ = 2.0 mL
V₁ = (C₂ × V₂) / C₁
V₁ = (0.01 mM × 2.0 mL) / 1 mM
V₁ = 0.02 mL
Convert to microlitres:
0.02 mL × 1000 µL/mL = 20 µL
Final DMSO concentration check
- Intermediate contains 10% DMSO
- Volume added = 20 µL
DMSO volume added = 10% × 20 µL = 2 µL
Final DMSO percentage:
(2 µL / 2000 µL) × 100 = 0.1%
This meets the solvent toxicity requirement.