Quantitative flow cytometry. Advancing the ability of flow cytometry to serve clinical and research purposes

immunological research, clinical discovery of potential therapeutics, development and approval of drugs and devices, disease diagnosis, and therapeutic treatment and monitoring.
However, the measurements made on different instrument platforms at different times and places often cannot be compared. Such discrepancies between and among measurements accompanied by discrepancies in data analysis procedures introduce uncertainty in diagnostic decisions, and impedes advances in basic science.

http://www.nist.gov/mml/bbd/bioassay/quantitative_flow_cytometry.cfm

substances such as cells, proteins, etc.
By providing quantitative flow cytometry measurement solutions, we ensure that researchers can produce better data, better drugs are developed, and patients get better treatment in a clinical setting.

The objective :

expression levels of surface and intracellular protein biomarkers.

B cells

Follicular
B cells

Immature B + B-1 a cells

computational cost
...

http://www.newsnshit.com/curse-of-dimensionality-interactive-demo/

Projection Pursuit

merging (DBM)

0
identity of indiscernibles d(x,y) = 0, if and only if x = y
symmetry d(x,y) = d(y,x)
triangle inequality d(x,z) ≤ d(x,y) + d(y,z)
be robust with respect to small changes
be non-parametric
be computationally efficient

Goals:
quantitate differences between samples and provide a standard error
identify changes in joint expression of multiple markers
appropriately rank test samples based on the amount of deviation from controls

Quantification index allows biologically informative interpretation

and Overton Subtraction (Sheskin, 2000)
Recent methods can be applied to multivariate flow cytometry
Probability Binning (Roederer et al., 2001)
Frequency Difference Gating (Roederer and Hardy, 2001)
Cytometric Fingerprinting (Rogers et al., 2008)
Quadratic Form Metric (Bernas et al., 2008)

How different are samples?
With respect to both the proportion of cells whose marker expression has changed and the magnitude of the change

Most of the current methods ask “Do samples differ?”

further from the center of the other

into the other where the cost is the amount of dirt moved times the distance by which it is moved

The biological interpretation of the EMD between two flow cytometry samples includes both the proportion of cells whose marker expression has changed and the magnitude of the change

Earth mover's distance (EMD)

where
pi,qi are bin centroids with frequencies wpi,wqi,
D = [dij] is the matrix of Euclidean distances between pi and qj for all i,j.
Find a flow F = [fij] between pi and qj that minimizes the total cost:

The optimal flow F between the source and destination signatures is determined by solving the linear programming problem.
EMD is then defined as a function of the optimal flow F=[fij] and the ground distance D=[dij]

Data were binned into the groups used in the signature according to (Roederer et al., 2001)

Earth mover's distance (EMD)
in terms of a linear programming problem

aspergillosis (ABPA) in CF

Surface CD203c in blood basophils after ex vivo stimulation with A. fumigatus (Af) allergen/extract (offending) or peanut (non offending) allergen. Gernez et al. J Cyst Fibros 11:502-10, 2012

Blood basophils from patients with ABPA are hyper-responsive to stimulation by Af allergen

Antibiotics

Corticosteroids
Anti-fungal
medicines

stimulation with the A. fumigatus allergen/extract

Total white blood cells (FSС-A/SSC-A)→singlets (FSС-A/FSC-H)→CD41a--live (CD41a/live/dead)→
Dump--CD123++ (CD3, CD66b, HLA-DR/CD123)

more accurately distinguish allergic (CF-ABPA) from non-allergic (CF) patients

value of the binding rate constant for each particular monoclonal antibody-antigen reaction measured with flow cytometry

Antigen-antibody interactions on the surface of cells

blood
sample (fix)

Antibody*

of cell

Mathematical model: kinetic of mean fluorescence

Reaction rate constant
Initial antibody concentration
n – binding sites per one bead/cell

K+

A0

FcgRIIIb receptors for different donors

The total number of cells is the same for each histogram

allowing predicting the binding rate constant for changes in experimental conditions.
We verify our theoretical approach comparing the results to experimentally measured binding rate constants for classical examples of monoclonal antibody-antigen interactions under different temperature regimes.

However, application of such rate constant approach is currently limited by the lack of measured binding rate constant values for most antigen-antibody pairs of interest and changes in experimental conditions (temperature, viscosity, fluorescent labels, etc.)

the radius b of the binding site (a circular approximation of the shape of the site placed on a spherical reagent) using following expression

where η is the viscosity of the media, kB is the Boltzmann constant, T is the temperature; R1 and R2 are radii, N1 and N2 are valences of the first and second reactants, correspondingly.

The radius of antibody molecules can be estimated from the diffusion coefficient using Stokes–Einstein equation :

On the other hand, the diffusion coefficient of the molecule can be estimated using the known relationship between the diffusion coefficient (in cm2 s-1) and the molar mass (in Da), M, of a protein (in water at room temperature)

radii for 6 antigen-antibody complexes at room temperature

temperature are in good agreement with published empirical binding rate constants for different temperature regimes

93-219 (1977).

Electrical analogue

capacitance

“Effective binding site” radius (b) can be calculated using the following expression:

where a and c are maximum length and maximum width (assuming a>c) of dominant amino acid residuals respectively (e.g. can be determine using HyperChem 7.5 software)

binding site radii calculated using empirical rate constant values

temperature are in good agreement with published empirical binding rate constants for different temperature regimes

*

Room B013
279 Campus Drive, Stanford, CA 94305
orlova@stanford.edu

al., 1999
I5] Ito et al., 1995
[6] Raman et al., 1992
[7] Nekrasov VM et al., 2014
[8] Ibrahim, M., et al., 1998.
[9] Wibbenmeyer et al., 1999
[10] Sheriff et al., 1987
[11] Chacko et al., 1996
[12] Kam-Morgan et al., 1993
[13] Novotny, 1991
[14] Padlan et al., 1989
[15] Dall’Acqua et al., 1998
[16] Pierce et al., 1999

Calculate % frequency for each cluster. Find the most separated (based on SC) pair of clusters with highest % frequency (cluster a and b).

2. Assign all other clusters on this 2D plot either to cluster a or cluster b based on SC.

a

b

3. Now you have only two clusters A and B (for each possible 2D plot).

4. Calculate SC between A and B. Calculate % frequency for A and B. Now you can rank all possible 2D plots based on then SC and % frequency distribution between A and B. On the first place should be 2D plot with SC closest to 1 and % frequency distribution closest to 50/50 between A and B.

5. Pick A or B from most highly ranked 2D plot, project A(or B) to all possible 2D plots and proceed recursively with the same procedure (1-5).

water solution