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Statistical modeling of single target cell encapsulation.

Moon S, Ceyhan E, Gurkan UA, Demirci U - PLoS ONE (2011)

Bottom Line: Statistical models can provide an understanding of the underlying processes and estimation of the relevant parameters, and enable reliable and repeatable control over the encapsulation of cells in droplets during the isolation process with high confidence level.We have modeled and experimentally verified a microdroplet-based cell encapsulation process for various combinations of cell loading and target cell concentrations.Here, we explain theoretically and validate experimentally a model to isolate and pattern single target cells from heterogeneous mixtures without using complex peripheral systems.

View Article: PubMed Central - PubMed

Affiliation: Demirci Bio-Acoustic-MEMS in Medicine Laboratory, Center for Bioengineering, Brigham and Women's Hospital, Harvard Medical School, Boston, Massachusetts, United States of America.

ABSTRACT
High throughput drop-on-demand systems for separation and encapsulation of individual target cells from heterogeneous mixtures of multiple cell types is an emerging method in biotechnology that has broad applications in tissue engineering and regenerative medicine, genomics, and cryobiology. However, cell encapsulation in droplets is a random process that is hard to control. Statistical models can provide an understanding of the underlying processes and estimation of the relevant parameters, and enable reliable and repeatable control over the encapsulation of cells in droplets during the isolation process with high confidence level. We have modeled and experimentally verified a microdroplet-based cell encapsulation process for various combinations of cell loading and target cell concentrations. Here, we explain theoretically and validate experimentally a model to isolate and pattern single target cells from heterogeneous mixtures without using complex peripheral systems.

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Schematic notation of random variables and probability distribution functions for statistical analysis.A heterogeneous solution of target and non-target cells is loaded to a droplet ejector. (a) Random cell encapsulation process. (b) Three random variables and one dependent variable were mapped to a patterned array of cell encapsulating droplets which represents number of droplets that contain cells, number of cells per droplet, number of target cells, and droplets encapsulating a single target cell, respectively. The probability of the process can be described as (c) binomial distribution, which represents success and failure corresponding to cell containing and empty droplets, respectively. (d) Poisson distribution is used for the random variable, Xc, since the number of cells per droplet is the count of occurrence of a rare event (i.e., probability of the event is very low) in probability space with respect to the number of sampled droplets and droplet volume. (e) Overall system random process becomes the combined function of suggested PDFs. The PDFs for the random variables, Xd and Xc, are used for the overall PDF of the system. The parameter λ represents the Poisson coefficient, and μ, and σ represent mean, and variance of the underlying probability distributions, respectively. All distribution functions were interpolated to a continuous curve with colored bars on graph indicating the discrete values.
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pone-0021580-g001: Schematic notation of random variables and probability distribution functions for statistical analysis.A heterogeneous solution of target and non-target cells is loaded to a droplet ejector. (a) Random cell encapsulation process. (b) Three random variables and one dependent variable were mapped to a patterned array of cell encapsulating droplets which represents number of droplets that contain cells, number of cells per droplet, number of target cells, and droplets encapsulating a single target cell, respectively. The probability of the process can be described as (c) binomial distribution, which represents success and failure corresponding to cell containing and empty droplets, respectively. (d) Poisson distribution is used for the random variable, Xc, since the number of cells per droplet is the count of occurrence of a rare event (i.e., probability of the event is very low) in probability space with respect to the number of sampled droplets and droplet volume. (e) Overall system random process becomes the combined function of suggested PDFs. The PDFs for the random variables, Xd and Xc, are used for the overall PDF of the system. The parameter λ represents the Poisson coefficient, and μ, and σ represent mean, and variance of the underlying probability distributions, respectively. All distribution functions were interpolated to a continuous curve with colored bars on graph indicating the discrete values.

Mentions: Random variables for cell encapsulation process in droplets were schematically shown in Fig. 1a, b and the setup was described in detail in Supporting Information S1A and Fig. S1. A heterogeneous solution of target and non-target cells is loaded to a droplet ejector. Three random variables represent number of droplets that contain cells, number of cells in a droplet, and number of droplets encapsulating only a single target cell, which are denoted as Xd, Xc, and Xt, respectively, and are defined at the sampling space from droplet array (n = 100 droplets forming a 10×10 array of patterned droplets). These random variables are proposed to have three probability distributions, Binomial, Poisson and a combined distribution, respectively as shown in Fig. 1c–e.


Statistical modeling of single target cell encapsulation.

Moon S, Ceyhan E, Gurkan UA, Demirci U - PLoS ONE (2011)

Schematic notation of random variables and probability distribution functions for statistical analysis.A heterogeneous solution of target and non-target cells is loaded to a droplet ejector. (a) Random cell encapsulation process. (b) Three random variables and one dependent variable were mapped to a patterned array of cell encapsulating droplets which represents number of droplets that contain cells, number of cells per droplet, number of target cells, and droplets encapsulating a single target cell, respectively. The probability of the process can be described as (c) binomial distribution, which represents success and failure corresponding to cell containing and empty droplets, respectively. (d) Poisson distribution is used for the random variable, Xc, since the number of cells per droplet is the count of occurrence of a rare event (i.e., probability of the event is very low) in probability space with respect to the number of sampled droplets and droplet volume. (e) Overall system random process becomes the combined function of suggested PDFs. The PDFs for the random variables, Xd and Xc, are used for the overall PDF of the system. The parameter λ represents the Poisson coefficient, and μ, and σ represent mean, and variance of the underlying probability distributions, respectively. All distribution functions were interpolated to a continuous curve with colored bars on graph indicating the discrete values.
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getmorefigures.php?uid=PMC3140975&req=5

pone-0021580-g001: Schematic notation of random variables and probability distribution functions for statistical analysis.A heterogeneous solution of target and non-target cells is loaded to a droplet ejector. (a) Random cell encapsulation process. (b) Three random variables and one dependent variable were mapped to a patterned array of cell encapsulating droplets which represents number of droplets that contain cells, number of cells per droplet, number of target cells, and droplets encapsulating a single target cell, respectively. The probability of the process can be described as (c) binomial distribution, which represents success and failure corresponding to cell containing and empty droplets, respectively. (d) Poisson distribution is used for the random variable, Xc, since the number of cells per droplet is the count of occurrence of a rare event (i.e., probability of the event is very low) in probability space with respect to the number of sampled droplets and droplet volume. (e) Overall system random process becomes the combined function of suggested PDFs. The PDFs for the random variables, Xd and Xc, are used for the overall PDF of the system. The parameter λ represents the Poisson coefficient, and μ, and σ represent mean, and variance of the underlying probability distributions, respectively. All distribution functions were interpolated to a continuous curve with colored bars on graph indicating the discrete values.
Mentions: Random variables for cell encapsulation process in droplets were schematically shown in Fig. 1a, b and the setup was described in detail in Supporting Information S1A and Fig. S1. A heterogeneous solution of target and non-target cells is loaded to a droplet ejector. Three random variables represent number of droplets that contain cells, number of cells in a droplet, and number of droplets encapsulating only a single target cell, which are denoted as Xd, Xc, and Xt, respectively, and are defined at the sampling space from droplet array (n = 100 droplets forming a 10×10 array of patterned droplets). These random variables are proposed to have three probability distributions, Binomial, Poisson and a combined distribution, respectively as shown in Fig. 1c–e.

Bottom Line: Statistical models can provide an understanding of the underlying processes and estimation of the relevant parameters, and enable reliable and repeatable control over the encapsulation of cells in droplets during the isolation process with high confidence level.We have modeled and experimentally verified a microdroplet-based cell encapsulation process for various combinations of cell loading and target cell concentrations.Here, we explain theoretically and validate experimentally a model to isolate and pattern single target cells from heterogeneous mixtures without using complex peripheral systems.

View Article: PubMed Central - PubMed

Affiliation: Demirci Bio-Acoustic-MEMS in Medicine Laboratory, Center for Bioengineering, Brigham and Women's Hospital, Harvard Medical School, Boston, Massachusetts, United States of America.

ABSTRACT
High throughput drop-on-demand systems for separation and encapsulation of individual target cells from heterogeneous mixtures of multiple cell types is an emerging method in biotechnology that has broad applications in tissue engineering and regenerative medicine, genomics, and cryobiology. However, cell encapsulation in droplets is a random process that is hard to control. Statistical models can provide an understanding of the underlying processes and estimation of the relevant parameters, and enable reliable and repeatable control over the encapsulation of cells in droplets during the isolation process with high confidence level. We have modeled and experimentally verified a microdroplet-based cell encapsulation process for various combinations of cell loading and target cell concentrations. Here, we explain theoretically and validate experimentally a model to isolate and pattern single target cells from heterogeneous mixtures without using complex peripheral systems.

Show MeSH
Related in: MedlinePlus