Central to life functions, protein expression in normal and diseased states is essential for quantifying altered patterns of gene expression. This is especially true in the era that the sequencing of human genome has been finished. To gain insights into protein expression, we have to transfect cells with kinds of expression vectors, based on plasmid, viral vector, or transposon, etc. Transfection may be one of the commonest but indispensable procedures for cellular biology. However, in the process of evolution, eukaryotic cells tend to have low transfection efficiency in order to protect their genomes from exogenous insults. Transfection difficulty manifests itself, especially in the cotransfection of mammalian cells. Theoretically, if the transfection efficiency of single kind of plasmid is E, which ranges from 0 to 1, the efficiency of double and triple cotransfection may decline to E² and E³, respectively. Therefore, it is of great importance to improve efficiency.

In order to enhance the transfection, several kinds of strategies are developed, which are categorized into two types: viral gene delivery carriers and non-viral gene delivery carriers. In non-viral gene delivery carriers, cationic liposomes has the widest application. Cationic liposomes are positively charged liposomes which interact with the negatively charged DNA molecules to form a stable complex. Cationic liposomes consist of a positively charged lipid and a co-lipid. A variety of positively charged lipid formulations are commercially available and many other are under development. Lipofection, one of the most frequently cited cationic lipids, was first reported by Felgner in 1987 to deliver genes to cells in culture [1]. Lipofection has been used to deliver linear DNA, plasmid DNA, and RNA to a variety of cells in culture. Liposomes offer several advantages in delivering genes to cells. (1) Liposomes have the ability to combine both with negatively and positively charged molecules. (2) Liposomes offer a degree of protection to the DNA from degradative processes. (3) Liposomes carry large pieces of DNA, potentially as large as a chromosome. (4) Liposomes can be targeted to specific cells or tissues. In addition, liposomes overcome problems inherent with viral vectors – specific concerns over immunogenicity and replication competent virus contamination. Liposomes resulted in a highly adaptable and flexible system capable of gene delivery both in vitro and in vivo. Current limitations regarding in vivo application of liposomes revolve around the low transfection efficiencies and transient gene expression. Also, liposomes display a small degree of cellular toxicity and appear to be inhibited by serum components. The ability to overcome these problems should greatly facilitate their application to a variety of gene delivery mechanisms.

Several factors have significant effects on the transfection efficiency of cationic liposomes, such as vigor of the host cells, the amount of plasmid, the amount of transfection agent, and the density of cells. However, it is hard to control vigor of host cells which has not a quantitative index. The other three factors are controllable in transfection, which can be adjusted according to the host cells and transfection agents. However, the adjustment of these three factors is a time and energy-consuming work. For most researchers, they may spend two to three months on optimizing transfection. Fortunately, several mathematical methods offer promising avenues to the resolution of this issue.

There are several ways to perform computer experiments, such as Latin Hypercube Sampling (LHS) and Uniform Design (UD). LHS was brought up by three scholars in the North American [2]. Uniform design, abbreviated as UD, was first developed by Fang et al in nineteen eighty [3]. UD seeks design points that are scattered uniformly on the domain. It has been popular since 1980. The main advantages of UD may be generalized as the following: first, it has the ability to greatly reduce the number of experiments while not to alter the representativeness; second, it generates a regression model based on the results and it's able to predict at what independent variables the dependent variable may gain the maximum.

As a relatively new algorithm used for classification and regression, support vector machine (SVM) was developed in the 1990s [4, 5]. It is a desired method for estimation based on finite-sample and therefore is able to solve a lot of practical problems in case of limited samples. Their practical successes may be attributed to solid theoretical foundations based on Vapnik Chervonenkis theory, and to the minimization of structural risk [6]. In order to implement the SVM into our transfection optimization, the least squares support vector machines (LS-SVM) was used, which has a growing popularity for regression problems [7]. It can be argued that LS-SVM would yield better generalization for regression problems on finite samples [8].

As was shown in Table 1 and Figure 1, transfection efficiency varied greatly with the changes of the amount of plasmid, LipofectAMINE, and the number of seeded cells. If these three independent varies did not match, transfection efficiency would decline sharply. In Table 1 and Figure 1, experiment L has the lowest efficiency (13.49%) for the ration of plasmid to transfection agent is too low, while experiment K has the highest efficiency owing to the designed ratios between the three independent factors. According to the established model, transfection efficiency would gain the maximum if 2.1×10⁵ of cells, 0.66 μg of plasmid and 1.32 μg of LipofectAMINE were used. And this was accord with the observed data (Table 2 and Figure 2). More than that, there was a high degree of coincidence between calculated transfection efficiency and the deduced date from the model (Figure 3). Thus, by virtue of UD and LS-SVM, only 15 experiments, which can be performed in two 24-well plates, are needed to get the optimal transfection conditions whereas more than 15³ experiments are needed to attain the expected purpose by using traditional method. What's more, if more accurate conditions were demanded, the number of experiments would greatly exceed 15³.

The discrepancy between the predicted value and their respective observed data was listed in Table 4. From Table 4, it could be find that the maximum of observed data was N7 (92.32%) and the maximum of predicted values based on LS-SVM was also N7 (84.04%). The error ratio between observed data and predicted value of LS-SVM was less than 10%. Thus, LS-SVM has an excellent predicted ability (generalization ability) on our problem. The mutual influence between the predicted value and two of all the three variables was shown in Figure 4, 5 and 6. In a three dimensional surface, each mesh point in the (x, y)-plane stood for a variable combination and the z-axis stood the predicted value. Figure 4, 5 and 6 showed that the change of LS-SVM predicted value on ten test samples was consistent with observed data.

	real observation	predicted value	Net difference	Error ratio
N1	57.25	51.91	5.34	0.093289
N2	63.56	59.86	3.70	0.058202
N3	69.73	67.43	2.30	0.033020
N4	77.64	74.10	3.54	0.045576
N5	83.47	79.38	4.09	0.048986
N6	86.42	82.81	3.61	0.041720
N7	92.32	84.04	8.28	0.089702
N8	85.19	82.81	2.38	0.027934
N9	81.29	79.03	2.26	0.027834
N10	73.61	72.74	0.87	0.011860

The contribution of a specific independent variable was also evaluated. Table 5 showed the average MSE when one specific variable was ignored. As is indicated by Table 5 and Figure 7, 8 and 9, amount of plasmid has the most significant effect on transfection efficiency, followed by amount of LipofectAMINE, while the density of seeded cells has the least effect on transfection efficiency. And this result coincided with our experience.

variable	average predicated value										average MSE
	N1	N2	N3	N4	N5	N6	N7	N8	N9	N10
x1	49.97	57.23	64.16	70.35	75.38	78.91	80.62	80.30	77.82	73.18	47.1928
x2	45.28	47.28	49.62	52.87	57.59	64.22	73.10	84.41	98.16	114.19	504.2573
x3	53.97	60.00	64.44	67.32	68.73	68.79	67.64	65.44	62.37	58.61	225.4837

x1: density of seeded cells; x2: amount of plasmid; x3: amount of LipofectAMINE

Owing to UD, the amount of test points required can be enormously reduced, especially when the experimental region has many factors and multiple levels, while the results that reflect the major characteristics of the experimental system are ensured. As an efficient fractional factorial design, UD has been widely applied in manufacturing, system engineering, pharmaceutics, and natural sciences in the past decades [10–12]. The UD was used in this research to describe factors that significantly influence transfection efficiency to obtain a smaller, more manageable set. To perform a computer experiment, in order to have a wide coverage of the entire design region with a limited number of runs, UD is a good recommendation.

The SVM is a machine learning technique with a strong theoretical foundation that has been used to improve classification accuracy in biological applications [13–19]. The SVM is a maximum margin classifier that can solve non-linear classification problems by learning an optimal separating hyperplane in a higher-dimensional feature space. By use of non-linear kernel functions such as a Gaussian kernel, complex and non-linear decision functions can be learned by the SVM. LS-SVM is a reformulation to standard SVM. It is closely related to regularization networks and Gaussian processes but it additionally emphasizes and exploits primal-dual interpretations from optimization theory. In our experiment, LS-SVM mapped the original input space into a high dimension feature space by a Gaussian kernel and then learns a smoothest hyperplane to fit the training data. From statistical learning theory, it can be expected that this hyperplane would have excellent generalization ability and has minor local extreme value. Together, UD has the ability to greatly reduce the number of experiments while not to alter the representativeness and LS-SVM would yield better generalization for regression problems on finite samples. Thereupon, the integrated application of UD and LS-SVM would have high prediction accuracy and would contribute to transfection optimization.

This paper investigates the integrated application of UD and LS-SVM to transfection, for obtaining precise information on the optimal conditions. Based on our experiments, UD and LS-SVM appear to have high efficiency and perform well even when undergone experiments are extremely scarce. With the established model, we are able to gain the optimal transfection conditions and the highest transfection efficiency that can be reached. Thus, the required time and experiments to improve transfection efficiency can be greatly reduced while the achieved efficiency may even be higher than traditional methods. It seems that LS-SVM has higher accuracy in the prediction of optimal transfection conditions than it does in the prediction of highest transfection efficiency; nevertheless, we usually have higher stringency of the information on optimal transfection conditions. It should be pointed out that the vigor of host cells and the purity of plasmid have crucial effect on the transfection efficiency too. However, these factors are uncontrollable in most settings. Further interpretation of the results obtained from other host cell lines is required. These issues are part of our ongoing research.