Multivariate Statistical Optimization of a Modified Protocol of the Ionic Polyelectrolyte Pre-Gelation Method to Synthesize Alginate–Chitosan-Based Nanoparticles

Abstract

Alginate [ALG] and chitosan [CS] are biomaterials of importance in drug-delivery because of their ability to form ionically-crosslinked nanosystems and polyelectrolyte-complexes under mild conditions. Here, a modified ionic-polyelectrolyte-pre-gelation method, with a controlled addition of reagents and sonication throughout the process, is reported to produce ALG¬¬-CS-based NPs. A mathematical study of the effects of the factors with influence in the process on the properties of NPs has been performed using a two-phase-design-of-experiment-based procedure, something never done to our knowledge. The concentration of ALG, CS and CaCl₂ and the ratio ALG:CS have significant influence on polydispersity (PDI), surface-charge (ZP) and encapsulation efficiency (EE%) of NPs. Moreover, CS flow rate has a significant effect over PDI and EE%. Thus, the values of ALG, CS and CaCl₂ concentration (mg/mL), ALG:CS (mL:mL) and CS flow rate (mL/min) to obtain the minimum-expected PDI (0.168) or the optimized EE% (86.7) are {0.30, 0.79, 1.00, 2.50:1.00, 0.86} or {0.30, 1.00, 1.00, 2.50:1.00, 2.00}, with ALG:CaCl₂ (mL:mL) and CaCl₂ flow rate (mL/min) fixed at 2.50:0.31 and 1.25. Although most of the conditions yielded highly-negative particles (minimum-expected of −67.8 mV using 0.69, 0.30 and 0.13 mg/mL of ALG, CS and CaCl₂ and ALG:CS of 2.50:0.59 mL:mL), varying the mass ratio of ALG:CS allowed for the generation of positively-charged particles (up to +21.1 mV with 0.30, 1.00 and 0.61 mg/mL of ALG, CS and CaCl₂ and ALG:CS of 2.50:1.00 mL:mL). In both cases, ALG:CaCl₂ (mL:mL), CaCl₂ and CS flow rates (mL/min) were fixed at 2.50:0.31, 1.25 and 1.25. The model for the NPs size depends only on CS and CaCl₂ concentrations, with the minimum- or maximum-expected (160 or 635 nm) at 0.30 and 1.00 or 1.00 and 0.30 of CS and CaCl₂, although the method allows a wide range of sizes (144.0–1965.0 nm).

1. Introduction

The use of natural biopolymers, mainly polysaccharides like alginate (ALG) and chitosan (CS), in the formulation of drug delivery systems is a practice commonly addressed by the scientific community since these biomaterials can be easily obtained from natural sources, showing low immunogenicity and toxicity and excellent biocompatibility/biodegradability, and, more importantly, they allow the synthesis of nanocarriers by mild-based techniques that avoid the use of organic solvents and high temperatures [1,2,3,4]. In this regard, the ionic gelation-based methods easily generate ionically crosslinked nanosystems by the simple interaction of the carboxyl groups of ALG or the amine groups of CS with counterions, such as calcium chloride (CaCl₂) or sodium tripolyphosphate (TPP), respectively [2,5,6]. Furthermore, the combination of the functional groups of ALG and CS allows the generation of polyelectrolyte complexes [7,8]. The incorporation of CS to ALG-based nanoparticles has been reported to slow down the drug release from the porous ALG matrix and stabilize and reinforce the nanosystem [2,9]. In any case, many authors have demonstrated the convenience of incorporating both biomaterials, ALG and CS, in the formulation of drug nanocarriers to take advantage of the synergies generated between both materials in terms of entrapment efficiency and controlled drug release [2,5,6,10].

Some authors have described two-step synthesis processes to prepare ALG–CS-based nanoparticles (ALG-CS NPs) by means of the ionic polyelectrolyte pre-gelation technique, which is mainly based on the generation of ALG pregels with Ca²⁺ ions (CaCl₂) that are further stabilized with CS to form polyelectrolyte complexes [5,6,7,9,11,12,13,14,15,16]. This methodology, which was first described in 1993 by the group of Prof. Couvreur [17], using poly-L-lysine as polycation, has evolved to enhance the properties of the nanoparticles and adapt the formulations to entrap different therapeutic molecules. However, a complete mathematical analysis to study how all the variables that are involved in the process of the synthesis affect their main characteristics (size, polydispersity and surface charge) has not yet been performed. Still, some authors have reported statistical studies to partially optimize this synthesis process. Thus, Kushwaha & Dwivedi [18] performed a 3² factorial design to observe the effect of ALG and CS concentrations on the mean particle size, surface charge (ZP) and encapsulation efficiency (EE%). Later, Zohri et al. [12] studied the effect of the CS:ALG ratio, the pH of CS and the stirring rate on the mean size, polydispersity (PDI), ZP, EE%, cumulative release and morphological degradation time of the particles, using a response surface methodology with a Box–Behnken design. Similarly, Kohli et al. [13] used a Box–Behnken statistical analysis to investigate the effect of three variables (CS, ALG and CaCl₂ concentrations) on mean size, PDI and ZP of the nanoparticles generated.

In this work, for the first time, a two-step design of experiments (DoE) methodology has been carried out to detect all the factors that can influence the ionic polyelectrolyte pre-gelation method to generate ALG–CS NPs, which was enhanced by introducing the controlled addition of reagents and sonication throughout the process to improve mixing of phases. Statistical methodology consists of an initial screening to remove the non-influential factors and a subsequent response surface methodology (RSM) to find the dependence of multiple response variables (size, PDI, ZP and EE%) on the influential factors of the synthesis process. The effects of these factors on the responses have been studied to provide the optimal conditions of synthesis (minimum PDI and maximum EE%) and the correlations between the influential factors and the responses size and ZP.

2. Materials and Methods

2.1. Materials

Alginate acid sodium salt (ALG) from brown algae (medium viscosity, ≥2000 cP, 2% at 25 °C), bovine serum albumin (BSA) and calcium chloride (CaCl₂) were provided by Sigma-Aldrich (Merck KGaA, St. Louis, MO, USA). Chitosan lactate (CS) from crustaceans (low viscosity, <200 cP, 1% at 25 °C, degree of deacetylation ≤ 95%) was acquired from ChitoLytic (Toronto, ON, Canada). All solutions were prepared employing purified water. Bradford’s solution for protein determination was acquired from PanReac AppliChem (Barcelona, Spain).

2.2. Synthesis and Characterization of Alginate-Chitosan Nanoparticles (ALG-CS NPs)

ALG–CS NPs were prepared in two steps by the ionic polyelectrolyte pre-gelation method described by Loquercio et al. [5], but with important modifications, such as the controlled addition of the reagents by means of a syringe pump and the use of sonication for mixing the phases during the whole procedure. Briefly, an ALG pregel was generated by adding an aqueous solution of CaCl₂ (0.13–1.00 mg/mL, pH: 6.8, µ: 30 mM) to an acidic (pH 3.7) aqueous ALG solution (0.30–1.00 mg/mL, µ: 5 mM), under sonication (55 W, amplitude: 20%, Q55, QSONICA LLC, Newtown, CT, USA) and with a controlled flow rate from 0.50 to 2.00 mL/min, using a syringe pump (Legato 110, Kd Scientific, Holliston, MA, USA). Subsequently, an aqueous CS solution (0.30–1.00 mg/mL, pH: 4.0, µ: 3 mM) was added to the previously generated ALG pregel under sonication at different flow rates (0.50–2.00 mL/min) using a syringe pump. Apart from the reagent concentrations and flow rates, the volume ratios ALG:CS and ALG:CaCl₂ were varied, using a fixed volume of ALG of 2.50 mL and varying the volumes of CS, from 0.25 to 1.00 mL, and CaCl₂, from 0.16 to 0.46 mL. BSA-loaded ALG–CS NPs were prepared following the above process but adding the protein in the CaCl₂ solution at a concentration ranging from 1.00 to 2.90 mg/mL. All ALG–CS NPs generated were isolated by centrifugation (19,000 RCF, 30 min). A scheme of the synthesis process is shown in Figure 1.

Once prepared, the ALG–CS NPs were characterized in terms of size and polydispersity (polydispersity index, PDI) by dynamic light scattering (DLS), and surface charge (Z Potential, ZP) by electrophoretic light scattering (ELS) (Zetasizer NanoZS, Malvern Panalytical, UK) in Servicio General de Apoyo a la Investigación of Universidad de La Laguna (SEGAI-ULL). The encapsulation efficiencies (EE%) of the nanoparticles were determined, using BSA as a model protein, with the Bradford protein assay, comparing the absorbance of each sample to a standard curve constructed by a set of protein standards, at 595 nm using a microplate reader (Infinite 200, Tecan Trading AG, Männedorf, Switzerland).

2.3. Experimental DoE Design and Statistical Analysis

A two-step DoE procedure was performed to detect the factors that may have influence on the synthesis process, estimate their effects and obtain the relation between factors and the set of responses (mean size, PDI, ZP and EE%), allowing the optimal synthesis conditions of the ALG–CS NPs to be obtained. Initially a screening approach was used to remove the non-influential factors, using two-level fractional factorial designs with maximal resolution to reduce the number of experiments and at the same time avoid the confusion of main factors with low-level interactions. Once the most important factors were identified, a response surface methodology (RSM) was performed to obtain second-order models that fit approximately the dependence of the response variables on the influential factors of the synthesis process. ANOVA methods were used to detect significant effects at the different stages of the procedure, using SPSS v.22 and Mathematica 13.2 software. The computation of the optimal conditions for maximizing/minimizing the responses was done by employing the corresponding RSM methods and numerical procedures with Mathematica.

3. Results and Discussion

3.1. Synthesis Approach to Obtain ALG-CS NPs by a Modified Ionic Polyelectrolyte Pregelation Method

The polyelectrolyte pre-gelation method permits to obtain ALG-CS-based NPs by using only three biocompatible reactants, ALG, CS and CaCl₂, avoiding the organic solvents and the emulsification steps, which are commonly used in the synthesis of nanoparticles but can endanger the integrity of encapsulated bioactive molecules [5,7,13]. As mentioned above, the addition of the polyelectrolyte complexation with CS to the ionotropic gelation reaction allows for improved controlled drug delivery and strengthens the integrity of the ALG-based nanosystem [9]. The literature suggests that pre-gelation of ALG with CaCl₂ is required for ionic interaction between CaCl₂, ALG and CS to take place, which will result in stable nanoparticles [5,13]. Thus, considering the standard ionic polyelectrolyte pre-gelation method, concentrations and volume ratios of all the reagents (ALG, CS and CaCl₂) can be identified as the main factors that can affect this synthesis process. Moreover, as far as we know to date, in this technique the addition of CaCl₂ and CS has been done dropwise, without controlling flow rates, so the use of syringe pumps to do that seems to be an interesting improvement to the conventional methodology, being their flow rates two new variables to take into account. It should be noted that a controlled addition of reagents, with stable and reproducible flow rates, is reflected in a better mixing of phases with a tight control on the gelation process, resulting in more uniform and reproducible conditions [19,20]. According to these facts, seven factors were identified with possible influence in this synthetic process. After some preliminary tests and a deep literature review, the levels of these seven factors were set as distant as possible to be able to determine the significance of them but allowing the correct generation of the ALG–CS NPs (

Table 1. Factors and levels considered for the modified ionic polyelectrolyte pregelation method.

Levels	[ALG] (mg/mL)	[CS] (mg/mL)	[CaCl2] (mg/mL)	ALG:CS (mL:mL)	ALG:CaCl2 (mL:mL)	CaCl2 FR (mL/min)	CS FR (mL/min)
−1	0.30	0.30	0.13	2.50:0.25	2.50:0.16	0.50	0.50
+1	1.00	1.00	1.00	2.50:1.00	2.50:0.46	2.00	2.00

ALG: alginate; CS: chitosan; CaCl₂: calcium chloride; FR: flow rate; −1: low level; +1: high level. Note that ALG:CS molar ratios (mol:mol) are: (−1): 12.7:1.0 and (+1): 3.2:1.0, and ALG:CaCl₂ molar ratios (mol:mol) are: (−1): 20.2:1.0 and (+1): 3.1:1.0, considering molecular weights of the repeating units of sodium ALG and CS lactate (degree of deacetylation ≤ 95%).

). Note that the general ranges for the levels were initially selected through a literature search, and were experimentally fixed considering all factors and using particle formation as the general criteria. Outside of the levels shown in Table 1, visible precipitates and/or aggregates in the micron range were obtained.

Furthermore, although sonication has been used by some authors in this procedure, it has generally been applied to the generated nanoparticles to avoid their aggregation, i.e., it is used after the mixing of the phases by magnetic stirring [5,7,13]. However, sonication throughout the synthesis process can improve mixing, both during pregel formation and in the subsequent polyelectrolyte complexation between ALG and CS, achieving more homogeneous and smaller particles [21]. Note that the local shear and cavitation generated by ultrasonication break the possible gelled aggregates and can influence the gelation reaction, reducing the hydrodynamic diameter of nanoparticles and narrowing their size distribution [22,23]. This claim was demonstrated by the values of size and PDI obtained when synthesizing ALG–CS NPs under ultrasonication or using magnetic stirring (

Table 2. Values of size and PDI for several conditions, using sonication or magnetic stirring.

	Experimental Conditions							Responses by Mixing Technique
								Sonication		Mag.stir.
	[ALG] (mg/mL)	[CS] (mg/mL)	[CaCl2] (mg/mL)	ALG:CS (mL:mL)	ALG:CaCl2 (mL:mL)	FR (mL/min) CaCl2 CS		Size (nm)	PDI (0–1)	Size (nm)	PDI (0–1)
1	0.30	1.00	1.00	2.50:0.25	2.50:0.16	0.50	2.00	281.1	0.298	525.0	0.383
2	0.30	0.30	1.00	2.50:0.25	2.50:0.46	2.00	2.00	278.6	0.258	520.9	0.352
3	1.00	1.00	0.13	2.50:1.00	2.50:0.16	0.50	0.50	524.0	0.482	1554.0	0.704
4	1.00	1.00	1.00	2.50:1.00	2.50:0.46	2.00	2.00	572.1	0.550	1652.0	0.834
5	0.30	1.00	1.00	2.50:1.00	2.50:0.16	2.00	0.50	656.1	0.297	1629.0	0.924

ALG: sodium alginate; CS: chitosan lactate; CaCl₂: calcium chloride; FR: flow rates; Mag.stir.: magnetic stirring; PDI: polydispersity index.

). Therefore, sonication was included in both stages of the synthesis process, not adding this factor to the other seven already considered since it was fixed because it meant a significant improvement in the process of synthesis.

As can be seen in

Table 3. Values of response variables (size, PDI, ZP, EE%) as a function of the levels of the factors.

	Factors and Their Values							Responses
	[ALG] (mg/mL)	[CS] (mg/mL)	[CaCl2] (mg/mL)	ALG:CS (mL:mL)	ALG:CaCl2 (mL:mL)	FR (mL/min) CaCl2 CS		Size (nm)	PDI (0–1)	ZP (mV)	EE% (%)
1	0.30	0.30	0.13	2.50:1.00	2.50:0.16	2.00	2.00	191.6	0.279	−38.5	77.1
2	0.30	0.30	0.13	2.50:1.00	2.50:0.46	2.00	2.00	144.0	0.262	−31.4	60.4
3	0.30	0.30	0.13	2.50:0.25	2.50:0.16	2.00	2.00	183.2	0.303	−46.4	72.1
4	0.30	0.30	0.13	2.50:0.25	2.50:0.46	2.00	2.00	146.2	0.293	−44.1	42.2
5	0.30	0.30	1.00	2.50:1.00	2.50:0.16	2.00	2.00	267.9	0.265	−25.6	89.4
6	0.30	0.30	1.00	2.50:1.00	2.50:0.46	2.00	2.00	332.9	0.204	−19.6	62.0
7	0.30	0.30	1.00	2.50:0.25	2.50:0.16	2.00	2.00	276.7	0.306	−33.6	76.4
8	0.30	0.30	1.00	2.50:0.25	2.50:0.46	2.00	2.00	292.9	0.243	−29.2	72.8
9	0.30	1.00	0.13	2.50:1.00	2.50:0.16	2.00	2.00	1965.0	0.563	14.0	99.6
10	0.30	1.00	0.13	2.50:1.00	2.50:0.46	2.00	2.00	1026.0	0.381	17.0	99.3
11	0.30	1.00	0.13	2.50:0.25	2.50:0.16	2.00	2.00	240.8	0.371	−39.5	77.0
12	0.30	1.00	0.13	2.50:0.25	2.50:0.46	2.00	2.00	169.9	0.322	−43.1	62.5
13	0.30	1.00	1.00	2.50:1.00	2.50:0.16	2.00	2.00	627.9	0.345	18.2	99.1
14	0.30	1.00	1.00	2.50:1.00	2.50:0.46	2.00	2.00	595.6	0.229	32.0	98.8
15	0.30	1.00	1.00	2.50:0.25	2.50:0.16	2.00	2.00	261.2	0.389	−37.6	83.3
16	0.30	1.00	1.00	2.50:0.25	2.50:0.46	2.00	2.00	403.9	0.227	−24.5	81.1
17	1.00	0.30	0.13	2.50:1.00	2.50:0.16	2.00	2.00	724.7	0.584	−78.1	27.4
18	1.00	0.30	0.13	2.50:1.00	2.50:0.46	2.00	2.00	485.4	0.609	−55.9	0.1
19	1.00	0.30	0.13	2.50:0.25	2.50:0.16	2.00	2.00	481.4	0.787	−69.4	23.2
20	1.00	0.30	0.13	2.50:0.25	2.50:0.46	2.00	2.00	361.8	0.969	−54.6	5.0
21	1.00	0.30	1.00	2.50:1.00	2.50:0.16	2.00	2.00	404.1	0.589	−68.1	14.6
22	1.00	0.30	1.00	2.50:1.00	2.50:0.46	2.00	2.00	339.1	0.587	−56.0	19.4
23	1.00	0.30	1.00	2.50:0.25	2.50:0.16	2.00	2.00	342.8	0.852	−65.4	39.3
24	1.00	0.30	1.00	2.50:0.25	2.50:0.46	2.00	2.00	555.6	0.606	−45.1	34.6
25	1.00	1.00	0.13	2.50:1.00	2.50:0.16	2.00	2.00	704.4	0.539	−59.0	41.5
26	1.00	1.00	0.13	2.50:1.00	2.50:0.46	2.00	2.00	663.9	0.540	−61.9	24.6
27	1.00	1.00	0.13	2.50:0.25	2.50:0.16	2.00	2.00	954.3	0.913	−64.9	29.3
28	1.00	1.00	0.13	2.50:0.25	2.50:0.46	2.00	2.00	804.5	0.928	−63.8	12.1
29	1.00	1.00	1.00	2.50:1.00	2.50:0.16	2.00	2.00	559.9	0.579	−55.1	44.1
30	1.00	1.00	1.00	2.50:1.00	2.50:0.46	2.00	2.00	511.2	0.438	−35.2	89.0
31	1.00	1.00	1.00	2.50:0.25	2.50:0.16	2.00	2.00	477.6	0.943	−61.9	31.0
32	1.00	1.00	1.00	2.50:0.25	2.50:0.46	2.00	2.00	453.7	1.000	−49.1	25.0

ALG: sodium alginate; CS: chitosan lactate; CaCl₂: calcium chloride; FR: flow rates; PDI: polydispersity index; ZP: Z Potential (surface charge); EE%: encapsulation efficiency.

, the modification of the factors considered, at the contemplated levels, allowed for the obtaining of ALG–CS NPs of very different mean sizes, which ranged from 144.0 to 1965.0 nm. Some experimental conditions (e.g., low concentration of ALG) permitted to achieve PDI values below 0.4, but, in most cases, this acceptable range of values was not obtained, so polydispersity should be a response to being minimized. The values of ZP showed that the surface charge of nanoparticles was mostly highly negative due to the carboxylic groups of ALG, except in cases where the proportion of CS was much higher than ALG. Regarding EE%, the values obtained were very much dependent on the levels of the factors, but reaching values as high as 99.6%, making this another response to be optimized, taking into account the values of the rest of the responses. The dispersion graphs of the four response variables are shown in Figure 2.

3.2. Two-Step DoE Statistical Analysis and Optimization

3.2.1. Screening Methodology

The factors with influence on the response variables were determined by a screening procedure using a main-effect model, i.e., containing just the effects of the seven factors and the constant term (eight parameters). A Plackett–Burman design was initially considered, but, after a thorough revision of the specialized literature, it was discarded to avoid confusion between the main effects and the two-factor interactions [24]. A 2_IV^7-3 fractional design, with maximum resolution and minimum aberration, was chosen, considering only 2 extreme values for each factor, −1 (low level) and +1 (high level), to reduce the number of experiments. When using this design, the main effects would be confounded, in the worst scenario, with three-factor or higher interactions (resolution 4) and the number of low-order interactions confounded is minimized. The complete defining relation is given at the end of Appendix A.

Table 4. Design matrix for the 2_IV^7-3 fractional design (screening procedure), including factors, levels and response values.

	Factors and Their Values							Response Variables
	x[1]	x[2]	x[3]	x[4]	x[5]	x[6]	x[7]	Size (nm)	PDI	ZP (mV)	EE% (%)
y[1]	−1	−1	−1	−1	−1	−1	−1	104.7	0.484	−52.4	20.3
y[2]	+1	−1	−1	−1	+1	−1	+1	434.0	0.839	−52.1	6.0
y[3]	−1	+1	−1	−1	+1	+1	−1	152.1	0.525	−50.2	25.0
y[4]	+1	+1	−1	−1	−1	+1	+1	901.3	1.000	−63.7	21.5
y[5]	−1	−1	+1	−1	+1	+1	+1	278.6	0.258	−23.0	69.3
y[6]	+1	−1	+1	−1	−1	+1	−1	296.9	0.917	−47.4	26.2
y[7]	−1	+1	+1	−1	−1	−1	+1	281.1	0.298	−32.5	78.0
y[8]	+1	+1	+1	−1	+1	−1	−1	353.9	0.582	−46.5	24.6
y[9]	−1	−1	−1	+1	−1	+1	+1	168.6	0.326	−42.1	81.4
y[10]	+1	−1	−1	+1	+1	+1	−1	354.7	0.545	−66.4	16.4
y[11]	−1	+1	−1	+1	+1	−1	+1	1886.0	0.687	8.7	99.2
y[12]	+1	+1	−1	+1	−1	−1	−1	524.0	0.482	−52.8	47.2
y[13]	−1	−1	+1	+1	+1	−1	−1	347.3	0.211	−22.1	85.0
y[14]	+1	−1	+1	+1	−1	−1	+1	393.2	0.617	−53.5	22.9
y[15]	−1	+1	+1	+1	−1	+1	−1	656.1	0.297	19.5	99.4
y[16]	+1	+1	+1	+1	+1	+1	+1	572.1	0.550	−41.9	82.6

x[1]: ALG concentration (mg/mL); x[2]: CS concentration (mg/mL); x[3]: CaCl₂ concentration (mg/mL); x[4]: ALG:CS volume ratio (mL:mL); x[5]: ALG:CaCl₂ volume ratio (mL:mL); x[6]: CaCl₂ flow rate; x[7]: CS flow rate; PDI: polydispersity index; ZP: Z Potential; EE%: encapsulation efficiency; y[1]–y[16]: number of runs.

shows the design matrix for the experiments and the values of the responses obtained in this step, highlighting that experiments were performed by two operators in a random order (although, when using these observations, it was checked that the operator had no effect on the responses). For the detailed results of the screening procedure see Appendix A.

In order to use all the available information, apart from data from Table 4, the preliminary experiments that were performed at the final levels of the factors (Table 3) were also considered in the screening procedure. It should be noted that many preliminary experiments were done to define the actual levels for the factors (assuring the correct generation of the ALG–CS NPs), with only those experiments that were performed at the final levels of the factors (as stated in Table 1) being shown in Table 3. The preliminary experiments of Table 3 were conducted under the same conditions as the ones obtained from the 2_IV^7-3 fractional design of Table 4. When preliminary experiments were considered in the analysis, the results found the operator’s influence significant in two of the responses, reducing the unexplained variability. Therefore, it is possible to talk about a ‘training effect’ since the operator’s influence is observed just in the preliminary experiments performed to define the factor levels, but not in the experiments performed later, designed to evaluate the factor’s influence and fitting the models for the responses.

Results indicated that the four first factors (ALG, CS and CaCl₂ concentrations and ALG:CS volume ratio) seem to have influence in at least one response variable, while ALG:CaCl₂ volume ratio and CaCl₂ flow rate show very little importance, and CS flow rate does not provide clear conclusions (see Appendix A. Detailed Results of the Screening Procedure). It is important to highlight that the last two factors (CaCl₂ and CS flow rates) were always observed at a constant level in the preliminary experiments (Table 3), so those experiments do not provide information about how the variation of the two factors may affect responses, maintaining uncertainty in the model about CS flow rate. Therefore, for all this, the reasonable proposal is the removal of factors 5 (ALG:CaCl₂ volume ratio) and 6 (CaCl₂ flow rate).

3.2.2. Response Surface Methodology

After identifying the factors with influence in the modified ionic polyelectrolyte pre-gelation synthesis method, the non-influential ones were removed from the model, which in the experimental language means that from this moment on the following experiments were performed for fixed values of these factors. A Response Surface Methodology (RSM) was applied to the remaining five factors to obtain approximate models for all the response variables (mean size, PDI, ZP and EE%). A new central level, “0” in coded variables, was added for every factor to use central and axial observations. In natural variables, this approach means taking observations at the mean of the extreme levels of the factor.

Table 5. Factors and levels used in the RSM procedure for the natural and coded variables.

Levels	[ALG] (mg/mL)	[CS] (mg/mL)	[CaCl2] (mg/mL)	ALG:CS (mL:mL)	ALG:CaCl2 (mL:mL)	CaCl2 FR (mL/min)	CS FR (mL/min)
−1	0.30	0.30	0.13	2.50:0.25	2.50:0.31	1.25	0.50
0	0.65	0.65	0.57	2.50:0.63			1.25
+1	1.00	1.00	1.00	2.50:1.00			2.00

ALG: alginate; CS: chitosan; CaCl₂: calcium chloride; FR: flow rate; +1: high level; 0: center level; −1: low level. Note that ALG:CS molar ratios (mol:mol) are: (−1): 12.7:1.0; (0): 5.1:1.0; (+1): 3.2:1.0; and ALG:CaCl₂ molar ratio (mol:mol) for the central level (0) is: 5.2:1.0, considering molecular weights of the repeating units of sodium ALG and CS lactate (degree of deacetylation ≤ 95%).

includes the new configuration of the levels of the factors, where the removed factors are fixed at the corresponding central level in the forthcoming experiments.

As previously mentioned, when fixing the levels of factors, those were taken as distant as possible, as long as they allowed for proper generation of nanoparticles, so the experimental region is cuboidal. Initially, a first order model was proposed to perform the Steepest Ascent Method, but the existence of curvature discarded this simple model. Then, full quadratic models were fitted to all the response variables using the least squares method, for which central and axial points in the faces of the hypercube were added to the full factorial design to create a non-rotatable Central Composite Design (CCD) for the procedure. Note that, when possible, rotatable designs are preferred since for these designs the variance of the prediction of the responses at a certain point (for specific conditions of the factors) only depends on the point’s distance to the center, that is, this variance is constant on spheres. However, to achieve this the nonzero coordinate of the axial points should be 2^5/4 > 1, which means that the observations should be taken out of the limits of the experimental region, and that is not possible since the limits of this region have been fixed at the extreme feasible values of the factors for the particle to be formed.

Table 6. CCD and experimental values of responses for RSM procedure (2⁵ factorial design).

	Factors					Response Variables
	x[1]	x[2]	x[3]	x[4]	x[7]	Size (nm)	PDI	ZP (mV)	EE% (%)
y[1]	−1	−1	−1	−1	−1	252.4	0.480	−51.4	17.5
y[2]	+1	−1	−1	−1	−1	451.0	0.727	−56.6	6.3
y[3]	−1	+1	−1	−1	−1	280.1	0.498	−44.1	22.8
y[4]	+1	+1	−1	−1	−1	892.8	0.617	−38.0	18.1
y[5]	−1	−1	+1	−1	−1	198.3	0.508	−34.7	12.6
y[6]	+1	−1	+1	−1	−1	340.8	0.815	−43.1	24.7
y[7]	−1	+1	+1	−1	−1	280.2	0.308	−23.3	33.8
y[8]	+1	+1	+1	−1	−1	381.8	0.640	−43.2	18.6
y[9]	−1	−1	−1	+1	−1	243.6	0.349	−48.5	3.8
y[10]	+1	−1	−1	+1	−1	433.7	0.483	−43.9	14.9
y[11]	−1	+1	−1	+1	−1	458.5	0.271	13.2	99.8
y[12]	+1	+1	−1	+1	−1	537.8	0.405	−47.1	37.5
y[13]	−1	−1	+1	+1	−1	224.1	0.269	−22.6	83.6
y[14]	+1	−1	+1	+1	−1	339.5	0.493	−4.9	19.4
y[15]	−1	+1	+1	+1	−1	398.5	0.167	17.7	99.9
y[16]	+1	+1	+1	+1	−1	467.9	0.356	−44.8	42.6
y[17]	−1	−1	−1	−1	+1	225.1	0.382	−46.3	41.4
y[18]	+1	−1	−1	−1	+1	484.5	0.779	−74.9	2.3
y[19]	−1	+1	−1	−1	+1	363.7	0.503	−58.5	60.2
y[20]	+1	+1	−1	−1	+1	821.0	0.890	−58.9	11.8
y[21]	−1	−1	+1	−1	+1	192.8	0.333	−29.9	70.2
y[22]	+1	−1	+1	−1	+1	391.5	0.814	−29.5	43.7
y[23]	−1	+1	+1	−1	+1	311.2	0.406	−36.5	79.4
y[24]	+1	+1	+1	−1	+1	583.9	0.897	−45.4	44.1
y[25]	−1	−1	−1	+1	+1	221.8	0.351	−46.2	64.3
y[26]	+1	−1	−1	+1	+1	583.0	0.550	−39.5	5.6
y[27]	−1	+1	−1	+1	+1	2181.0	0.803	8.9	99.8
y[28]	+1	+1	−1	+1	+1	670.0	0.564	−47.1	26.1
y[29]	−1	−1	+1	+1	+1	231.3	0.267	−22.9	61.9
y[30]	+1	−1	+1	+1	+1	361.0	0.580	−34.6	33.9
y[31]	−1	+1	+1	+1	+1	549.3	0.261	12.0	99.7
y[32]	+1	+1	+1	+1	+1	560.5	0.528	−33.7	34.9

x[1]: ALG concentration (mg/mL); x[2]: CS concentration (mg/mL); x[3]: CaCl₂ concentration (mg/mL); x[4]: ALG:CS volume ratio; x[7] CS flow rate; y[1]–y[32]: number of runs; −1: low level; +1: high level. Note that in this design, the experiments were carried out using the center level (0) for the factors x[5]: ALG:CaCl₂ volume ratio and x[6]: CaCl₂ flow rate.

and

Table 7. CCD and experimental values of responses for RSM procedure (central and axial points).

	Factors					Response Variables
	x[1]	x[2]	x[3]	x[4]	x[7]	Size (nm)	PDI	ZP (mV)	EE% (%)
y[33]	0	0	0	0	0	419.1	0.388	−39.1	25.7
y[34]	0	0	0	0	0	454.8	0.390	−32.9	26.4
y[35]	0	0	0	0	0	383.1	0.535	−48.0	17.1
y[36]	0	0	0	0	0	378.5	0.458	−36.1	15.1
y[37]	0	0	0	0	0	403.3	0.496	−39.4	20.0
y[38]	−1	0	0	0	0	212.8	0.226	−23.2	37.1
y[39]	+1	0	0	0	0	632.0	0.521	−24.1	14.7
y[40]	0	−1	0	0	0	284.4	0.539	−34.3	6.2
y[41]	0	+1	0	0	0	391.4	0.468	−27.1	20.3
y[42]	0	0	−1	0	0	474.4	0.493	−63.4	11.5
y[43]	0	0	+1	0	0	363.1	0.461	−35.4	36.9
y[44]	0	0	0	−1	0	535.6	0.602	25.6	0.1
y[45]	0	0	0	+1	0	325.9	0.331	−32.1	22.0
y[46]	0	0	0	0	−1	356.9	0.481	−49.5	24.0
y[47]	0	0	0	0	+1	462.3	0.536	−19.7	13.2

x[1]: ALG concentration (mg/mL); x[2]: CS concentration (mg/mL); x[3]: CaCl₂ concentration (mg/mL); x[4]: ALG:CS volume ratio; x[7] CS flow rate; y[33]–y[47]: number of runs; −1: low level; +1: high level; 0: center level. Note that in this design, the experiments were carried out using the center level (0) for the factors x[5]: ALG:CaCl₂ volume ratio and x[6]: CaCl₂ flow rate.

include the CCD design matrix, as well as the values of the responses for all these experiments, including Table 6 the 32 rows from the 2⁵ factorial design and Table 7 the central points (5 rows) and the axial points (the last 10 rows). All the experiments were carried out in a random order.

Below are the results of the application of the RSM-based procedure to the modified ionic polyelectrolyte pre-gelation synthesis method for all the response variables considered in this study. Model and parameter statistics are shown in Appendix B (Model Statistics for RSM Models), together with fitting statistics of the final model-proposals, the standard error prediction at the optimal conditions for each response, and for each one a graph of residuals vs. predicted values, which do not show any particular pattern.

Model for the response variable “EE%”.

One of the main characteristics that any formulation must have is the possibility of incorporating a drug to transport it to the therapeutic target and generate its controlled release there. Therefore, it is very important to find the conditions that maximize EE% in the ALG–CS NPs prepared by the synthesis approach reported in this work, taking into account its loading capacity. Figure 3 plots the p-values of the tests for the model parameters with effect in this modified synthesis procedure, showing that the significant factors are the concentration of all the reactants (‘[ALG]’, ‘[CS]’ and ‘[CaCl₂]’), the ALG:CS volume ratio (‘ALG:CS’) and the CS flow rate (‘CSflow’), as well as some interaction terms of the main effects. Then, the final fitted model for EE% is stated in Equation (1) that depends on the five factors through the five main effects and five two-factor interactions.

EE% = −62.655 + 20.027 [CaCl₂] + 27.192 [CS] + 34.566 CSflow + 37.973 [ALG] + 58.241 ALG:CS
−19.333 [ALG:CS] CSflow − 21.762 [ALG] CSflow − 40.102 [ALG] [CS] + 43.524 ALG:CS [CS]
−54.667 [ALG] ALG:CS

(1)

where ‘[ALG]’ refers to ALG concentration, ‘[CS]’ to CS concentration, ‘[CaCl₂]’ to CaCl₂ concentration, ‘ALG:CS’ to ALG:CS volume ratio and ‘CSflow’ to CS flow rate.

Considering that the proposed model here is not valid out of the borders of the experimental region, the conditions that maximize the EE% are attained in some of the vertices of the cuboid. Thus, the maximum value expected for EE% (86.7%) can be achieved for the five factor values {−1, 1, 1, 1, 1}, in coded variables, i.e., [ALG] = 0.30 mg/mL; [CS] = 1.00 mg/mL; [CaCl₂] = 1.00 mg/mL; ALG:CS volume ratio = 2.50:1.00 mL:mL (molar ratio = 1.0:1.0 mol:mol); CS flow rate = 2.00 mL/min, in natural variables, the rest being fixed at the central levels. The most influential factors seem to be [ALG] and ALG:CS volume ratio, that participate in every interaction, including their own; Figure 4 shows the response as a function of the two factors assuming constant (central) values for the rest of the factors. Moreover, it should be noted that BSA is incorporated in the CaCl₂ solution (pH: 6.8), as the model drug, which implies that the protein behaves as a negatively charged molecule (pI: 4.7), potentially competing with ALG for CS reacting groups and slightly altering the ALG:CS optimal ratio.

Model for the response variable “PDI”.

Obtaining monodisperse nanoparticles is crucial for their application as drug delivery systems since it assures the stability and control of the formulation, as well as its reproducibility batch to batch, and permits a consistent controlled drug release and predictable interaction with biological systems. To obtain monodisperse nanocarriers, PDI should be minimized, with values below 0.4 being acceptable, although values below 0.2 are desirable [25].

According to the parameter test of significance for the coded variables (Figure 5), four main effects, ‘[ALG]’, ‘[CaCl₂]’, ‘ALG:CS’ and ‘CSflow’ and four two-factor interactions involving the five factors, are statistically significant for the PDI response variable. The usual significance level is 5%; thus, just parameters with a t-test significance p-value less than 0.05 are initially included in the model, unless there could be other reasonable causes to do so. In this case, the main effect ‘[CS]’ was not significant, but considering its participation in several significant interactions, ‘[CS] [CaCl₂]’ and ‘[CS] CSflow’, the proposed function for PDI includes this main effect as well. Once the model in coded factors is obtained, it is necessary to change to natural variables using the relationship X_i = (F_i − c_i)/d_i, or F_i = c_i + d_i X_i, where F_i denotes the original factor, X_i is the corresponding coded one, c_i is the central point of the factor and d_i is the distance from the center to the extreme levels of the factor (See Appendix C. Relation Between Natural and Codified Factors X_i). Thus, the final proposal for PDI is expressed in Equation (2).

PDI = 0.370 − 0.0104 ALG:CS − 0.0665 CSflow − 0.105 [CaCl₂] − 0.135 [CS]
+ 0.446 [ALG]+ 0.197 [CS] CSflow − 0.198 [CS] [CaCl₂] + 0.252 [ALG] [CaCl₂] − 0.367 [ALG] ALG:CS

(2)

where ‘[ALG]’ refers to ALG concentration, ‘[CS]’ to CS concentration, ‘[CaCl₂]’ to calcium chloride concentration, ‘ALG:CS’ to ALG:CS volume ratio and ‘CSflow’ to CS flow rate.

The conditions minimizing the PDI contain some coordinates equal to (+1) or (−1), so they are in the borders of the cuboidal design region. Thus, the minimum expected value for PDI (0.168) for the experimental region can be reached at {−1, 0.396, 1, 1, −0.515} in coded variables for the five factors, or at [ALG] = 0.30 mg/mL, [CS] = 0.79 mg/mL, [CaCl₂] = 1.00 mg/mL, ALG:CS volume ratio = 2.50:1.00 mL:mL (molar ratio = 1.2:1.0 mol:mol) and CS flow rate = 0.86 mL/min, in natural variables. Here, the concerns from EE% regarding the ALG:CS ratio should also be taken into account, as all the experiments considered in this work were performed using the protein BSA.

Model for the response variable “Size”.

The modified ionic polyelectrolyte pre-gelation method reported here permits to obtain ALG–CS NPs with a wide range of sizes (144–1965 nm). It should be noted that the optimal range of sizes for drug delivery depends on the administration route and the biological barrier being targeted. However, the preferred typical range of sizes is usually considered to be between 50 and 200 nm for conventional administration routes, i.e., parenteral/oral delivery. Specifically, once in systemic administration, particles with smaller sizes than 20 nm are subject to renal clearance and above 200 nm are removed by the mononuclear phagocyte system (MPS). Both tissue and mucus penetration and cellular uptake are amplified when the particle size is less than 200 nm [26]. Even so, in certain cases, the use of larger NPs may be advisable, as is the case of oral vaccines [27], when a higher payload is required [28], or to increase drug retention in gastrointestinal (inflammatory bowel disease) [29] or intra-articular delivery [30]. Thus, a model to predict the values of this response variable as a function of the significant factors of the synthesis process seems to be very useful. Based on the parameter test of significance (Figure 6), only the main effects ‘[CS]’ and ‘[CaCl₂]’ are significant at the 5% significance level (the CS flow rate and the interaction of [ALG] with the ALG:CS volume ratio are between 5 and 10%), so, with the usual significance level, this response just depend linearly on the two main factors, as is stated in Equation (3). In Figure 7, the size of the particles is plotted as a function of CaCl₂ and CS concentrations, showing the linear relation between this response variable and the significant factors, without curvature.

Size = 271.629 − 229.797 [CaCl₂] + 392.503 [CS]

(3)

where ‘[CS]’ refers to CS concentration and ‘[CaCl₂]’ to calcium chloride concentration.

Using this quite simple model, the minimum expected value of the mean size is close to 160 nm for ‘[CS]’ at the minimum value and ‘[CaCl₂]’ at the maximum. However, the maximum expected value (635 nm), which can be obtained in the opposite corner (maximum value of ‘[CS]’ and minimum of ‘[CaCl₂]’), is far from the experimental maximum value. In any case, it should be noted that just 3 out of the 47 experiments have size values significantly greater than 635 nm, 2 of them between 800 and 900 nm and another with an extreme value of 2181 nm (see Figure 8). Furthermore, due to the random component, the experimental “mean size” may move beyond the predicted extreme values, but such differences, especially with experiment #27, should come from other causes, and the corresponding values do not represent most of the data (outliers).

Model for the response variable “Surface charge” (ZP).

Finally, although the ALG–CS NPs generated with the synthesis method reported in this work show, in most cases, highly negative surface charge (ZP) values (below −30 mV), there are some combinations of factors, which involve an increase of the proportion of CS with respect to ALG, that allow obtaining positive values of ZP (above +20 mV). Therefore, the modelling of this response variable seems to be of great interest for future applications, e.g., interactions with biological membranes.

Figure 9 shows the parameter test of significance for the coded factors. It can be seen that the model for ZP has strong dependence on the ALG:CS volume ratio through the main and the quadratic effect. Something similar can be observed for ‘[CaCl₂]’, with the main effect at the 5% significance level and the quadratic one very close to this level (p-value = 0.059). Furthermore, the main effect ‘[ALG]’ and its interaction with ‘[CS]’ are significant. However, the main effect ‘[CS]’ is just at the border of 10% significance (p-value 0.104). Still, due to its participation in the only significant interaction, it seems reasonable to include it in the model. Therefore, the final model can be expressed by Equation (4).

ZP = −42.434 + 14.053 [ALG] + 51.103 [CS] + 147.485 [CaCl₂] − 198.245 ALG:CS
− 56.913 [ALG] [CS]−113.315 [CaCl₂]² + 175.701 ALG:CS²

(4)

where ‘[ALG]’ refers to ALG concentration, ‘[CS]’ to CS concentration, ‘[CaCl₂]’ to calcium chloride concentration and ‘ALG:CS’ to ALG:CS volume ratio.

From the proposed model for ZP, the expected minimum value is −67.8 mV for the four coded factor values {0.106, −1, −1, −0.106}, that is [ALG] = 0.69 mg/mL; [CS] = 0.30 mg/mL; [CaCl₂] = 0.13 mg/mL; ALG:CS volume ratio = 2.50:0.59 mL:mL (molar ratio = 12.4:1.0 mol:mol), in natural variables. The expected maximum is +21.1 mV for the factor values {−1, 1, 0.1, 1}, in coded variables, that is [ALG] = 0.30 mg/mL; [CS] = 1.00 mg/mL; [CaCl₂] = 0.61 mg/mL; ALG:CS volume ratio = 2.50:1.00 mL:mL (molar ratio = 0.95:1.0 mol:mol), in natural variables. Note that the rest of factors are fixed at the corresponding central levels. In Figure 10, it can be seen that of the 47 samples of the central composite design, just #18, with a value −74.9 mV, is smaller than the expected minimum, and only #44, with a value of 25.6 mV, is greater than the expected maximum, both quite close to the limits. These differences can be explained by the random component that may always appear in the experimentation. Note that, as with EE% and PDI, the optimal ALG:CS ratios may also vary slightly in this case due to the competition of BSA with ALG for CS reacting groups.

4. Conclusions and Future Perspectives

In this work, substantial modifications of the two-step ionic polyelectrolyte pre-gelation method to synthesize alginate–chitosan nanoparticles (ALG-CS NPs) have been reported. The addition of CaCl₂ to alginate (ALG) to obtain a pregel and the subsequent addition of chitosan (CS) to the pregel to form a polyelectrolyte complex that stabilizes the system were performed in a controlled manner by using syringe pumps and under sonication to enhance the mixing of the phases. This synthesis process was mathematically studied by a two-step design of experiments (DoE)-based methodology. Of the seven factors initially identified as having a possible influence on this technique, only five of them (ALG, CS and CaCl₂ concentrations, ALG:CS volume ratio and the CS flow rate) showed a significant effect after applying a screening procedure with a 2_IV^7-3 fractional design. These five selected factors were subjected to a Response Surface Methodology (RSM) using Central Composite Designs (CCD) to obtain fitted approximated models that correlate these significant factors with the mean size, polydispersity (PDI) and surface charge (ZP) of the ALG–CS NPs generated and their encapsulation efficiency (EE%), using bovine serum albumin (BSA) as model drug.

The mean size of the ALG–CS NPs generated, whose values were mostly between 200 and 700 nm (although nanoparticles close to 100 nm and larger than 1000 nm were obtained), depends on only two factors (the concentrations of CS and CaCl₂, i.e., ‘[CS]’ and ‘[CaCl₂]’) through a plain 3-parameter model. The maximum “mean size” expected with the proposed model (635 nm) can be achieved for ‘[CS]’ at the maximum level and ‘[CaCl₂]’ at the minimum, being located in the opposite corner of the design region the minimum expected value (160 nm) of this response variable. However, it should be noted that the final model proposed for ‘size’, although computed taking the statistically significant terms, is quite poor compared to the rest of responses, explaining just 23.6% of the data variability (adjusted R² = 0.201). Trying to improve the model, if the factor effects that are significant at 10% were also added to the model, only a small improvement would be achieved (R² = 0.345, adjusted R² = 0.222). Thus, it is not worth changing the usual assumption (5% of significance) employed in the rest of the analyses. Therefore, the logical explanation is that there might be other non-considered factors that may have influence on this response (and not so much in the other responses). Further research on these influential sources will be the objective of future studies.

Regarding the surface charge (“ZP”), most of the synthesis conditions yielded highly negative ALG–CS NPs (mainly between −20 and −60 mV), although increasing the mass proportion of CS with respect to ALG also made it possible to obtain positively charged nanoparticles (up to values above +20 mV). This response is dependent on four factors (the concentrations of the reactants and the ALG:CS volume ratio), with its minimum (−67.8 mV) and maximum (+21.1 mV) values obtained for the coded values of the factors ‘[ALG]’, ‘[CS]’, ‘[CaCl₂]’ and ‘ALG:CS’ of {0.106, −1, −1, −0.106} and {−1, 1, 0.1, 1}, respectively.

Finally, the response variables “PDI” and “EE%” depend on all the five selected factors after applying the RSM methodology and are susceptible to be optimized (minimized and maximized, respectively). Thus, the minimum “PDI” expected value within the experimental region (0.168) can be achieved in the borders of the cuboidal design region, {−1, 0.396, 1, 1, −0.515} in coded variables, and the maximum EE% expected (close to the 90%) is obtained at the vertices of the experimental region, {−1, 1, 1, 1, 1} in coded variables.

Table 8. Comparative of the expected values of the four responses at the factor conditions for the extreme values of each one. Expected extreme values are shown in boldface style.

Extremes	Coded Factors {X1, X2, X3, X4, X7}	EE (%)	PDI	Size (nm)	ZP (mV)
Max. EE%	{−1, 1, 1, 1, 1}	86.7	0.282	434.0	+7.4
Min. PDI	{−1, 0.396, 1, 1, −0.515}	64.4	0.168	351.0	+0.2
Min. Size	{0, −1, 1, 0, 0}	15.2	0.454	160.0	−50.1
Max. Size	{0, 1, −1, 0, 0}	17.6	0.515	634.0	−57.2
Min. ZP	{0.106, −1, −1, −0.106, 0}	0.0	0.474	360.0	−67.8
Max. ZP	{−1, 1, 0.1, 1, 0}	72.3	0.273	524.0	+21.1

X1, X2 and X3: ALG, CS and CaCl₂ concentrations (mg/mL); X4: ALG:CS volume ratio (mL:mL); X7: CS flow rate.

shows a comparative of the values of the four responses for the extreme conditions above, highlighting the extreme values. It can be seen that the conditions maximizing EE% are also good for minimizing PDI, and conversely (the conditions minimizing PDI produce high values of EE%). Note that the conditions maximizing ZP are also good for both maximizing EE% and minimizing PDI (last row of Table 8).

In any case, further research needs to be done to propose a reasonable multi-objective function considering at the same time several responses (or even all of them) with weight coefficients depending on the objectives of the researcher. For instance, if the aim is maximizing EE% as well as minimizing PDI, the function to maximize should be f = w₁ EE% − w₂ PDI, where the weights w₁ and w₂ reflect the overall preferences of the researcher (w₁ = w₂ since maximizing EE% seems equally important as minimizing PDI). When considering responses of different scales (as in this case), it would be sensible to transform them previously (e.g., getting transformed variables with mean 0 and standard deviation 1) before using them together in the same objective function.

Validation experiments have been performed, especially at or near extreme conditions, proving the goodness of EE% and PDI models (

Table 9. Validation runs at the extreme conditions of the responses.

Predicted Extreme Conditions {X1, X2, X3, X4, X5, X6, X7} (Coded Factors)		Observed (n = 3)			Predicted
		PDI (0–1)	ZP (mV)	EE% (%)	PDI (0–1)	ZP (mV)	EE% (%)
EE% (optimum)	{−1, 1, 1, 1, 0, 0, 1}			82.2 ± 5.7			86.7
PDI (optimum)	{−1, 0.396, 1, 1, 0, 0, −0.515}	0.203 ± 0.07			0.168
ZP (at max.)	{−1, 1, 0.1, 1, 0, 0, 0}		+23.3 ± 2.7			+21.1
ZP (at min.)	{0.106, −1, −1, −0.106, 0, 0, 0}		−34.7 ± 2.0			−67.8
ZP (near min.)	{1, 1, 1, −0.162, 0, 0, 0}		−46.5 ± 1.9			−55.94

X1, X2 and X3: ALG, CS and CaCl₂ concentrations (mg/mL); X4: ALG:CS volume ratio (mL:mL); X5: ALG:CaCl₂ volume ratio (mL:mL); X6: CaCl₂ flow rate; X7 CS flow rate. Note that the “size” model was not validated since it explains just 23.6% of the data variability.

). For ZP the conditions for the maximum expected value are also confirmed for the experimental values, however, the discrepancy is greater when trying at the conditions related to the minimum expected value, being −46.5 mV the closest value obtained in the environment of these conditions (Table 9). It should be considered that the greater discrepancy between models and actual data will always be at the borders of the design region. Also, note that BSA is included in the CaCl₂ solution (pH: 6.8) in all cases, which implies that the protein behaves as a negatively charged molecule (pI: 4.7), competing with ALG for CS reacting groups and potentially altering the ALG:CS optimal ratio. It is also worth noting that the proposed models and the optimal conditions of synthesis provided are only valid for specification ranges indicated for reagents and nanoparticle preparation in the “Materials and Methods” section (Section 2.1 and Section 2.2).

In this work, a toolbox of classical designs, including factorial, fractional factorial and non-rotatable central composite designs, has been employed. A complementary approach can be the use of optimal experimental design techniques to obtain the best designs to be employed in the different phases of the study. This is a subject that has experienced high development in recent years, allowing the improvement of any experimental process from different points of view, depending on the objectives of the scientist [31]. Furthermore, in this case, with several responses to be observed, multiresponse models can be considered, studying and developing the correlation structure between them [32,33]. Using this correlation structure, specific designs can be computed for the most-accuracy prediction of the four responses simultaneously, using optimal experimental design approaches. All this can be part of future work.