**2. Liposomes: Structure, formation, and characterization**

In general, amphiphile molecules, when dispersed in a liquid medium, undergo internal selforganization, generating colloidal aggregates. Liposomes are formed through the aggregation of phospholipid molecules in an aqueous medium. Initially, a plain bilayer structure is formed when the relative volumes between the non-polar and polar parts of the phospholipid molecules are favorable (packing factor is close to 1) for vesiculation in closed structures. The timing of spontaneous self-aggregation is long, and in technological processes this time is reduced by promoting vesiculation via the addition of energy to the system and remotion of the organic solvent or detergent in which the lipids were initially dispersed (Gregoriadis, 1990; Lasic, 1993). Primary aggregation generates unilamellar liposomes, which undergo secondary aggregation, forming multilamellar liposomes (Figure 1).

Fig. 1. Unilamellar and multilamellar liposomes.

The main physico-chemical characterization of cationic liposomes for gene vaccines includes average hydrodynamic diameter and size distribution, zeta potential, and morphology. These characterizations have been well described in the modern literature, including techniques, equipment, and the software used for analyzing data.

Regarding the average hydrodynamic diameter and size distribution, photon correlation spectroscopy (PCS) and dynamic laser light scattering using a Ne-He laser are generally used for measurements at various incidence angles. Particle diameter is calculated from the translational diffusion coefficient using the Stokes-Einstein equation:

$$\text{cl}(\text{H}) = \text{(kT)} / \text{(\$\text{Sym}\$D\$)}\tag{1}$$

Where d(H) is the hydrodynamic diameter, D is the translational diffusion coefficient, k is Boltzmann's constant, T is the absolute temperature, and η is the viscosity. The mean diameter and size distribution are estimated by an adequate algorithm analysis. The results of the population distributions are expressed as the intensity of scattered light and automatically converted to number-weighted mean diameter and size distribution by adequate software. For more accurate size characterization, intensity and number-weighted

Technological Aspects of Scalable Processes for the

the SAXS analysis is the determination of the electron density

Considering that the particles are spheres with radius r, it yields:

unilamellar of multilamellar vesicles as will be discussed next.

angles, θ, which can satisfy Bragg's condition (Azaroff 1968):

several procedures that can be applied to determine

coefficient proportional to Rg2.

**2.2 X ray diffraction (XRD)** 

Production of Functional Liposomes for Gene Therapy 271

higher the total scattering intensity. Lipid/water systems generally contain light atoms (low atomic number) and, consequently, very low electronic density contrast. A way to increase the scattering intensity is to use high flux X-ray sources, such as synchrotrons. The SAXS experiment will give information on the particle/system structure. Usually, the main goal of

inverse scattering problem since the information is given in reciprocal space. There are

calculation of a theoretical intensity obtained for an assumed model object and the comparison to the experimental data. The more information one has about the sample, the more consistent the model will be and, consequently, the simpler the SAXS analysis. Nevertheless, some parameters can be determined directly from the scattering curve, for instance, the radius of gyration of a particle, Rg, which is the root mean square of the distances of all electrons from the center of gravity of the particle. The Rg is determined using the Guinier method, which approximates the scattering function to a simple distribution in the limit of very small angles (q~0.01Å-1). A graph plotting ln I(q) versus q2 in the limit for very low angles might be characterized by a straight line with an angular

> 2 2 3 5

The two requirements for using Guinier approximation are: the sample should be a monodisperse colloidal system, which implies no interaction between the scattering centers, and the experimental data must have a minimum q such that d<π/q, where d is the maximum particle dimension that can be studied (Glatter 1982). For systems of large unilamellar vesicles in which the dimensions of the particles are not inside the limit of SAXS experiments, other methods, such as visible light scattering, can be used (Glatter 2002). In some cases, determining the cross section distance would be interesting, such as in large unilamellar vesicle systems, where the thickness of the lamellae is inside the limits of the Guinier approximation. In this case, the graph of I(q)q2 versus q, called the "thickness Guinier plot", is used to determine the radius of gyration of the thickness RT com *RT T*= / 12 , were T is the bilayer thickness). Another approach is to obtain the electron density across the thickness of the vesicle, ρt(x). The latter approach can be applied both for

Diffraction can be viewed as a particular case of scattering: Due to the periodicity, d, of the system, the sum or integration of all scattered intensities turns into an interference pattern. In analogy, the function S(q) which is the result of the integration, is called the "structure factor". The scattering curve, or diffraction pattern, presents peaks for certain scattering

> *n d* λ

Where λ is the wavelength of the incident X-ray beam and n is the order of diffraction. We can observe a diffraction pattern, for example, in multilamellar lipid vesicles, which have a

 θ ρ( )*r*

*R r <sup>g</sup>* = (4)

= 2 sin (5)

ρ( )*r* . This is the so called

. One possible approach is the

mean diameters are considered. Although the whole range of diameters is shown in the intensity-weighted distribution, the proportionality to the sixth power of particle diameter underestimates small particles, which are only very weakly weighted (Egelhaaf et al., 1996). The corresponding number-weighted distribution converted using the Mie theory is in equivalent proportion to the first power of the diameter and determines the actual number of particles yielding the observed intensity in each size class (Hulst, 1969).

Several structural parameters involved in the process of liposome preparation can be studied and controlled using X-ray techniques. The simple piling of several polar lipid bilayers produces an X-ray diffraction pattern from which one can determine the periodicity, the type of lattice, and an estimate of water molecules in the interface. The colloidal size of self aggregates, such as the dispersion of liposomes, can be characterized by small angle X-ray scattering techniques directly in the liquid buffer media, complementing some indirect microscopy methods (Kratky 1988). Structural phase transition, swelling, crystallization, permeation, nucleation, and other properties will be reflected in a change in the scattering pattern. More than a few dimensions in polar lipid/water systems, such as, lattice periodicity and arrangement, aggregate size, and defects, are on the order of magnitude of the X-ray wavelength, a few Angstroms. The bigger the particle (up to a few hundred Angstroms), the smaller the scattering angle. The terms small angle X-ray scattering (SAXS) and wide angle X-ray scattering (WAXS) are applied. X-ray diffraction is a particular case of scattering for ordered systems.

#### **2.1 Small angle X-ray scattering (SAXS)**

Here, we present an outline of the main features of the general X-ray techniques applied specifically to the case of liposome characterization. For better comprehension of the theory of X-ray scattering, the reader may like to consult the works of Glatter (Glatter & Kratky 1982, Glatter 1991) and Kratky (Kratky & Laggner 2001). For the notation, as a convention in the literature, and in order to avoid dependence on wavelength values, the scattering angle is normalized using the following equation:

$$q = \left| \mathbf{q} \right| = \frac{4\pi}{\lambda} \sin \theta \tag{2}$$

Where q is the wave vector, 2θ the scattering angle, and λ the incident wavelength. By using the wave vector instead of angles, one can directly compare experiments performed with different X-ray wavelengths. SAXS is the elastic scattering that occurs when X-rays strike a sample of given material. The electrons of each atom in the sample will re-emit the same energy isotropically. The total scattering amplitude, or amplitude "form factor" F(q), is a sum of all scattered waves in all directions as defined in Equation 3,

$$F(\vec{q}) = \int \rho(\vec{r}) e^{-i\vec{q}\cdot\vec{r}} d\vec{r} \tag{3}$$

Where ( ) *iq r* ρ *r e*− ⋅ is the amplitude of the wave scattered by an atom located at position r. The result is a maximum intensity in the direction of the incident beam decreasing smoothly as a function of the scattering angle. The intensity of the scattering will depend directly on the electronic density ρ( )*r* of the sample, i.e., the number of electrons per unit of volume. More specifically, for our case, the higher the difference between the electronic densities of the scattering centers of the sample (e.g., liposomes) and the media (e.g., buffer solution), the

mean diameters are considered. Although the whole range of diameters is shown in the intensity-weighted distribution, the proportionality to the sixth power of particle diameter underestimates small particles, which are only very weakly weighted (Egelhaaf et al., 1996). The corresponding number-weighted distribution converted using the Mie theory is in equivalent proportion to the first power of the diameter and determines the actual number

Several structural parameters involved in the process of liposome preparation can be studied and controlled using X-ray techniques. The simple piling of several polar lipid bilayers produces an X-ray diffraction pattern from which one can determine the periodicity, the type of lattice, and an estimate of water molecules in the interface. The colloidal size of self aggregates, such as the dispersion of liposomes, can be characterized by small angle X-ray scattering techniques directly in the liquid buffer media, complementing some indirect microscopy methods (Kratky 1988). Structural phase transition, swelling, crystallization, permeation, nucleation, and other properties will be reflected in a change in the scattering pattern. More than a few dimensions in polar lipid/water systems, such as, lattice periodicity and arrangement, aggregate size, and defects, are on the order of magnitude of the X-ray wavelength, a few Angstroms. The bigger the particle (up to a few hundred Angstroms), the smaller the scattering angle. The terms small angle X-ray scattering (SAXS) and wide angle X-ray scattering (WAXS) are applied. X-ray diffraction is a

Here, we present an outline of the main features of the general X-ray techniques applied specifically to the case of liposome characterization. For better comprehension of the theory of X-ray scattering, the reader may like to consult the works of Glatter (Glatter & Kratky 1982, Glatter 1991) and Kratky (Kratky & Laggner 2001). For the notation, as a convention in the literature, and in order to avoid dependence on wavelength values, the scattering angle

> 4 *q* sin π

Where q is the wave vector, 2θ the scattering angle, and λ the incident wavelength. By using the wave vector instead of angles, one can directly compare experiments performed with different X-ray wavelengths. SAXS is the elastic scattering that occurs when X-rays strike a sample of given material. The electrons of each atom in the sample will re-emit the same energy isotropically. The total scattering amplitude, or amplitude "form factor" F(q), is a

> () () *iq r F q r e dr* ρ

result is a maximum intensity in the direction of the incident beam decreasing smoothly as a function of the scattering angle. The intensity of the scattering will depend directly on the

specifically, for our case, the higher the difference between the electronic densities of the scattering centers of the sample (e.g., liposomes) and the media (e.g., buffer solution), the

*r e*− ⋅ is the amplitude of the wave scattered by an atom located at position r. The

of the sample, i.e., the number of electrons per unit of volume. More

sum of all scattered waves in all directions as defined in Equation 3,

λ

θ

= = **<sup>q</sup>** (2)

− ⋅ <sup>=</sup> (3)

of particles yielding the observed intensity in each size class (Hulst, 1969).

particular case of scattering for ordered systems.

**2.1 Small angle X-ray scattering (SAXS)**

is normalized using the following equation:

Where ( ) *iq r* ρ

electronic density

ρ( )*r* higher the total scattering intensity. Lipid/water systems generally contain light atoms (low atomic number) and, consequently, very low electronic density contrast. A way to increase the scattering intensity is to use high flux X-ray sources, such as synchrotrons. The SAXS experiment will give information on the particle/system structure. Usually, the main goal of the SAXS analysis is the determination of the electron density ρ( )*r* . This is the so called inverse scattering problem since the information is given in reciprocal space. There are several procedures that can be applied to determine ρ( )*r* . One possible approach is the calculation of a theoretical intensity obtained for an assumed model object and the comparison to the experimental data. The more information one has about the sample, the more consistent the model will be and, consequently, the simpler the SAXS analysis. Nevertheless, some parameters can be determined directly from the scattering curve, for instance, the radius of gyration of a particle, Rg, which is the root mean square of the distances of all electrons from the center of gravity of the particle. The Rg is determined using the Guinier method, which approximates the scattering function to a simple distribution in the limit of very small angles (q~0.01Å-1). A graph plotting ln I(q) versus q2 in the limit for very low angles might be characterized by a straight line with an angular coefficient proportional to Rg2.

Considering that the particles are spheres with radius r, it yields:

$$\left| \, R\_{\,\,\,\,g} \right|^2 = \frac{\mathfrak{Z}}{\mathfrak{Z}} r^2 \tag{4}$$

The two requirements for using Guinier approximation are: the sample should be a monodisperse colloidal system, which implies no interaction between the scattering centers, and the experimental data must have a minimum q such that d<π/q, where d is the maximum particle dimension that can be studied (Glatter 1982). For systems of large unilamellar vesicles in which the dimensions of the particles are not inside the limit of SAXS experiments, other methods, such as visible light scattering, can be used (Glatter 2002). In some cases, determining the cross section distance would be interesting, such as in large unilamellar vesicle systems, where the thickness of the lamellae is inside the limits of the Guinier approximation. In this case, the graph of I(q)q2 versus q, called the "thickness Guinier plot", is used to determine the radius of gyration of the thickness RT com *RT T*= / 12 , were T is the bilayer thickness). Another approach is to obtain the electron density across the thickness of the vesicle, ρt(x). The latter approach can be applied both for unilamellar of multilamellar vesicles as will be discussed next.

#### **2.2 X ray diffraction (XRD)**

Diffraction can be viewed as a particular case of scattering: Due to the periodicity, d, of the system, the sum or integration of all scattered intensities turns into an interference pattern. In analogy, the function S(q) which is the result of the integration, is called the "structure factor". The scattering curve, or diffraction pattern, presents peaks for certain scattering angles, θ, which can satisfy Bragg's condition (Azaroff 1968):

$$m\mathcal{X} = \mathcal{Z}d\sin\theta\tag{5}$$

Where λ is the wavelength of the incident X-ray beam and n is the order of diffraction. We can observe a diffraction pattern, for example, in multilamellar lipid vesicles, which have a

Technological Aspects of Scalable Processes for the

enabling a more flexible and stable model procedure.

 *z a G zz G z z* σ

standard deviations (σ values) are defined as follows:

4

1

=

*n*

ρ

Production of Functional Liposomes for Gene Therapy 273

Where ΔρH and ΔρT are respectively the head group and tail group electron density contrasts and δH and δT are the sizes of the head group and tail group. Following the step model strategy, Glatter and co-workers developed the deconvolution square root method (Glatter & Kratky 1982, Fritz & Glatter 2006) where the electron density is described by several step functions and it is applied a constrained least squares fitting routine to obtain the step heights. Another strategy was proposed by Pabst et.al (Pabst et al. 2000), which models the bilayer using a two Gaussian system: a central Gaussian placed at the origin, which can model the central part of the tail groups, and is known to have negative contrast with respect to a water buffer (when using X-Rays), and a second Gaussian placed at a certain distance Z in such a way that it can model the position of the head group region. This approach and the two step model cannot describe high quality data, principally for high q values (Oliveira et al. Unpublished work). In a recent development, Oliveira and co-workers combined the advantages of the Gaussian description with the stability introduced by the Glatter method,

In this approach the profile is described by a symmetric sum of several equally spaced Gaussian functions. The amplitude of each Gaussian is smoothened by extra constraints. The constraints are used to ensure the numerical stability of the nonlinear least-square fit. By proper choice of the amplitude of each Gaussian it is possible to build a smooth profile that can describe more accurately the electron density of the bilayer. Usually, 4 Gaussians function are sufficient to describe a bilayer profile satisfactorily. The electron density is defined as

<sup>1</sup> 2 2 ( , , ) exp ( ) / 2 <sup>2</sup>

and the Kroninger delta function δi1 is used to avoid double counting for the central Gaussian. n is the order of Gaussian used. The profile is defined by the values of the amplitude factors an. Given a half bilayer thickness Z the centers of the Gaussians and the

1 2 , 2 2ln 2 *<sup>n</sup>*

This choice of the centers and standard deviations gives a reasonable overlap between the Gaussian functions enabling the construction of smooth profiles. A typical profile built using equation 11 is shown in the figure 2 (left). One of the advantages of using a Gaussian set of functions for the representation of the profile is that, for the one-dimensional case of centro-symmetric bilayers, the integral in equation 3 has one analytical solution, given by:

( ) ( )

() ( ) 4

1

*n F q a F q n* =

= −

πσ

The final scattering amplitude is just the addition of all the F(q,n) terms:

, 2 exp cos 2 *<sup>n</sup> <sup>q</sup> <sup>F</sup> <sup>q</sup> <sup>n</sup> <sup>q</sup> <sup>z</sup>*

2 2

σ

, *<sup>n</sup>*

 σ

*<sup>n</sup>* = − σ

σδ

1

*z z*

max

*Z*

 σ

= −− (12)

1

= (13)

<sup>=</sup> (15)

*i i*

δ

δ

1, 1 0, 2,3,4

= = (11)

(14)

*i i*

= =

[ ] ( )

*G zz s n <sup>n</sup>*

σ π

= + − + <sup>1</sup>

() (, , ) (, , )/1 *n s nn s nn i*

σ

( )

*z n*

lipid bilayer periodicity on the order of 50 Å. The determination of the period of the bilayer is useful for characterizing the structural phase of the system and its transitions. If several orders of diffraction are observed, the structure factor function can be reconstructed and the electronic density profile of the lipid bilayer determined (Pachence & Blasie 1991). The incorporation of compounds inside the lipid bilayer can alter the density profile and be controlled (Sato et al. 2009). Also the matrix of acyl chains is a periodic arrangement with distances between chains on the order of 5 Å. The determination of this parameter is helpful for controlling the stability of the liposome. Any change in these distances will be followed by a dislocation of the diffraction peak.

#### **2.3 Simultaneous determination of form factor and structure factor**

Some systems present both form factor and structure factor. The scattering intensity from such a system can be written by the following expression:

$$I(q) = c \left\langle P(q)S(q) \right\rangle \tag{6}$$

Where c is related to the concentration of particles in the system, P(q)=|F(q)|2 is the intensity form factor of the particles and carries information about particle shape and contrast and S(q) is the system structure factor, which carries information about possible interparticle interactions or arrangements. The brackets " " indicate that in the general case these two contributions have to be averaged together in the calculation. For highly anisotropic systems, like vesicles for example, where the transversal dimensions are much larger than the perpendicular dimension, the form factor can be considered as only corresponding to the perpendicular direction (1D function) and equation 6 can be rewritten as,

$$I(q) = \frac{c}{q^2} \left\{ P(q)S(q) \right\} \tag{7}$$

One usual approach is to use the decoupling approximation and treat the form factor and structure factor separately. For a lamellar system, the structure factor is well described by the MCT theory (Zhang et al. 1994)

$$S(q) = 1 + 2\sum\_{n=1}^{N-1} \left(1 - \frac{n}{N}\right) \cos\left(nqd\right) \ e^{-\left(d/2\pi\right)^2 q^2 \eta \gamma} \left(\pi q\right)^{-\left(d/2\pi\right)^2 q^2 \eta} \tag{8}$$

The average number of coherent scattering bilayers in the stack is denoted as N, γ is Eulers' constant and d the separation between layers. The Caillé parameter η involves both the bending modulus K of lipid bilayers and the bulk modulus B for compression (Caille 1972, Zhang et al. 1994).

$$
\eta = \frac{\pi \text{ k } T}{2d^2 \sqrt{BK}} \tag{9}
$$

The description of the form factor can be done in several levels of detail. One of the simplest approximations is to consider a two step model given by (Nallet et al. 1993),

$$P(q) = \frac{4}{q^2} \left\{ \Delta \rho\_H \sin \left[ q \left( \delta\_H + \delta\_\Gamma \right) \right] - \Delta \rho\_H \sin \left( q \delta\_\Gamma \right) + \Delta \rho\_\Gamma \sin \left( q \delta\_\Gamma \right) \right\}^2 \tag{10}$$

lipid bilayer periodicity on the order of 50 Å. The determination of the period of the bilayer is useful for characterizing the structural phase of the system and its transitions. If several orders of diffraction are observed, the structure factor function can be reconstructed and the electronic density profile of the lipid bilayer determined (Pachence & Blasie 1991). The incorporation of compounds inside the lipid bilayer can alter the density profile and be controlled (Sato et al. 2009). Also the matrix of acyl chains is a periodic arrangement with distances between chains on the order of 5 Å. The determination of this parameter is helpful for controlling the stability of the liposome. Any change in these distances will be followed

Some systems present both form factor and structure factor. The scattering intensity from

Where c is related to the concentration of particles in the system, P(q)=|F(q)|2 is the intensity form factor of the particles and carries information about particle shape and contrast and S(q) is the system structure factor, which carries information about possible interparticle interactions or arrangements. The brackets " " indicate that in the general case these two contributions have to be averaged together in the calculation. For highly anisotropic systems, like vesicles for example, where the transversal dimensions are much larger than the perpendicular dimension, the form factor can be considered as only corresponding to the

<sup>2</sup> () ()() *<sup>c</sup> Iq PqSq*

One usual approach is to use the decoupling approximation and treat the form factor and structure factor separately. For a lamellar system, the structure factor is well described by

( ) ( ) 2 2 2 2 <sup>1</sup>

The average number of coherent scattering bilayers in the stack is denoted as N, γ is Eulers' constant and d the separation between layers. The Caillé parameter η involves both the bending modulus K of lipid bilayers and the bulk modulus B for compression (Caille 1972,

> <sup>2</sup> 2 *k T d BK* π

The description of the form factor can be done in several levels of detail. One of the simplest

( ) { } ( ) () () <sup>2</sup>

 ρ  δ

<sup>4</sup> *P q H HT H T T T* sin *<sup>q</sup>* sin *<sup>q</sup>* sin *<sup>q</sup>*

<sup>−</sup> − −

1 2 1 cos ( )

*<sup>n</sup> S q nqd e <sup>q</sup> <sup>N</sup>*

η

approximations is to consider a two step model given by (Nallet et al. 1993),

 δδ

*Iq c PqSq* () ()() = (6)

*<sup>q</sup>* <sup>=</sup> (7)

π η

= (9)

 ρ

+ − Δ + Δ (10)

 δ

( /2 ) ( /2 )

(8)

π ηγ

*dq dq*

π

**2.3 Simultaneous determination of form factor and structure factor** 

perpendicular direction (1D function) and equation 6 can be rewritten as,

1

= =+ −

*N*

*n*

2

*q* = Δρ

such a system can be written by the following expression:

by a dislocation of the diffraction peak.

the MCT theory (Zhang et al. 1994)

Zhang et al. 1994).

Where ΔρH and ΔρT are respectively the head group and tail group electron density contrasts and δH and δT are the sizes of the head group and tail group. Following the step model strategy, Glatter and co-workers developed the deconvolution square root method (Glatter & Kratky 1982, Fritz & Glatter 2006) where the electron density is described by several step functions and it is applied a constrained least squares fitting routine to obtain the step heights.

Another strategy was proposed by Pabst et.al (Pabst et al. 2000), which models the bilayer using a two Gaussian system: a central Gaussian placed at the origin, which can model the central part of the tail groups, and is known to have negative contrast with respect to a water buffer (when using X-Rays), and a second Gaussian placed at a certain distance Z in such a way that it can model the position of the head group region. This approach and the two step model cannot describe high quality data, principally for high q values (Oliveira et al. Unpublished work). In a recent development, Oliveira and co-workers combined the advantages of the Gaussian description with the stability introduced by the Glatter method, enabling a more flexible and stable model procedure.

In this approach the profile is described by a symmetric sum of several equally spaced Gaussian functions. The amplitude of each Gaussian is smoothened by extra constraints. The constraints are used to ensure the numerical stability of the nonlinear least-square fit. By proper choice of the amplitude of each Gaussian it is possible to build a smooth profile that can describe more accurately the electron density of the bilayer. Usually, 4 Gaussians function are sufficient to describe a bilayer profile satisfactorily. The electron density is defined as

$$\rho(\mathbf{z}) = \sum\_{n=1}^{4} a\_n \left[ \mathbf{G}\_s(\mathbf{z}, \mathbf{z}\_n, \sigma\_n) + \mathbf{G}\_s(\mathbf{z}, -\mathbf{z}\_n, \sigma\_n) \right] / \left( 1 + \delta\_{i1} \right) \qquad \begin{array}{c} \delta\_{i1} = 1, i = 1 \\ \delta\_{i1} = 0, i = 2, 3, 4 \end{array} \tag{11}$$

$$\mathcal{G}\_s(z, z\_n, \sigma) = \frac{1}{\sigma \sqrt{2\pi}} \exp\left[ -(z - z\_n)^2 / 2\sigma^2 \right] \tag{12}$$

and the Kroninger delta function δi1 is used to avoid double counting for the central Gaussian. n is the order of Gaussian used. The profile is defined by the values of the amplitude factors an. Given a half bilayer thickness Z the centers of the Gaussians and the standard deviations (σ values) are defined as follows:

$$z\_n = (n-1)2\sigma, \qquad \sigma = \frac{Z}{2n\_{\text{max}}\sqrt{2\ln 2}}\tag{13}$$

This choice of the centers and standard deviations gives a reasonable overlap between the Gaussian functions enabling the construction of smooth profiles. A typical profile built using equation 11 is shown in the figure 2 (left). One of the advantages of using a Gaussian set of functions for the representation of the profile is that, for the one-dimensional case of centro-symmetric bilayers, the integral in equation 3 has one analytical solution, given by:

$$F(q, n) = \sqrt{2\pi} \sigma \exp\left(-\frac{\sigma^2 q^2}{2}\right) \cos\left(q \ z\_n\right) \tag{14}$$

The final scattering amplitude is just the addition of all the F(q,n) terms:

$$F(\boldsymbol{\eta}) = \sum\_{n=1}^{4} a\_n F(\boldsymbol{\eta}, n) \tag{15}$$

Technological Aspects of Scalable Processes for the

for liposome production.

**4. Technological processes** 

**3. Top-down and bottom-up approaches in processes** 

Production of Functional Liposomes for Gene Therapy 275

In general, the processes for producing nanomaterials can be characterized as two main approaches, top-down or bottom-up. The top-down approach starts with large particles that are comminuted to a nanometric size through the application of high-energy forces. This is the classical approach for the majority of nanoparticle production processes. Top-down approaches require highly precise control of the variables of the process in order to obtain the narrow particle size (Mijatovic et al., 2005). Lithography is the classical example. Other high-energy processes include grinding, high impact homogenization, ultrasound waves,

Bottom-up approaches are based on the self-organization of molecules under thermodynamic control, generating nanostructures from atoms and molecules as a result of the effects of the chemical, physical, and process interventions on the balance of the intermolecular and intramolecular forces of the system components (Sanguansri & Augustin, 2006). Bottom-up approaches focus on the construction of functional materials, mimetizing the hierarchic organization of the molecules in live organisms, though the

Regarding liposome production, top-down approaches comprise the high-energy comminution of a polydispersed population of multilamellar liposomes formed under noncontrolled aggregation. The bottom-up approach manipulates the phospholipid molecules in controlled local aggregation in space and time, generating a monodispersed population of nano-sized unilamellar liposomes. Figure 3 illustrates top-down and bottom-up approaches

and extrusion through nanoporous membranes (Sanguansri & Augustin, 2006).

science still does not dominate the complex auto-aggregate structures in nature.

Fig. 3. Scheme of top-down and bottom-up approaches for liposome production.

Most of the conventional methods for liposome production require an additional unit operation for size reduction and polydispersity, as they are top-down approaches. In this approach, liposomes are produced from the hydration of a thin film of lipids using Bangham's method (Bangham et al., 1965), multitubular system (Torre et al., 2007; Tournier et al., 1999), detergent depletion or emulsion methods, ether/ethanol injection, and reverse phase evaporation (Lasic, 1993; New, 1990). All of these processes are discontinuous and only the ether/ethanol injection and multitubular system are scalable. Shearing or impact strategies are

Regardless the methodology to calculate the form factor, this procedure gives the scattering contribution from the built shape of the electron density profile. For the multilamelar vesicles this profile will be a repeating unit for each vesicle layer. By using the structure factor given from the modified Caillé theory (equation 8), the final scattering intensity is then given by:

$$I\_{MLV}\left(q\right) = \left(\left|F\left(q\right)\right|^2 S\_{MCT}\left(q\right) + N\_{diff}\left|F\left(q\right)\right|^2\right) \tag{16}$$

Where the second term gives rise to a diffusive scattering which might appear from the presence of single bilayers in the sample. Smearing effects, which are a consequence of the collimation of the camera pinholes, wavelength bandwidth, detector resolution, etc, can be taken into account by the use of the resolution function R(q,q), as described in the work of Pedersen (Pedersen et al. 1990). The final expression used to describe the data from multilamellar vesicles is given by:

$$I(q)\_{FIT} = Sc\_1 \frac{I\_{MLV}\left(\{q\}\right)}{q^2} + BG \tag{17}$$

Sc1 is an overall scale factor and BG is a constant background. Both are optimized during data fitting. Using the above mentioned procedure it is possible to perform a full curve fitting, retrieving simultaneously information about the form factor and structure factor. A simulated example and an application to real experimental data are shown in Figure 2(right).

Fig. 2. Left: Construction of the electron density profile using four Gaussians (G1, G2, G3 and G4) with four different amplitudes (-1, -0.3, 1, 0.3). They are shown in four different lines. The final resultant electron density profile from the Gaussian model is shown in solid thick line. Right: Fitting of experimental data using the 4-Gaussians approach. Open circles: experimental data for Egg phosphatidylcholine (EPC) liposome system. Solid curve: Theoretical intensity I(q). Dotted line: structure factors S(q). Dashed line: intensity form factor P(q). The obtained number of layers was N=50, Interplanar distance d=73.5±0.2Å, Caillé parameter of η=0.13±0.01 and bilayer half size of Z=30.00±0.06Å. The obtained electron density profile is shown in the inset.

Regardless the methodology to calculate the form factor, this procedure gives the scattering contribution from the built shape of the electron density profile. For the multilamelar vesicles this profile will be a repeating unit for each vesicle layer. By using the structure factor given from the modified Caillé theory (equation 8), the final scattering intensity is

() () ( () () ) 2 2

Where the second term gives rise to a diffusive scattering which might appear from the presence of single bilayers in the sample. Smearing effects, which are a consequence of the collimation of the camera pinholes, wavelength bandwidth, detector resolution, etc, can be taken into account by the use of the resolution function R(q,q), as described in the work of Pedersen (Pedersen et al. 1990). The final expression used to describe the data from

> ( ) ( ) 1 2 *MLV*

Fig. 2. Left: Construction of the electron density profile using four Gaussians (G1, G2, G3 and G4) with four different amplitudes (-1, -0.3, 1, 0.3). They are shown in four different lines. The final resultant electron density profile from the Gaussian model is shown in solid thick line. Right: Fitting of experimental data using the 4-Gaussians approach. Open circles: experimental data for Egg phosphatidylcholine (EPC) liposome system. Solid curve: Theoretical intensity I(q). Dotted line: structure factors S(q). Dashed line: intensity form factor P(q). The obtained number of layers was N=50, Interplanar distance d=73.5±0.2Å, Caillé parameter of η=0.13±0.01 and bilayer half size of Z=30.00±0.06Å. The obtained

*I q I q Sc BG q*

Sc1 is an overall scale factor and BG is a constant background. Both are optimized during data fitting. Using the above mentioned procedure it is possible to perform a full curve fitting, retrieving simultaneously information about the form factor and structure factor. A simulated example and an application to real experimental data are shown in Figure

*FIT*

*MLV MCT diff I q Fq S q N Fq* = + (16)

= + (17)

then given by:

2(right).

multilamellar vesicles is given by:

electron density profile is shown in the inset.
