4. Lypolitic enzyme activity in lipid phases with multiple substrate domains

The above kinetics expressions can be generalized to any amount of substrate domains, even to infinite number of domains, and this latter is very useful for modeling any kind of substrate distribution in the total lipid phase [22].

In this extended theoretical frame, we have the following:

In homogenous condition, f is the molar fraction of phospholipid substrate. S reorders into n homogeneous domains, with the ith domain (i = 1, 2,…, n) with normalized area ai and molar fraction fi of S.

The total conservation equation is given as:

The ratio between the enzymes binding into the two domains (indicated as

<sup>¼</sup> <sup>f</sup> <sup>d</sup> km <sup>þ</sup> <sup>f</sup> <sup>d</sup> � � f <sup>n</sup> km þ f <sup>n</sup>

> <sup>¼</sup> km <sup>þ</sup> <sup>f</sup> <sup>d</sup> km þ f <sup>n</sup>

Furthermore, there are different expressions for the molar concentration of total

Naming the molar concentration of total enzyme binding to the lipid phase ½ � EB ,

2 i � �

> 2 i � �

1

CA,

1

CA,

� � (10)

<sup>S</sup> <sup>þ</sup> <sup>E</sup>´ SS � �

<sup>S</sup> <sup>þ</sup> <sup>E</sup>´ SS � � (11)

(12)

(13)

ES þ ESS E´ <sup>S</sup> <sup>þ</sup> <sup>E</sup>´ SS

> ES þ ESS E´ <sup>S</sup> <sup>þ</sup> <sup>E</sup>´ SS

½ �� EB La Eð Þþ <sup>S</sup> <sup>þ</sup> ESS <sup>L</sup>ð Þ <sup>1</sup> � <sup>a</sup> <sup>E</sup>´

½ �� EB La Eð Þþ <sup>S</sup> <sup>þ</sup> ESS <sup>L</sup>ð Þ <sup>1</sup> � <sup>a</sup> <sup>E</sup>´

km þ f

<sup>L</sup> <sup>þ</sup> km <sup>þ</sup> <sup>f</sup>

Then, due to the difference between Eqs. 12 and 13, the two enzymatic models could be easily distinguishable by means of the observed change in the total lipid metabolizing enzyme binding to the lipid phase under substrate reordering: phospholipid-binding model predicts changes in total membrane enzyme upon domain formation, unlike the surface-binding model, in which there are no changes

kmks

in total membrane enzyme, whatever the distribution of the substrate is.

lipid phase or its interface concentration can be considered negligible.

3. Redistribution effect versus competitive effect of a lipid-inducing

Similar to the enzyme, again we will not consider the substrate dilution due to the protein insertion in the bilayer. That is because the number of molecules binding to the lipid phase is much smaller than the number of the phospholipid substrate molecules, and besides, the domain-inducing peptide either would not penetrate the

As seen before, depending on the enzymatic model, substrate redistribution such as the transitions from homogeneous distribution to nonhomogeneous

0

B@

kmks

0

B@

kmf þ f

<sup>L</sup> <sup>þ</sup> kmf <sup>þ</sup> <sup>f</sup>

¼ ET

¼ ET

primed and nonprimed) is described as follows: for the phospholipid-binding model:

Extracellular Vesicles and Their Importance in Human Health

for the surface-binding model:

enzyme binding to the lipid phase, ½ � EB :

for the phospholipid-binding model,

for the surface-binding model.

domain peptide

76

we have:

and

$$\mathbf{1} = \sum\_{i=1}^{n} a\_i \tag{14}$$

5. Effects of Poisson distribution of substrate on enzyme activity

Effects of Vesicular Membranes Reordering on the Activity of Lipid Metabolizing Enzymes

as a substrate domain represented in a summation term in Eq. 17.

and Poisson-distributed substrate, it can be demonstrated that [22]

f 2 Si <sup>¼</sup> <sup>f</sup>

V ¼

enzyme activity are due to Poisson distribution of the substrate.

5.1 Substrate-distribution dependence of PLA2 activity in mixed micelles

The mentioned kinetic theory applied to Poisson-distributed substrate on lipid particles has been verified with experimental results, and their obtained parameters have been compared with those of the canonical phospholipid-binding model originally developed for homogeneously distributed substrate on mixed micelles

kmks

but Poisson distributed over the same population of particles. Then, the 〈 f

kCET f

CL þ kmf þ f

That is, Eq. 22 is an expression of the rates of enzyme activity on Poissondistributed phospholipid substrates. Applying this equation to published kinetic parameters for PLC acting on PIP2 in Triton X-100 micelles (CL = 200 μM,

km = 0.13, and ks = 170 μM) [23], the ratio between "the enzyme activity on micelles with Poisson-distributed substrate" (Eq. 22) and "the enzyme activity on micelles with homogeneously distributed substrate" (Eq. 1) was calculated. Assuming a range of f from 10�<sup>1</sup> to 10�<sup>3</sup> (as in published work [12, 13]), activity ratios between 1.0 and 6.0 (α ¼ 200) and between 1.1 and 11.0 (α ¼ 100) were obtained. We can see that without considering cooperative effects, a simple explanation for a very high departure from the homogeneous standard model may be that the increases in

<sup>2</sup> <sup>1</sup> <sup>þ</sup> <sup>1</sup> fα 

> <sup>2</sup> <sup>1</sup> <sup>þ</sup> <sup>1</sup> fα

Since the extended theory shown above does not consider boundaries, the same can be applied to a population of lipid particles (like vesicles or micelles), each one

Frequently, data from in vitro kinetic studies of lipid metabolizing enzymes have been interpreted as indicating cooperative phenomena [23–25]. Alternatively, there is an explanation based on the idea that phospholipid substrate molecules are not homogeneously distributed within a population of lipid particles, although simultaneously we can suppose the substrate having homogeneous distribution within each particle. Then, modeling the nonhomogeneous substrate distribution on the population of lipid particles, it is assumed that the probability of finding a substrate molecule on a lipid particle does not depend on the number of previous substrate molecules in the same lipid particle. A consequence of this assumption is a Poisson distribution of the substrate on the mixture

Defining α as the average number of lipid molecules per lipid particle (in micellar case, this parameter is known as aggregation number), and according to Eq. 17

<sup>2</sup> <sup>1</sup> <sup>þ</sup>

We consider a lipolytic enzyme following the phospholipid-binding model in a system of multiple domains of substrate, and such that the lipid phase is composed by a mixture of lipid particles, each one with homogeneously distributed substrate,

1 fα

(21)

(22)

2 Si〉 value

following the phospholipid binding model

DOI: http://dx.doi.org/10.5772/intechopen.85972

of the lipid particles.

79

in Eq. 21 is replaced into Eq. 16 obtaining

The cross-sectional areas of any lipid molecules in any phases are equal and conserved, and then the total phospholipid S normalized area conservation equation is given as:

$$f = \sum\_{i=1}^{n} a\_i f\_{S^i} \tag{15}$$

Thus, again, it can be demonstrated that the enzyme activity for the surface kinetic model does not depend on the substrate ordering, and it is equal to the enzyme activity for the completely homogenous substrate distribution case (Eq. 2). For the phospholipid-binding model, the enzyme activity even depends on the reordering of the substrate on the lipid phase, such that some terms in Eq. 1 must be replaced by more general ones, even more than in Eq. 3. Thus, in case of multiple domains in the phospholipid-binding model, it has been demonstrated theoretically that the enzymatic activity on n substrate domains is given as:

$$V = \frac{kC\_{E\_T} \langle f\_{S'}^2 \rangle}{\frac{k\_m k\_r}{C\_L} + k\_m f + \langle f\_{S'}^2 \rangle} \tag{16}$$

where f is defined in according to Eq. 15 and 〈 f 2 Si〉 is the average of the square of the substrate molar fraction weighted by the domain areas:

$$\left\langle f\_{\boldsymbol{S}^i}^2 \right\rangle \equiv \sum\_{i=1}^n a\_i f\_{\boldsymbol{S}^i}^2 \tag{17}$$

Two abovementioned results can be represented by Eqs. 16 and 17: First, when the lipid substrate distribution is completely homogeneous (n = 1), Eq. 1 is obtained. Secondly, when there are only two domains of lipid substrate (enriched substrate domain and nonenriched substrate domain; n = 2), Eq. 3 is obtained.

To calculate any V-value, 〈 f 2 <sup>S</sup><sup>i</sup>〉 must be calculated as a summation over the whole surface of the lipid phase. Thus, minimum and maximum V-values are calculated from minimum and maximum 〈 f 2 <sup>S</sup><sup>i</sup>〉 values, respectively:

$$\left\langle f\_{S'}^2 \right\rangle\_{\text{min}} = \sum\_{i=1}^n a\_i f^2 = f^2 \sum\_{i=1}^n a\_i = f^2 \tag{18}$$

(using Eq. 14, i.e., the conservation of the total lipid area) and

$$
\left< f\_{\mathcal{S}}^2 \right>\_{\max} = f \tag{19}
$$

Thus, the minimum V-value as a function of substrate distribution was obtained for a homogeneous distribution ( f <sup>S</sup><sup>i</sup> ¼ f ). The maximum V-value was obtained for one domain composed only by molecules of phospholipid substrate, and the other one without substrate (e.g., f1 = 1 and f2 = 0). Then, the enzymatic activities are within the following limiting values when there are multiple membrane domains:

$$k\frac{kC\_{E\_{\rm T}}f^2}{\frac{k\_mk\_{\rm r}}{\rm C\_{\rm L}}+k\_mf\,+f^2} \le V \le \frac{kC\_{E\_{\rm T}}f}{\frac{k\_mk\_{\rm r}}{\rm C\_{\rm L}}+k\_mf\,+f} \tag{20}$$

Effects of Vesicular Membranes Reordering on the Activity of Lipid Metabolizing Enzymes DOI: http://dx.doi.org/10.5772/intechopen.85972

## 5. Effects of Poisson distribution of substrate on enzyme activity following the phospholipid binding model

Since the extended theory shown above does not consider boundaries, the same can be applied to a population of lipid particles (like vesicles or micelles), each one as a substrate domain represented in a summation term in Eq. 17.

Frequently, data from in vitro kinetic studies of lipid metabolizing enzymes have been interpreted as indicating cooperative phenomena [23–25]. Alternatively, there is an explanation based on the idea that phospholipid substrate molecules are not homogeneously distributed within a population of lipid particles, although simultaneously we can suppose the substrate having homogeneous distribution within each particle. Then, modeling the nonhomogeneous substrate distribution on the population of lipid particles, it is assumed that the probability of finding a substrate molecule on a lipid particle does not depend on the number of previous substrate molecules in the same lipid particle. A consequence of this assumption is a Poisson distribution of the substrate on the mixture of the lipid particles.

Defining α as the average number of lipid molecules per lipid particle (in micellar case, this parameter is known as aggregation number), and according to Eq. 17 and Poisson-distributed substrate, it can be demonstrated that [22]

$$
\langle f\_S^2 \rangle = f^2 \left( 1 + \frac{1}{fa} \right) \tag{21}
$$

We consider a lipolytic enzyme following the phospholipid-binding model in a system of multiple domains of substrate, and such that the lipid phase is composed by a mixture of lipid particles, each one with homogeneously distributed substrate, but Poisson distributed over the same population of particles. Then, the 〈 f 2 Si〉 value in Eq. 21 is replaced into Eq. 16 obtaining

$$V = \frac{kC\_{E\_{\mathbb{T}}}f^2\left(1 + \frac{1}{f^a}\right)}{\frac{k\_mk\_i}{C\_L} + k\_mf + f^2\left(1 + \frac{1}{f^a}\right)}\tag{22}$$

That is, Eq. 22 is an expression of the rates of enzyme activity on Poissondistributed phospholipid substrates. Applying this equation to published kinetic parameters for PLC acting on PIP2 in Triton X-100 micelles (CL = 200 μM, km = 0.13, and ks = 170 μM) [23], the ratio between "the enzyme activity on micelles with Poisson-distributed substrate" (Eq. 22) and "the enzyme activity on micelles with homogeneously distributed substrate" (Eq. 1) was calculated. Assuming a range of f from 10�<sup>1</sup> to 10�<sup>3</sup> (as in published work [12, 13]), activity ratios between 1.0 and 6.0 (α ¼ 200) and between 1.1 and 11.0 (α ¼ 100) were obtained. We can see that without considering cooperative effects, a simple explanation for a very high departure from the homogeneous standard model may be that the increases in enzyme activity are due to Poisson distribution of the substrate.

#### 5.1 Substrate-distribution dependence of PLA2 activity in mixed micelles

The mentioned kinetic theory applied to Poisson-distributed substrate on lipid particles has been verified with experimental results, and their obtained parameters have been compared with those of the canonical phospholipid-binding model originally developed for homogeneously distributed substrate on mixed micelles

1 ¼ ∑ n i¼1

The cross-sectional areas of any lipid molecules in any phases are equal and conserved, and then the total phospholipid S normalized area conservation equation

> f ¼ ∑ n i¼1

<sup>V</sup> <sup>¼</sup> kCET <sup>f</sup>

kmks

f 2 Si � <sup>∑</sup>

domain and nonenriched substrate domain; n = 2), Eq. 3 is obtained.

min ¼ ∑ n i¼1 aif <sup>2</sup> <sup>¼</sup> <sup>f</sup> <sup>2</sup> ∑ n i¼1

> f 2 Si

Thus, the minimum V-value as a function of substrate distribution was obtained for a homogeneous distribution ( f <sup>S</sup><sup>i</sup> ¼ f ). The maximum V-value was obtained for one domain composed only by molecules of phospholipid substrate, and the other one without substrate (e.g., f1 = 1 and f2 = 0). Then, the enzymatic activities are within the following limiting values when there are multiple membrane domains:

<sup>2</sup> ≤V ≤

(using Eq. 14, i.e., the conservation of the total lipid area)

kCET f 2

CL þ km f þ f

kmks

whole surface of the lipid phase. Thus, minimum and maximum V-values are

2

2 Si 

> 2 Si

2

<sup>S</sup><sup>i</sup>〉 must be calculated as a summation over the

<sup>S</sup><sup>i</sup>〉 values, respectively:

max ¼ f (19)

CL <sup>þ</sup> km <sup>f</sup> <sup>þ</sup> <sup>f</sup> (20)

ai ¼ f

kCET f

kmks

CL þ km f þ f

n i¼1 ai f 2

Two abovementioned results can be represented by Eqs. 16 and 17: First, when the lipid substrate distribution is completely homogeneous (n = 1), Eq. 1 is obtained. Secondly, when there are only two domains of lipid substrate (enriched substrate

2

that the enzymatic activity on n substrate domains is given as:

where f is defined in according to Eq. 15 and 〈 f

Extracellular Vesicles and Their Importance in Human Health

To calculate any V-value, 〈 f

and

78

calculated from minimum and maximum 〈 f

f 2 Si 

the substrate molar fraction weighted by the domain areas:

Thus, again, it can be demonstrated that the enzyme activity for the surface kinetic model does not depend on the substrate ordering, and it is equal to the enzyme activity for the completely homogenous substrate distribution case (Eq. 2). For the phospholipid-binding model, the enzyme activity even depends on the reordering of the substrate on the lipid phase, such that some terms in Eq. 1 must be replaced by more general ones, even more than in Eq. 3. Thus, in case of multiple domains in the phospholipid-binding model, it has been demonstrated theoretically

is given as:

ai (14)

ai f Si (15)

(16)

<sup>S</sup><sup>i</sup> (17)

Si〉 is the average of the square of

<sup>2</sup> (18)


#### Table 1.

Values for fitting kinetic parameters for PLA2 activity on Triton X-100 mixed micelles regarding either homogeneous substrate distribution or Poisson substrate distribution, with adjustable εTt parameter (the molar concentration of detergent that is not kinetically active, a proposed parameter that enhance the fitting).

[12, 13]. Both models ("nonhomogeneous model" and "homogeneous model," respectively) can be represented simultaneously by the following general equation:

$$V = \frac{kC\_{E\_T}f^2}{\frac{(k\_m/F\_{f,s} - a)k\_r}{C\_L} + (k\_m/F\_{f,a})f + f^2} \tag{23}$$

where

$$F\_{f,a} = \mathbf{1},\tag{24}$$

Here, only two kinetic models have been considered, but similar theoretical framework could be applied on other ones. The general mathematical expression for the surface-binding model does not depend on whether the substrate distribution is homogeneous or nonhomogeneous (Eq. 2). Thus, in this kinetic model, any sub-

Effects of Vesicular Membranes Reordering on the Activity of Lipid Metabolizing Enzymes

On the contrary, considering the phospholipid-binding model, the calculations predict how the substrate distribution may affect the activity of the lipid metabolizing enzyme. In particular, the enzyme activity is increased by the transition from the homogeneous substrate distribution to any nonhomogeneous one

Concordantly, in erythrocytes, the Ca2+-induced domains increase the activity of PLA2 [27], an enzyme that follows the phospholipid-binding model [12, 13]. The increased activity agrees with an observed enzyme reordering, which may be due to formed enriched-substrate domains. Then, there will be more enzyme molecules binding to areas of higher substrate molar fraction, causing a larger local enzyme activity. On the other hand, PLCβ kinetic data from micellar experiments have fitted to the phospholipid-binding model using Hill coefficients [28–30], but the usage of this type of coefficients was not useful in monolayers having with large increases in enzyme activity after small increases in the PIP2 fraction [31]. The analysis of pressure versus area isotherm of the monolayers suggested a

nonhomogeneous distribution of the lipids and was proposed that the PIP2 molecules get together into enriched lateral domains, favoring the PLCβ activity, an enzyme following the phospholipid-binding model. This agrees with what is expected

upon addition of domain-inducing molecules [17, 23, 32, 33]).

Poisson distribution on the lipid particles [34, 35].

81

In other cases, since basic molecules can induce formation of acidic phospholipid domains in membranes, the increased activity of PLC δ1 and PLC δ3 by addition of polyamines or basic proteins such as spermine, protamine, histone, and melittin [32] also can be explained by substrate redistribution. Differently, PLCβ activity decreases in experiments with vesicles containing acidic phospholipid domains induced by the basic molecules, pentalysine, spermine, and MARCKS (151–175) [17]. However, assuming that PLCβ is a phospholipid-binding enzyme, the decrease in enzyme activity may be due to a high competitive effect of the substrate-domaininducing peptide. Such competitive effect overcomes the rise in activity that substrate redistribution would produce. Finally, the importance of each effect is dependent on the used amount of domain-inducing molecule and this could explain the apparent contradictory results of the activities of lipid-metabolizing enzymes, such as PLC (an enzyme following the phospholipid-binding model [24, 29, 30]

Substrate distribution also must be considered in in vitro kinetic experiments of enzymes following the phospholipid-binding model. In this sense, the application of the theory developed here is useful for kinetic experiments with mixed lipid particles (i.e., liposomes or micelles, instead of lipid domains). We assumed that each one of the particles will have a homogeneous molar fraction, which follows a

If the average of substrate molecules per lipid particle in suspension ( f α) is very large ( f α ≫ 1), then Eq. 22 predicts that the enzymatic activity tends to the value obtained for a homogeneously distributed substrate (Eq. 1, or its equivalent, Eqs. 23 and 24). However, in case of decreased average of substrate molecules per lipid particle in suspension ( f α ≪ 1), Eq. 22 predicts that the enzyme activity will be larger than in the homogeneous case at equal f value. Concordantly, some PLC isoenzymes [24, 29, 30] and PLA2 [13] have an increased activity in cases of small substrate molar fractions, similar to cooperative phenomena. However, if these kinetic data could be fitted to Eq. 22, they will contribute to a more simple

strate distribution changing has no kinetic effect.

DOI: http://dx.doi.org/10.5772/intechopen.85972

(Eqs. 16 and 17).

from the theory presented here.

in a homogeneous model (Eq. 1), and

$$F\_{f,a} = \mathbf{1} + \frac{\mathbf{1}}{q\mathcal{f}},\tag{25}$$

in a nonhomogeneous model (Eq. 22).

In micelles, it has been found that α, the average number of lipid molecules per mixed micelle (i.e., the aggregation number), depends on the molar fraction of phospholipid (but not on total detergent concentration [26]) within the concentration range of Triton X-100 and phospholipid used in Hendrickson et al.'s study [13]. Therefore, in order to find the parameters for modeling, the functional dependence of α from f must be taken into account in micellar experiments [22].

In Table 1, all the values of parameters km and kS obtained for homogeneous and nonhomogeneous substrate distributions are compared. The differences indicate that the values of these kinetic parameters can depend critically on the distribution of the substrate.

### 6. Discussion

To understand the effect of lipid substrate reordering on their metabolizing enzymes, theoretical results are shown. A simple kinetic model considers a nonhomogeneous membrane with the lipid substrate reordered in two domains with different molar fractions. The results are included in a more general extended theory considering substrate multidomains on either lipid surface of vesicles. Because the calculations do not regard any domain boundaries, the same models obtained from this theory (Eqs. 2 and 16) can be applied on a mixture of lipid particles (vesicles or micelles).

#### Effects of Vesicular Membranes Reordering on the Activity of Lipid Metabolizing Enzymes DOI: http://dx.doi.org/10.5772/intechopen.85972

Here, only two kinetic models have been considered, but similar theoretical framework could be applied on other ones. The general mathematical expression for the surface-binding model does not depend on whether the substrate distribution is homogeneous or nonhomogeneous (Eq. 2). Thus, in this kinetic model, any substrate distribution changing has no kinetic effect.

On the contrary, considering the phospholipid-binding model, the calculations predict how the substrate distribution may affect the activity of the lipid metabolizing enzyme. In particular, the enzyme activity is increased by the transition from the homogeneous substrate distribution to any nonhomogeneous one (Eqs. 16 and 17).

Concordantly, in erythrocytes, the Ca2+-induced domains increase the activity of PLA2 [27], an enzyme that follows the phospholipid-binding model [12, 13]. The increased activity agrees with an observed enzyme reordering, which may be due to formed enriched-substrate domains. Then, there will be more enzyme molecules binding to areas of higher substrate molar fraction, causing a larger local enzyme activity. On the other hand, PLCβ kinetic data from micellar experiments have fitted to the phospholipid-binding model using Hill coefficients [28–30], but the usage of this type of coefficients was not useful in monolayers having with large increases in enzyme activity after small increases in the PIP2 fraction [31]. The analysis of pressure versus area isotherm of the monolayers suggested a nonhomogeneous distribution of the lipids and was proposed that the PIP2 molecules get together into enriched lateral domains, favoring the PLCβ activity, an enzyme following the phospholipid-binding model. This agrees with what is expected from the theory presented here.

In other cases, since basic molecules can induce formation of acidic phospholipid domains in membranes, the increased activity of PLC δ1 and PLC δ3 by addition of polyamines or basic proteins such as spermine, protamine, histone, and melittin [32] also can be explained by substrate redistribution. Differently, PLCβ activity decreases in experiments with vesicles containing acidic phospholipid domains induced by the basic molecules, pentalysine, spermine, and MARCKS (151–175) [17]. However, assuming that PLCβ is a phospholipid-binding enzyme, the decrease in enzyme activity may be due to a high competitive effect of the substrate-domaininducing peptide. Such competitive effect overcomes the rise in activity that substrate redistribution would produce. Finally, the importance of each effect is dependent on the used amount of domain-inducing molecule and this could explain the apparent contradictory results of the activities of lipid-metabolizing enzymes, such as PLC (an enzyme following the phospholipid-binding model [24, 29, 30] upon addition of domain-inducing molecules [17, 23, 32, 33]).

Substrate distribution also must be considered in in vitro kinetic experiments of enzymes following the phospholipid-binding model. In this sense, the application of the theory developed here is useful for kinetic experiments with mixed lipid particles (i.e., liposomes or micelles, instead of lipid domains). We assumed that each one of the particles will have a homogeneous molar fraction, which follows a Poisson distribution on the lipid particles [34, 35].

If the average of substrate molecules per lipid particle in suspension ( f α) is very large ( f α ≫ 1), then Eq. 22 predicts that the enzymatic activity tends to the value obtained for a homogeneously distributed substrate (Eq. 1, or its equivalent, Eqs. 23 and 24). However, in case of decreased average of substrate molecules per lipid particle in suspension ( f α ≪ 1), Eq. 22 predicts that the enzyme activity will be larger than in the homogeneous case at equal f value. Concordantly, some PLC isoenzymes [24, 29, 30] and PLA2 [13] have an increased activity in cases of small substrate molar fractions, similar to cooperative phenomena. However, if these kinetic data could be fitted to Eq. 22, they will contribute to a more simple

[12, 13]. Both models ("nonhomogeneous model" and "homogeneous model," respectively) can be represented simultaneously by the following general equation:

Values for fitting kinetic parameters for PLA2 activity on Triton X-100 mixed micelles regarding either homogeneous substrate distribution or Poisson substrate distribution, with adjustable εTt parameter (the molar concentration of detergent that is not kinetically active, a proposed parameter that enhance the fitting).

2

Phospholipid-binding model with homogeneous substrate distribution

km = 0.0532 0.0216 kS = 1.9168 mM 6.2170 mM

km = 0.1379 0.0942 kS = 0.1132 mM 0.4107 mM

> 1 αf

<sup>f</sup> <sup>þ</sup> <sup>f</sup>

2

Ff,<sup>α</sup> ¼ 1, (24)

, (25)

(23)

Phospholipid-binding model with Poissondistributed substrate

CL þ km=Ff,<sup>α</sup>

Ff,<sup>α</sup> ¼ 1 þ

of α from f must be taken into account in micellar experiments [22].

In micelles, it has been found that α, the average number of lipid molecules per mixed micelle (i.e., the aggregation number), depends on the molar fraction of phospholipid (but not on total detergent concentration [26]) within the concentration range of Triton X-100 and phospholipid used in Hendrickson et al.'s study [13]. Therefore, in order to find the parameters for modeling, the functional dependence

In Table 1, all the values of parameters km and kS obtained for homogeneous and nonhomogeneous substrate distributions are compared. The differences indicate that the values of these kinetic parameters can depend critically on the distribution

To understand the effect of lipid substrate reordering on their metabolizing enzymes, theoretical results are shown. A simple kinetic model considers a nonhomogeneous membrane with the lipid substrate reordered in two domains with different molar fractions. The results are included in a more general extended theory considering substrate multidomains on either lipid surface of vesicles. Because the calculations do not regard any domain boundaries, the same models obtained from this theory (Eqs. 2 and 16) can be applied on a mixture of lipid

<sup>V</sup> <sup>¼</sup> kCET <sup>f</sup>

ð Þ km=Ff, <sup>α</sup> ks

in a homogeneous model (Eq. 1), and

Parameter values are taken from Table II in Salinas et al. 2011 [14].

Extracellular Vesicles and Their Importance in Human Health

in a nonhomogeneous model (Eq. 22).

where

Kinetic parameters for PLA2 activity on Triton X-100/thio-

Kinetic parameters for PLA2 activity on Triton X-100/thio-

PC mixed micelles

PE mixed micelles

Table 1.

of the substrate.

6. Discussion

80

particles (vesicles or micelles).

explanation based on the substrate distribution. In other case, in experiments with PLA2, increase in enzyme activity has been associated with decrease of the size of lipid vesicles, suggesting that PLA2 activity happens in areas with structural defects [36]. Again, here our approach based on substrate distribution provides a simple alternative explanation: if the substrate molar fraction in the mixture of lipid particles is Poisson distributed, then Eq. 22 could be applied. Considering that substrate is fixed ( f fixed), the decreasing vesicle sizes (α decrease) produces decreasing average of substrate molecules per vesicle ( f α). Therefore, in according to Eq. 22, at low values of f α and for Poisson-distributed substrate, the relative enzyme activity must increase more notoriously, regarding the case of homogeneous distribution of substrate as reference.

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The application of the theoretical model (Eq. 22) in published results of the PLA2 activity on Triton X-100 mixed micelles of phospholipids [13], considering Poisson-distribution substrate, allows a very good fit to the data. Interestingly, the estimated values of the kinetic parameters strongly depend on whether the substrate distribution used in the fitting is distributed either homogeneously or according to Poisson.

On the other hand, detergent-based micelles are not capable to mimic the lipid environment of membranes. In such case, the activities of most membrane protein could be affected. As a solution, liposomes or high-density apolipoprotein particles have been proposed [2]. However, compared with those experimental models, the EVs offer a number of potential benefits, such as providing a more adequate membrane environment for membrane proteins, in terms of both dynamics and stability.

In summary, depending on the enzyme model, the lipid substrate reordering can regulate the enzyme activity, giving to the membrane organization a topological role in the control of cell process. In order to a good estimation of kinetic parameters in phospholipase enzymology, in vitro kinetic experiments must consider the substrate distribution effects. Also, many complex metabolic effects of substratedomain-inducing molecules can be explained by a result of the balance between the competitive effects of the substrate domain inducers and substrate redistribution. All these considerations should be taken into account even in case of EVs, in relation to their formation, functionality, and action on membrane targets.

## Author details

Dino G. Salinas Centro de Investigación Biomédica, Facultad de Medicina, Universidad Diego Portales, Santiago, Chile

\*Address all correspondence to: dino.salinas@udp.cl

© 2019 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Effects of Vesicular Membranes Reordering on the Activity of Lipid Metabolizing Enzymes DOI: http://dx.doi.org/10.5772/intechopen.85972
