Structural Modifications and Clustering of Low-Density Lipoproteins in Solution Induced by Heating

Abstract

This work presents a systematic study of low-density lipoprotein (LDL) in solutions subjected to subtle temperature changes, monitored by small angle X-ray scattering. From the data analysis, information about the equilibrium aggregation of the particles, as well as changes on the internal structure of the lipoproteins, were observed. The electron density profiles of the LDL particles were retrieved with a recently developed deconvolution method. Our results indicate that LDL particles keep their structure in the temperature range from about 22 °C up to 60 °C. Moreover, the formation of aggregates and their evolution as a function of time were monitored. Interestingly, when the temperature is raised to 80 °C, the results indicate the rupture of the particle and unspecific aggregation.

Appendix 1

a) Derivation of Eqs. 8 and 9

The scattering intensity for a system composed of two populations is given by:

$$ I{(0)}_{tot}={c}_{LDL}{\left(\varDelta \rho \right)}^2{V}_{LDL}^2+{c}_{agg}{\left(\varDelta \rho \right)}^2{V}_{agg}^2 $$

(a1)

$$ I{(0)}_{tot}={c}_{LDL}{\left(\varDelta \rho \right)}^2{V}_{LDL}^2\left(1+{S}_C^{agg}\right) $$

(a2)

where,

$$ {S}_C^{agg}=\frac{c_{agg}{V}_{agg}^2}{c_{LDL}{V}_{LDL}^2} $$

(a3)

The fraction of the particles in each population is the ratio between the number of particles in one population divided by the total number of particles weighted in a given way. For the number fraction, it is not necessary to use weighting, for the volume fraction one has to weight by the volume and for the intensity fraction the weighting function is the volume square. It is possible to write a single formula for the fractions if one uses as weighting function the volume to the power 2-α :

$$ \begin{array}{c}\hfill {f}_{LDL}^i=\frac{c_{LDL}{\left(\varDelta \rho \right)}^2{V}_{LDL}^{2-\alpha }}{c_{LDL}{\left(\varDelta \rho \right)}^2{V}_{LDL}^{2-\alpha }+{c}_{agg}{\left(\varDelta \rho \right)}^2{V}_{LDL}^{2-\alpha }}\hfill \\ {}\hfill {f}_{LDL}^i=\frac{c_{LDL}{V}_{LDL}^{2-\alpha }}{c_{LDL}{V}_{LDL}^{2-\alpha }+{c}_{agg}{V}_{LDL}^{2-\alpha }}=\frac{c_{LDL}{V}_{LDL}^{2-\alpha }/{c}_{LDL}{V}_{LDL}^{2-\alpha }}{\left({c}_{LDL}{V}_{LDL}^{2-\alpha }+{c}_{agg}{V}_{LDL}^{2-\alpha}\right)/{c}_{LDL}{V}_{LDL}^{2-\alpha }}=\frac{1}{1+\frac{c_{agg}{V}_{agg}^{2-\alpha }}{c_{LDL}{V}_{LDL}^{2-\alpha }}}\hfill \\ {}\hfill {f}_{LDL}^i=\frac{1}{1+{S}_C^{agg}\frac{V_{LDL}^2}{V_{agg}^2}\frac{V_{agg}^{2-\alpha }}{V_{LDL}^{2-\alpha }}}=\frac{1}{1+{S}_C^{agg}{\left(\frac{V_{agg}}{V_{LDL}}\right)}^{-\alpha }}\Rightarrow {f}_{LDL}^i=\frac{1}{1+{S}_C^{agg}{\left(\frac{V_{LDL}}{V_{agg}}\right)}^{\alpha }}\hfill \end{array} $$

(a4)

For the fraction of aggregates weighted by the volume to the power 2-α, simple algebraic operations lead to,

$$ {f}_{agg}^i=\frac{1}{1+\frac{1}{S_C^{agg}}{\left(\frac{V_{agg}}{V_{LDL}}\right)}^{\alpha }} $$

(a5)

By inspection, one can show that f ⁱ _LDL  + f ⁱ _agg  = 1.

If one assumes that the LDL particles and aggregates have a globular shape, the volume scales with the cube of the particle radius of gyration, so

$$ {f}_{LDL}^i=\frac{1}{1+{S}_C^{agg}{\left(\frac{{\left({R}_G^{LDL}\right)}^3}{{\left({R}_G^{agg}\right)}^3}\right)}^{\alpha }}=\frac{1}{1+{S}_C^{agg}{\left(\frac{R_G^{LDL}}{R_G^{agg}}\right)}^{3\alpha }} $$

(a6)

$$ {f}_{agg}^i=\frac{1}{1+\frac{1}{S_C^{agg}}{\left(\frac{R_G^{agg}}{R_G^{LDL}}\right)}^{3\alpha }} $$

(a7)

For the numerical fraction, i = “num” and α = 2; for volume fraction, i = “vol” and α = 1; and for the intensity fraction, i = “int” and α = 0.