Legumes as food ingredient: characterization, processing, and applications

Editores: Jiménez-López, José Carlos (CSIC); Clemente, Alfonso (CSIC

Effective model for the mechanical properties of a partially covered polymer.

<p>(Panel A) Scheme of a polymer (red), partially covered by ligands (green), under a tension <i>F</i>. (Panel B) Zoom of a ligand bound to a polymer. Each ligand covers <i>m</i> monomers, and the end-to-end distance of the DNA segment covered by one ligand is given by the parameter <i>a</i>. (Panel C) Effective mechanical decomposition of the partially covered polymer in two chains: one chain corresponds to the naked region and the other chain corresponds to the covered region. Note that distribution of ligands along the polymer is important for thermodynamic properties, this effective mechanical decomposition was done to effectively compute the extension. An extensible worm-like chain (XWLC) model is considered for the naked region, while a freely-jointed chain (FJC) model is assumed for the covered region.</p

Extensions per contour length of a XWLC as function of the pulling force.

<p>Comparison of the extensions per contour length of a XWLC as function of the pulling force given by: the Marko-Siggia implicit equation (solid red line), the analytic approximations valid for the low force regime (dashed blue line), and the analytic approximation for the high force regime (dot-dashed green line). The dotted black vertical line marks the force which splits the low and high force regimes, <i>K</i>_<i>B</i><i>T</i>/<i>L</i>_<i>p</i>. This figure corresponds to the the following sets of parameters: <i>L</i>_<i>p</i> = 0.715 <i>nm</i>, <i>K</i>₀ = 700 <i>pN</i> (which are of the order of the values for ssDNA [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0174830#pone.0174830.ref024" target="_blank">24</a>]) and <i>K</i>_<i>B</i><i>T</i> = 4.11 <i>pN nm</i>.</p

Equilibrium coverage and extension of the polymer in the presence of ligands.

<p>(Panel A): Equilibrium coverage of a polymer as function of the tension <i>F</i>, assuming that the ligands bind to the polymer in a unique mode. The elastic contribution to the free energy of the naked monomers was estimated using the Marko-Siggia formula Eq (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0174830#pone.0174830.e003" target="_blank">2</a>). The equilibrium coverage was computed using both the ideal gas [Eq (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0174830#pone.0174830.e040" target="_blank">18</a>)] and the Tonks gas [Eq (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0174830#pone.0174830.e047" target="_blank">20</a>)] models. We also consider that the maximum possible coverage is 100%. (Panel B): Equilibrium extension of the covered polymer as function of the pulling force, resulting from employing the coverage of Panel A in the force-extension relation Eq (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0174830#pone.0174830.e013" target="_blank">9</a>). In this figure the values of the parameters of the polymer are of the order of those of ssDNA [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0174830#pone.0174830.ref024" target="_blank">24</a>]: <i>N</i> = 5080, <i>d</i>₀ = 0.57 <i>nm</i>, <i>L</i>_<i>p</i> = 0.715 <i>nm</i>, <i>K</i>₀ = 700 <i>pN</i> and <i>K</i>_<i>B</i><i>T</i> = 4.11 <i>pN nm</i>, while, for the ligands, we consider two different binding modes, with parameters of the order of those of E. Coli SSB [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0174830#pone.0174830.ref047" target="_blank">47</a>,<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0174830#pone.0174830.ref059" target="_blank">59</a>] and HmtSSB proteins [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0174830#pone.0174830.ref061" target="_blank">61</a>]: <i>m</i> = 65 or 35, <i>a</i> = 5 <i>nm</i> and <i>ϵ</i>^<i>b</i> = <i>m</i> × 0.5 × <i>K</i>_<i>B</i><i>T</i>.</p

Mechanics, thermodynamics, and kinetics of ligand binding to biopolymers.

Ligands binding to polymers regulate polymer functions by changing their physical and chemical properties. This ligand regulation plays a key role in many biological processes. We propose here a model to explain the mechanical, thermodynamic, and kinetic properties of the process of binding of small ligands to long biopolymers. These properties can now be measured at the single molecule level using force spectroscopy techniques. Our model performs an effective decomposition of the ligand-polymer system on its covered and uncovered regions, showing that the elastic properties of the ligand-polymer depend explicitly on the ligand coverage of the polymer (i.e., the fraction of the polymer covered by the ligand). The equilibrium coverage that minimizes the free energy of the ligand-polymer system is computed as a function of the applied force. We show how ligands tune the mechanical properties of a polymer, in particular its length and stiffness, in a force dependent manner. In addition, it is shown how ligand binding can be regulated applying mechanical tension on the polymer. Moreover, the binding kinetics study shows that, in the case where the ligand binds and organizes the polymer in different modes, the binding process can present transient shortening or lengthening of the polymer, caused by changes in the relative coverage by the different ligand modes. Our model will be useful to understand ligand-binding regulation of biological processes, such as the metabolism of nucleic acid. In particular, this model allows estimating the coverage fraction and the ligand mode characteristics from the force extension curves of a ligand-polymer system