Cao García, Francisco Javier

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First Name
Francisco Javier
Last Name
Cao García
Universidad Complutense de Madrid
Faculty / Institute
Ciencias Físicas
Estructura de la Materia, Física Térmica y Electrónica
Física Aplicada
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Now showing 1 - 3 of 3
  • Publication
    Mechanics of Constriction during Cell Division: A Variational Approach
    (PUBLIC LIBRARY SCIENCE, 2013-08-21) Almendro Vedia, Víctor Galileo; Monroy Muñoz, Francisco; Cao García, Francisco Javier; Thierry Soldati
    During symmetric division cells undergo large constriction deformations at a stable midcell site. Using a variational approach, we investigate the mechanical route for symmetric constriction by computing the bending energy of deformed vesicles with rotational symmetry. Forces required for constriction are explicitly computed at constant area and constant volume, and their values are found to be determined by cell size and bending modulus. For cell-sized vesicles, considering typical bending modulus of k = 10kBT, we calculate constriction forces in the range 0.1 - 1pN. The instability of symmetrical constriction is shown and quantified with a characteristic coefficient of the order of - 50kBT, thus evidencing that cells need a robust mechanism to stabilize constriction at midcell.
  • Publication
    Analytical results for cell constriction dominated by bending energy
    (American Physical Society, 2015-01-28) Almendro Vedia, Víctor Galileo; Monroy Muñoz, Francisco; Cao García, Francisco Javier
    Analytical expressions are obtained for the main magnitudes of a symmetrically constricted vesicle. These equations provide an easy and compact way to predict minimal requirements for successful constriction and its main magnitudes. Thus, they can be useful for the design of synthetic divisomes and give good predictions for magnitudes including constriction energy, length of the constriction zone, volume and area of the vesicle, and the stability coefficient for symmetric constriction. The analytical expressions are derived combining a perturbative expansion in the Lagrangian for small deformations with a cosine ansatz in the constriction region. Already the simple fourth-order (or sixth-order) approximation provides a good approximation to the values of the main physical magnitudes during constriction, as we show through comparison with numerical results. Results are for vesicles with negligible effects from spontaneous curvature, surface tension, and pressure differences. This is the case when membrane components generating spontaneous curvature are scarce, membrane trafficking is present with low energetic cost, and the external medium is isotonic
  • Publication
    Modeling the Mechanics of Cell Division: Influence of Spontaneous Membrane Curvature, Surface Tension, and Osmotic Pressure
    (Frontiers Media SA, 2017) Beltrán de Heredia Rodríguez, Elena; Almendro Vedia, Víctor Galileo; Monroy, Francisco; Cao García, Francisco Javier
    Many cell division processes have been conserved throughout evolution and are being revealed by studies on model organisms such as bacteria, yeasts, and protozoa. Cellular membrane constriction is one of these processes, observed almost universally during cell division. It happens similarly in all organisms through a mechanical pathway synchronized with the sequence of cytokinetic events in the cell interior. Arguably, such a mechanical process is mastered by the coordinated action of a constriction machinery fueled by biochemical energy in conjunction with the passive mechanics of the cellular membrane. Independently of the details of the constriction engine, the membrane component responds against deformation by minimizing the elastic energy at every constriction state following a pathway still unknown. In this paper, we address a theoretical study of the mechanics of membrane constriction in a simplified model that describes a homogeneous membrane vesicle in the regime where mechanical work due to osmotic pressure, surface tension, and bending energy are comparable. We develop a general method to find approximate analytical expressions for the main descriptors of a symmetrically constricted vesicle. Analytical solutions are obtained by combining a perturbative expansion for small deformations with a variational approach that was previously demonstrated valid at the reference state of an initially spherical vesicle at isotonic conditions. The analytic approximate results are compared with the exact solution obtained from numerical computations, getting a good agreement for all the computed quantities (energy, area, volume, constriction force). We analyze the effects of the spontaneous curvature, the surface tension and the osmotic pressure in these quantities, focusing especially on the constriction force. The more favorable conditions for vesicle constriction are determined, obtaining that smaller constriction forces are required for positive spontaneous curvatures, low or negative membrane tension and hypertonic media. Conditions for spontaneous constriction at a given constriction force are also determined. The implications of these results for biological cell division are discussed. This work contributes to a better quantitative understanding of the mechanical pathway of cellular division, and could assist the design of artificial divisomes in vesicle-based self-actuated microsystems obtained from synthetic biology approaches.