Thermodynamics of vesicle growth and instability

Primordial sex facilitates the emergence of evolution

Compartments are ubiquitous throughout biology, and they have very likely played a crucial role at the origin of life. Here we assume that a protocell, which is a compartment enclosing functional components, requires N such components in order to be evolvable. We calculate the timescale in which a minimal evolvable protocell is produced. We show that when protocells fuse and share information, the timescales polynomially in N By contrast, in the absence of fusion, the worst-case scenario is exponential in N We discuss the implications of this result for the origin of life and other biological processes.

Directed Growth of Biomimetic Microcompartments

Contemporary biological cells are sophisticated and highly compartmentalized. Compartmentalization is an essential principle of prebiotic life as well as a key feature in bottom-up synthetic biology research. In this review, the dynamic growth of compartments as an essential prerequisite for enabling self-reproduction as a fundamental life process is discussed. The micrometer-sized compartments are focused on due to their cellular dimensions. Two types of compartments are considered, membraneless droplets and membrane-bound microcompartments. Growth mechanisms of aqueous droplets such as protein (condensates) or macromolecule-rich droplets (aqueous two phase systems) and coacervates are discussed, for which growth occurs via Ostwald ripening or coalescence. For membrane-bound compartments, vesicles are considered, which are composed of fatty acids, lipids, or polymers, where directed growth can occur via fusion or uptake of material from the surrounding. The development of novel approaches for growth of biomimetic microcompartments can eventually be utilized to construct new synthetic cells.

On the Relation between Chemical Oscillations and Self-Replication

One proposed scenario for the emergence of biochemical oscillations is that they may have provided the basic mechanism behind cellular self-replication by growth and division. However, alternative scenarios not requiring any chemical oscillation have also been proposed. Each of the various protocell models proposed to support one or another scenario comes with its own set of specific assumptions, which makes it difficult to ascertain whether chemical oscillations are required or not for cellular self-replication. This article compares these two cases within a single whole-cell model framework. This model relies upon a membrane embedding a chemical reaction network (CRN) synthesizing all the cellular constituents, including the membrane, by feeding from an external nutrient. Assuming the osmolarity is kept constant, the system dynamics are governed by a set of nonlinear differential equations coupling the chemical concentrations and the surface-area-to-volume ratio. The resulting asymptotic trajectories are used to determine the cellular shape by minimizing the membrane bending energy (within an approximate predefined family of shapes). While the stationary case can be handled quite generally, the oscillatory one is investigated using a simple oscillating CRN example, which is used to identify features that are expected to hold for any network. It is found that cellular self-replication can be reached with or without chemical oscillations, and that a requirement common to both stationary and oscillatory cases is that a minimum spontaneous curvature of the membrane is required for the cell to divide once its area and volume are both doubled. The oscillatory case can result in a greater variety of cellular shape trajectories but raises additional constraints for cellular division and self-replication: (i) the ratio of doubling time to oscillation period should be an integer, and (ii) if the oscillation amplitude is sufficiently high, then the spontaneous curvature must be below a maximum value to avoid early division before the end of the cycle. Because of these additional stringent constraints, it is likely that early protocells did not rely upon chemical oscillations. Biochemical oscillations typical of modern evolved cells may have emerged later through evolution for other reasons (e.g., metabolic advantage) and must have required additional feedback mechanisms for such a self-replicating system to be robust against even slight environmental variations (e.g., temperature fluctuations).

Filamentation as primitive growth mode?

Osmotic pressure influences cellular shape. In a growing cell, chemical reactions and dilution induce changes in osmolarity, which in turn influence the cellular shape. Using a protocell model relying upon random conservative chemical reaction networks with arbitrary stoichiometry, we find that when the membrane is so flexible that its shape adjusts itself quasi-instantaneously to balance the osmotic pressure, the protocell either grows filamentous or fails to grow. This behavior is consistent with a mathematical proof. This suggests that filamentation may be a primitive growth mode resulting from the simple physical property of balanced osmotic pressure. We also find that growth is favored if some chemical species are only present inside the protocell, but not in the outside growth medium. Such an insulation requires specific chemical schemes. Modern evolved cells such as E. coli meet these requirements through active transport mechanisms such as the phosphotransferase system.

Relaxation and curvature-induced molecular flows within multicomponent membranes

The quantitative understanding of membranes is still rooted in work performed in the 1970s by Helfrich and others, concerning amphiphilic bilayers. However, most biological membranes contain a wide variety of nonamphiphilic molecules too. Drawing analogy with the physics of nematic-non-nematic mixtures, we present a dynamical (out-of-equilibrium) description of such multicomponent membranes. The approach combines nematohydrodynamics in the linear regime and a proper use of (differential-) geometry. The main result is to demonstrate that one can obtain equations describing a cross-diffusion effect (similar to the Soret and Dufour effects) between curvature and the (in-membrane) flow of amphiphilic molecules relative to nonamphiphilic ones. Surprisingly, the shape of a membrane relaxes according to a simple heat equation in the mean curvature, a process that is accompanied by a simultaneous boost to the diffusion of amphiphiles away from regions of high curvature. The model also predicts the inverse process, by which the forced bending of a membrane induces a flow of amphiphilic molecules towards areas of high curvature. In principle, numerical values for the relevant diffusion coefficients should be verifiable by experiment.

Stability of growing vesicles

We investigate the stability of growing vesicles using the formalism of nonequilibrium thermodynamics. The vesicles are growing due to the accretion of lipids to the bilayer which forms the vesicle membrane. The thermodynamic description is based on the hydrodynamics of a water and lipid mixture together with a model of the vesicle as a discontinuous system in the sense of linear nonequilibrium thermodynamics. This formulation allows the forces and fluxes relevant to the dynamic stability of the vesicle to be identified. The method is used to analyze the stability of a spherical vesicle against arbitrary axisymmetric perturbations. It is found that there are generically two critical radii at which changes of stability occur. In the case where the perturbation takes the form of a single zonal harmonic, only one of these radii is physical and is given by the ratio 2L(p)/L(γ), where L(p) is the hydraulic conductivity and L(γ) is the Onsager coefficient related to changes in membrane area due to lipid accretion. The stability of such perturbations is related to the value of l corresponding to the particular zonal harmonic: those with lower l are more unstable than those with higher l. Possible extensions of the current work and the need for experimental input are discussed.

Dynamical description of vesicle growth and shape change

We systematize and extend the description of vesicle growth and shape change using linear nonequilibrium thermodynamics. By restricting the study to shape changes from spheres to axisymmetric ellipsoids, we are able to give a consistent formulation which includes the lateral tension of the vesicle membrane. This allows us to generalize and correct a previous calculation. Our present calculations suggest that, for small growing vesicles, a prolate ellipsoidal shape should be favored over oblate ellipsoids, whereas for large growing vesicles oblates should be favored over prolates. The validity of this prediction is examined in the light of the various assumptions made in its derivation.

Spatial model of autocatalytic reactions

Biological cells with all of their surface structure and complex interior stripped away are essentially vesicles--membranes composed of lipid bilayers which form closed sacs. Vesicles are thought to be relevant as models of primitive protocells, and they could have provided the ideal environment for prebiotic reactions to occur. In this paper, we investigate the stochastic dynamics of a set of autocatalytic reactions, within a spatially bounded domain, so as to mimic a primordial cell. The discreteness of the constituents of the autocatalytic reactions gives rise to large sustained oscillations even when the number of constituents is quite large. These oscillations are spatiotemporal in nature, unlike those found in previous studies, which consisted only of temporal oscillations. We speculate that these oscillations may have a role in seeding membrane instabilities which lead to vesicle division. In this way synchronization could be achieved between protocell growth and the reproduction rate of the constituents (the protogenetic material) in simple protocells.

Achievements and open questions in the self-reproduction of vesicles and synthetic minimal cells

Supramolecular chemistry was enriched, about twenty years ago, by the discovery of the self-reproduction of micelles and vesicles. The dynamic aspects and complexity of these systems makes them good models for biological compartments. For example, the self-reproduction of vesicles suggests that the growth in size and number of a vesicle population resembles the pattern of living cells in several aspects, but it take place solely due to physical forces. Several reports demonstrate that reverse micelles, micelles, sub-micrometric and giant vesicles can self-reproduce, generating new particles at the expenses of a suitable precursor. Recently, similar studies are in progress on more complex vesicle-based systems, namely semi-synthetic minimal cells. These are artificial cell-like compartments that are built by filling liposomes with the minimal number of biomolecules, such as DNA, ribosomes, enzymes, etc., in order to construct a living cell in the laboratory. This approach aims to investigate the minimal requirements for molecular systems in order to display some living properties, while it finds relevance in origins of life studies and in synthetic (constructive) biology.

Comment on "Thermodynamics of vesicle growth and instability"

Fanelli and McKane [Phys. Rev. E 78, 051406 (2008)] recently described the growth of vesicles due to the accretion of lipid molecules onto their surface in terms of linear irreversible thermodynamics. They calculated the critical radius at which the shape of a spherical vesicle becomes unstable. Their treatment is different from those previously put forward and, in the following, we explain why we regard their thermodynamic description to be deficient.