Mathematical modeling of a minimal protocell with coordinated growth and division

Data integration strategies for whole-cell modeling

Data makes the world go round-and high quality data is a prerequisite for precise models, especially for whole-cell models (WCM). Data for WCM must be reusable, contain information about the exact experimental background, and should-in its entirety-cover all relevant processes in the cell. Here, we review basic requirements to data for WCM and strategies how to combine them. As a species-specific resource, we introduce the Yeast Cell Model Data Base (YCMDB) to illustrate requirements and solutions. We discuss recent standards for data as well as for computational models including the modeling process as data to be reported. We outline strategies for constructions of WCM despite their inherent complexity.

Towards Design of Self-Organizing Biomimetic Systems

The ability of designing biosynthetic systems with well-defined functional biomodules from scratch is an ambitious and revolutionary goal to deliver innovative, engineered solutions to future challenges in biotechnology and process systems engineering. In this work, several key challenges including modularization, functional biomodule identification, and assembly are discussed. In addition, an in silico protocell modeling approach is presented as a foundation for a computational model-based toolkit for rational analysis and modular design of biomimetic systems.

A comprehensive mechanistic model of iron metabolism in Saccharomyces cerevisiae

The ironome of budding yeast (circa 2019) consists of approximately 139 proteins and 5 nonproteinaceous species. These proteins were grouped according to location in the cell, type of iron center(s), and cellular function. The resulting 27 groups were used, along with an additional 13 nonprotein components, to develop a mesoscale mechanistic model that describes the import, trafficking, metallation, and regulation of iron within growing yeast cells. The model was designed to be simultaneously mutually autocatalytic and mutually autoinhibitory - a property called autocatinhibitory that should be most realistic for simulating cellular biochemical processes. The model was assessed at the systems' level. General conclusions are presented, including a new perspective on understanding regulatory mechanisms in cellular systems. Some unsettled issues are described. This model, once fully developed, has the potential to mimic the phenotype (at a coarse-grain level) of all iron-related genetic mutations in this simple and well-studied eukaryote.

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).

Necessary and sufficient conditions for protocell growth

We consider a generic protocell model consisting of any conservative chemical reaction network embedded within a membrane. The membrane results from the self-assembly of a membrane precursor and is semi-permeable to some nutrients. Nutrients are metabolized into all other species including the membrane precursor, and the membrane grows in area and the protocell in volume. Faithful replication through cell growth and division requires a doubling of both cell volume and surface area every division time (thus leading to a periodic surface area-to-volume ratio) and also requires periodic concentrations of the cell constituents. Building upon these basic considerations, we prove necessary and sufficient conditions pertaining to the chemical reaction network for such a regime to be met. A simple necessary condition is that every moiety must be fed. A stronger necessary condition implies that every siphon must be either fed, or connected to species outside the siphon through a pass reaction capable of transferring net positive mass into the siphon. And in the case of nutrient uptake through passive diffusion and of constant surface area-to-volume ratio, a sufficient condition for the existence of a fixed point is that every siphon be fed. These necessary and sufficient conditions hold for any chemical reaction kinetics, membrane parameters or nutrient flux diffusion constants.

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.

Minimal conditions for protocell stationary growth

We show that self-replication of a chemical system encapsulated within a membrane growing from within is possible without any explicit feature such as autocatalysis or metabolic closure, and without the need for their emergence through complexity. We use a protocell model relying upon random conservative chemical reaction networks with arbitrary stoichiometry, and we investigate the protocell's capability for self-replication, for various numbers of reactions in the network. We elucidate the underlying mechanisms in terms of simple minimal conditions pertaining only to the topology of the embedded chemical reaction network. A necessary condition is that each moiety must be fed, and a sufficient condition is that each siphon is fed. Although these minimal conditions are purely topological, by further endowing conservative chemical reaction networks with thermodynamically consistent kinetics, we show that the growth rate tends to increase on increasing the Gibbs energy per unit molecular weight of the nutrient and on decreasing that of the membrane precursor.

Systems biology perspectives on minimal and simpler cells

The concept of the minimal cell has fascinated scientists for a long time, from both fundamental and applied points of view. This broad concept encompasses extreme reductions of genomes, the last universal common ancestor (LUCA), the creation of semiartificial cells, and the design of protocells and chassis cells. Here we review these different areas of research and identify common and complementary aspects of each one. We focus on systems biology, a discipline that is greatly facilitating the classical top-down and bottom-up approaches toward minimal cells. In addition, we also review the so-called middle-out approach and its contributions to the field with mathematical and computational models. Owing to the advances in genomics technologies, much of the work in this area has been centered on minimal genomes, or rather minimal gene sets, required to sustain life. Nevertheless, a fundamental expansion has been taking place in the last few years wherein the minimal gene set is viewed as a backbone of a more complex system. Complementing genomics, progress is being made in understanding the system-wide properties at the levels of the transcriptome, proteome, and metabolome. Network modeling approaches are enabling the integration of these different omics data sets toward an understanding of the complex molecular pathways connecting genotype to phenotype. We review key concepts central to the mapping and modeling of this complexity, which is at the heart of research on minimal cells. Finally, we discuss the distinction between minimizing the number of cellular components and minimizing cellular complexity, toward an improved understanding and utilization of minimal and simpler cells.

Mechanics of constriction during cell division: a variational approach

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 [Formula: see text], we calculate constriction forces in the range [Formula: see text]. The instability of symmetrical constriction is shown and quantified with a characteristic coefficient of the order of [Formula: see text], thus evidencing that cells need a robust mechanism to stabilize constriction at midcell.