Models for biological cells

Let us now look at some properties of vesicles and liposomes (liposomes can be defined as vesicles made out of lipids, although often the two terms are used synonymously). This will be a preliminary to the next chapter, where the reactivity of vesicles as models for biological cells will be considered in more detail. 

Vesicles are commonly considered models for biological cells. This is due to the bilayer spherical structure which is also present in most biological cells, and to the fact that vesicles can incorporate biopolymers and host biological reactions. Self-reproduction, an autocatalytic reaction already illustrated in the chapters on self-reproduction and autopoiesis, also belongs to the field of reactivity of vesicles. Some additional aspects of this process will be considered here, together with some particular properties of the growth of vesicles - the so-called matrix effect. 

Models for biological membranes have either been realized as planar lipid monolayers at the gas-water interface (3) or as bi-molecular lipid membranes (BLM) (4) and spherical liposomes (vesicles), respectively (5 6) (Figure 2.). All these models that are only composed of lipid molecules exhibit a diminished stability compared to natural cell membranes. Obviously the protein part besides being functionally important plays a role in terms of stability of biomembranes. This is the case not only for the integral but especially for the boundary proteins ( 7). 

As indicated above, theoretical models for biological rhythms were first used in ecology to study the oscillations resulting from interactions between populations of predators and preys [6]. Neural rhythms represent another field where such models were used at an early stage The formalism developed by Hodgkin and Huxley [7] stiU forms the core of most models for oscillations of the membrane potential in nerve and cardiac cells [33-35]. Models were subsequently proposed for oscillations that arise at the cellular level from regulation of enzyme, receptor, or gene activity (see Ref. 31 for a detailed fist of references). 

The fluid-mosaic model for biological membranes as envisioned by Singer and Nicolson. Integral membrane proteins are embedded in the lipid bilayer peripheral proteins are attached more loosely to protruding regions of the integral proteins. The proteins are free to diffuse laterally or to rotate about an axis perpendicular to the plane of the membrane. For further information, see S. J. Singer and G. L. Nicolson, The fluid mosaic model of the structure of cell membranes, Science 175 720, 1972. 

Figure 13.7 The fluid mosaic model of biological cells, (image courtesy of www.wikipedia.org). See plate section for colour version of this image.

The automaton model for the cell cycle represents a cellular automaton. Because the latter term has been used in a partly different context, it is useful to distinguish the present model from those considered in previous studies. Cellular automata are often used to describe the spatiotemporal evolution of chemical or biological... 

Of course, it is impossible to include all possible chemicals in a model. Because our constructive biology is aimed at neither making a complicated realistic model for a cell nor imitating a specific cellular function, we set up a minimal model with reaction network, to answer the questions raised in Section I. Now, there are several levels of modeling, depending on what question we are trying to answer. 

It is important to note that alkane oxidation reactions by various oxygen atom donors in cases when a metal-complex catalyst is a metalloporphyrin (or even any other complex) can he considered to he a model for biological hydrocarbon oxidation. The next chapter will be fully devoted to the oxidations of alkanes and arenes in living cells and modeling these processes using metal complexes. 

The rationale for and development of mathematical models for single-cells are reviewed. The potential use of a computer model for Escherichia coll in ascertaining the plausibility of basic biological hypotheses is Illustrated with respect to the control of the Initiation of DNA synthesis and with respect to ammonium ion assimilation. 

In these situations (biological membranes and polymer-resin membranes), the fixed charge membrane theory with various aqueous pore sizes may be a better theoretical model to explain the mechanism of the observed transmembrane potential. Ohki attempted to analyze the transmembrane potential for a membrane having an aqueous pore the surface of which possesses fixed charges. He used a number of assumptions to simplify the mathematical treatment. Further development of such a membrane potential theory therefore seems to be necessary in order to describe the observed membrane potential for biological cell systems. 

Micelles are important in many uses of surfactants for their capacity to solubilize water-insoluble compounds. Vesicles are model systems for biological cells and can be used for entrapping active compounds in their insides. Besides, vesicles and micelles are used as microreactors for performing chemical reactions and preparing solid nanoparticles of varied shapes. 

FIGURE 3b Schematic illustration of mathematical model for the cell cycle. SOURCE Reprinted with permission from the American Society for Cell Biology (Chen et al., 2000). 

Plickert G, Frank U, Muller WA. Hydractinia, a pioneering model for stem cell biology and reprograming somatic cells to pluripotency. Int J Dev Biol. 2012 56 519-34. 

Until the 1990s, the most widely accepted model for the cell membrane was the fluid mosaic model. In this model, lipids and embedded membrane proteins were described as randomly distributed, with no particular in-plane distribution. This model is now considered simplistic, and current thinking is that biological membranes have a complicated in-plane organization. It is a controversial question whether the thermodynamic phase behavior of the constituent membrane lipids can play an important role in membrane function, and a large amount of literature on the subject has been written. 

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