Quantum processes in evolution of regulation of living system (mathematical modelling)

We have developed an imitation model of the appearance of regulation of physiological functions of protocell at the initial stages of evolution of living system. It is based on suggestion of the appearance of signal function in spontaneously formed products of partial hydrolysis of the protocell polypeptides, based on which there appear the regulatory molecules--quanta of regulation. For construction of the model, the mathematical apparatus of final automats and of genetic algorithm is used. The model has demonstrated the positive role of involvement of regulatory peptides in the system of regulation of protocell functions to provide its viability under the changing envelopment conditions.     

Imitational modeling of process of evolution: From organic macromolecules to protocell and animal cell

A dynamic imitational model of initial stages of cell evolution has been developed based on role of environmental calcium concentration. The model is designed from our hypothesis about the medium of the appearance of protocells, which could be potassium water reservoirs rather than sea salt water with its predominance of sodium salts. The necessary elements of the appearance of the protocells served organic molecules, code of their synthesis, and formation of macromolecules under favorable ion concentration in environment: a high K⁺ and Mg²⁺ and a low Na⁺ concentration. The model is based on an assumption that one of the first stages in evolution of life was the appearance in the potassium-magnesium water reservoirs of organic molecules capable for self-replication on the basis of genetic code and formation of protocell with the potassium cytoplasm. The model has demonstrated necessity of formation of cell envelope for development of the protocell. Replacement of the dominant cation in water reservoirs—potassium by sodium—required the appearance of ion-transporting devices in plasma membrane and their participation in adaptation of cells to environment. This stage of evolution was accompanied by the most important morphofunctional event—formation of the plasma membrane instead of cell envelope. The membrane provided the ion asymmetry in the cell (preservation of K⁺ in it) relatively to the sodium external medium for maintaining optimal intracellular medium. In the model system, predecessors of animal cells elaborated mechanism of maintenance of the potassium cytoplasm with the sodium counterion dominating in the environment.     

Primordial transport of sugars and amino acids via Schiff bases

Experimental support is given for a model concerning the origin of a primordial transport system. The model is based on the facilitated diffusion of amino acids stimulated by aliphatic aldehyde carriers and sugars stimulated by aliphatic amine carriers. The lipid-soluble diffusing species is the Schiff base. The possible role of this simple transport system in the origin of an early protocell is discussed.     

The Origins of Cellular Life

Understanding the origin of cellular life on Earth requires the discovery of plausible pathways for the transition from complex prebiotic chemistry to simple biology, defined as the emergence of chemical assemblies capable of Darwinian evolution. We have proposed that a simple primitive cell, or protocell, would consist of two key components: a protocell membrane that defines a spatially localized compartment, and an informational polymer that allows for the replication and inheritance of functional information. Recent studies of vesicles composed of fatty-acid membranes have shed considerable light on pathways for protocell growth and division, as well as means by which protocells could take up nutrients from their environment. Additional work with genetic polymers has provided insight into the potential for chemical genome replication and compatibility with membrane encapsulation. The integration of a dynamic fatty-acid compartment with robust, generalized genetic polymer replication would yield a laboratory model of a protocell with the potential for classical Darwinian biological evolution, and may help to evaluate potential pathways for the emergence of life on the early Earth. Here we discuss efforts to devise such an integrated protocell model.The emergence of the first cells on the early Earth was the culmination of a long history of prior chemical and geophysical processes. Although recognizing the many gaps in our knowledge of prebiotic chemistry and the early planetary setting in which life emerged, we will assume for the purpose of this review that the requisite chemical building blocks were available, in appropriate environmental settings. This assumption allows us to focus on the various spontaneous and catalyzed assembly processes that could have led to the formation of primitive membranes and early genetic polymers, their coassembly into membrane-encapsulated nucleic acids, and the chemical and physical processes that allowed for their replication. We will discuss recent progress toward the construction of laboratory models of a protocell (Fig. 1), evaluate the remaining steps that must be achieved before a complete protocell model can be constructed, and consider the prospects for the observation of spontaneous Darwinian evolution in laboratory protocells. Although such laboratory studies may not reflect the specific pathways that led to the origin of life on Earth, they are proving to be invaluable in uncovering surprising and unanticipated physical processes that help us to reconstruct plausible pathways and scenarios for the origin of life.Open in a separate windowFigure 1.A simple protocell model based on a replicating vesicle for compartmentalization, and a replicating genome to encode heritable information. A complex environment provides lipids, nucleotides capable of equilibrating across the membrane bilayer, and sources of energy (left), which leads to subsequent replication of the genetic material and growth of the protocell (middle), and finally protocellular division through physical and chemical processes (right). (Reproduced from Mansy et al. 2008 and reprinted with permission from Nature Publishing ©2008.)The term protocell has been used loosely to refer to primitive cells or to the first cells. Here we will use the term protocell to refer specifically to cell-like structures that are spatially delimited by a growing membrane boundary, and that contain replicating genetic information. A protocell differs from a true cell in that the evolution of genomically encoded advantageous functions has not yet occurred. With a genetic material such as RNA (or perhaps one of many other heteropolymers that could provide both heredity and function) and an appropriate environment, the continued replication of a population of protocells will lead inevitably to the spontaneous emergence of new coded functions by the classical mechanism of evolution through variation and natural selection. Once such genomically encoded and therefore heritable functions have evolved, we would consider the system to be a complete, living biological cell, albeit one much simpler than any modern cell (Szostak et al. 2001).     

The "protocell": a mathematical model of self-maintenance

The concepts of self-generation, autonomous boundary and self-maintenance are explained briefly. The "protocell" is presented as a model of self-maintenance which is based on simple physical mechanisms of diffusion and reaction. The time evolution of the surface of the protocell is taken into account explicitly in the form of a Stefan condition giving rise to a non-linear feedback of the surface motion to the reaction and diffusion processes inside the protocell. The spatio-temporal dynamics are investigated, particularly in the neighbourhood of the stationary states, showing a self-maintaining behaviour under a certain range of nutritional conditions. Under another set of conditions we find an instability leading to a division process so that the population of protocells becomes self-maintaining instead of the single individual. The presented formulation of the protocell model is crucially improved compared with a previous version which required boundary conditions at infinity. The previous version was not strictly self-maintaining since dynamics outside the cell were essential for its behaviour.     

Imitational modeling of evolution: from organic macromolecules to protocell and animal cell

A dynamic imitational model is developed of initial stages of cell evolution based on role of environmental cation concentration. The model is developed on our hypothesis, concerning the medium of the appearance of protocells. Could be potassium water reservoirs rather than sea salt water with its predominance of sodium salts. The necessary elements of appearance the protocells served organic molecules, code of their synthesis, and formation of macromolecules under favorable ion concentration in environment High K+ and Mg2+ concentration and bow Na+. The model is based on an assumption that one of the first stages in evolution of life was the appearance in potassium-magnesium water reservoirs of organic molecules capable for selfreplication on the basis of genetic code and formation of protocells with potassium cytoplasm. The model has demonstrated necessity of formation of cell envelope for development of the protocell. Replacement of the dominant cation in water reservoirs-potassium by sodium-required the appearance of ion-transporting devices in plasma membrane and their participation in adaptation of cells to environment. This stage of evolution was accompanied by the most important morpho-functional event--formation of the plasma membrane instead of cell envelope. The membrane provided the ion asymmetry in the cell (preservation of K+ in it) relatively to the sodium external medium for maintaining optimal intracellular medium. In the model system, predecessors of animal cells elaborated mechanism of maintenance of the potassium cytoplasm with the sodium counter-ion dominating in the environment.     

An overlooked riddle of life's origins: energy-dependent nucleic acid unzipping

The imposing progress in understanding contemporary life forms on Earth and in manipulating them has not been matched by a comparable progress in understanding the origins of life. This paper argues that a crucial problem of unzipping of the double helix molecule of nucleic acid during its replication has been underrated, if not plainly overlooked, in the theories of life's origin and evolution. A model is presented of how evolution may have solved the problem in its early phase. Similar to several previous models, the model envisages the existence of a protocell, in which osmotic disbalance is being created by accumulation of synthetic products resulting in expansion and division of the protocell. Novel in the model is the presence in the protocell of a double-stranded nucleic acid, with each of its two strands being affixed by its 3'-terminus to the opposite sides of the membrane of a protocell. In the course of the protocell expansion, osmotic force is utilized to pull the two strands longitudinally in opposite directions, unzipping the helix and partitioning the strands between the two daughter protocells. The model is also being used as a background for arguments of why life need operate in cycles. Many formal models of life's origin and evolution have not taken into account the fact that logical possibility does not equal thermodynamic feasibility. A system of self-replication has to consist of both replicators and replicants.     

Social and ethical checkpoints for bottom-up synthetic biology, or protocells

An alternative to creating novel organisms through the traditional “top-down” approach to synthetic biology involves creating them from the “bottom up” by assembling them from non-living components; the products of this approach are called “protocells.” In this paper we describe how bottom-up and top-down synthetic biology differ, review the current state of protocell research and development, and examine the unique ethical, social, and regulatory issues raised by bottom-up synthetic biology. Protocells have not yet been developed, but many expect this to happen within the next five to ten years. Accordingly, we identify six key checkpoints in protocell development at which particular attention should be given to specific ethical, social and regulatory issues concerning bottom-up synthetic biology, and make ten recommendations for responsible protocell science that are tied to the achievement of these checkpoints.     

On the origin of photophosphorylation

A model based on quinol phosphates is proposed for the origin of photophosphorylation. This model is divided into three time periods. In the early period, when the primitive earth was under reducing conditions, quinol phosphates were produced through quinol radical intermediates formed by the activation of hydroquinones with ultraviolet light. Phosphorylation of a number of acceptor molecules including inorganic orthophosphate and adenosine diphosphate occurred when quinol phosphate was oxidized by Fe⁺³ or a water soluble iron-sulfur complex. After the appearance of a rudimentary ozone layer (middle period), ultraviolet light was no longer an important factor in primordial chemistry. Quinol phosphates were then produced by visible light activation of porphyrin-quinone charge transfer complexes. In the presence of light, electrons from H₂S, H₂ and several reduced organic compounds were transfered through the porphyrin to quinone yielding the quinol radical. Again, quinol phosphate was produced from breakdown of the free radical. Phosphorylation of a number of acceptor molecules was achieved when quinol phosphates were oxidized by the iron-sulfur complexes. Evolutionary pressure to increase the efficiency of these reactions resulted in the electron donor-porphyrin-quinone-iron-sulfur complex becoming more lipophilic and thus associated with the protomembrane of the evolving protocell. In the late period the protomembrane became more sophisticated and quinone was replaced as the primary electron acceptor in the photoprocess by one of the iron-sulfur complexes originally present as oxidizing agents for the quinol phosphates. Quinones eventually lost their role as phosphorylating agents and became only electron and proton shuttles in the evolving electron transport chain. The protocell evolved the ability to use water as the electron donor as the relative roles of iron and quinone in the photoprocess switched.     

Global dynamics of two-compartment models for cell production systems with regulatory mechanisms

We present a global stability analysis of two-compartment models of a hierarchical cell production system with a nonlinear regulatory feedback loop. The models describe cell differentiation processes with the stem cell division rate or the self-renewal fraction regulated by the number of mature cells. The two-compartment systems constitute a basic version of the multicompartment models proposed recently by Marciniak-Czochra and collaborators [25] to investigate the dynamics of the hematopoietic system. Using global stability analysis, we compare different regulatory mechanisms. For both models, we show that there exists a unique positive equilibrium that is globally asymptotically stable if and only if the respective reproduction numbers exceed one. The proof is based on constructing Lyapunov functions, which are appropriate to handle the specific nonlinearities of the model. Additionally, we propose a new model to test biological hypothesis on the regulation of the fraction of differentiating cells. We show that such regulatory mechanism is incapable of maintaining homeostasis and leads to unbounded cell growth. Potential biological implications are discussed.     

Thermally driven fission of protocells

We propose a simple mechanism for the self-replication of protocells. Our main hypothesis is that the amphiphilic molecules composing the membrane bilayer are synthesized inside the protocell through exothermic chemical reactions. The slow increase of the inner temperature forces the hottest molecules to move from the inner leaflet to the outer leaflet of the bilayer. Because of this outward translocation flow, the outer leaflet grows faster than the inner leaflet. This differential growth increases the mean curvature and amplifies any local shrinking of the protocell until it splits in two. The proposed model, based on mere laws of physics, is a step in the study of the origin of life, as well as a clue for a better understanding of cell proliferation in cancer.     

Facilitated diffusion as a method for selective accumulation of materials from the primordial oceans by a lipid-vesicle protocell

A model is proposed for the selective accumulation of amino acids, sugars, nucleotides, cations and protons from the primordial oceans into a lipid vesicle type of protocell. The model is built on facilitated diffusion using simple, primordial, lipid-soluble carriers. The advantages a lipid vesicle protocell would have had over the other potential types of protocells are discussed.     

Clinical Physiology: Role in Studying Basic Problems of the Regulation of Renal Functions in Humans

Clinical physiology is described as a unique branch of human physiology that allows basic regulatory mechanisms of renal functions to be revealed. The analysis of physiological mechanisms that change the renal functions under the influence of endogenous or exogenous factors made it possible to detect new aspects of the regulatory system involved. The following problems are discussed: (1) the role of autacoids in the regulation of ion and water transport in the kidney; (2) the significance of functional loading tests for assessing the main components of the regulatory system of water and electrolyte balance; (3) the variety of sources of human blood hormones; and (4) the intranephron redistribution of water and electrolyte flows, which does not change their excretion by the kidney but affects the regulation of the totality of body functions.     

An Optimal Free Energy Dissipation Strategy of the MinCDE Oscillator in Regulating Symmetric Bacterial Cell Division

Sustained molecular oscillations are ubiquitous in biology. The obtained oscillatory patterns provide vital functions as timekeepers, pacemakers and spacemarkers. Models based on control theory have been introduced to explain how specific oscillatory behaviors stem from protein interaction feedbacks, whereas the energy dissipation through the oscillating processes and its role in the regulatory function remain unexplored. Here we developed a general framework to assess an oscillator’s regulation performance at different dissipation levels. Using the Escherichia coli MinCDE oscillator as a model system, we showed that a sufficient amount of energy dissipation is needed to switch on the oscillation, which is tightly coupled to the system’s regulatory performance. Once the dissipation level is beyond this threshold, unlike stationary regulators’ monotonic performance-to-cost relation, excess dissipation at certain steps in the oscillating process damages the oscillator’s regulatory performance. We further discovered that the chemical free energy from ATP hydrolysis has to be strategically assigned to the MinE-aided MinD release and the MinD immobilization steps for optimal performance, and a higher energy budget improves the robustness of the oscillator. These results unfold a novel mode by which living systems trade energy for regulatory function.     

Dual regulation by phospho-OmpR of ssrA/B gene expression in Salmonella pathogenicity island 2

Expression of genes located on Salmonella pathogenicity island 2 (SPI-2) is required for systemic infection in mice. This region encodes a type III secretion system, secreted effectors and the two-component regulatory system SsrA/B (also referred to as SpiR), as well as additional uncharacterized genes. In the present work, we demonstrate that phospho-OmpR (OmpR-P) functions as an activator at the spiC-ssrA/B locus. There are two promoters at spiR; one is upstream of ssrA and the other upstream of ssrB. Our results indicate that, in contrast to many two-component regulatory systems, regulation of the sensor kinase SsrA appears to be uncoupled and distinct from regulation of the response regulator SsrB. OmpR regulation of ssrA/B is one of only a few examples known in which a two-component response regulator directly regulates the expression of another two-component regulatory system.     

Computer simulation on the cooperation of functional molecules during the early stages of evolution

It is very likely that life began with some RNA (or RNA-like) molecules, self-replicating by base-pairing and exhibiting enzyme-like functions that favored the self-replication. Different functional molecules may have emerged by favoring their own self-replication at different aspects. Then, a direct route towards complexity/efficiency may have been through the coexistence/cooperation of these molecules. However, the likelihood of this route remains quite unclear, especially because the molecules would be competing for limited common resources. By computer simulation using a Monte-Carlo model (with "micro-resolution" at the level of nucleotides and membrane components), we show that the coexistence/cooperation of these molecules can occur naturally, both in a naked form and in a protocell form. The results of the computer simulation also lead to quite a few deductions concerning the environment and history in the scenario. First, a naked stage (with functional molecules catalyzing template-replication and metabolism) may have occurred early in evolution but required high concentration and limited dispersal of the system (e.g., on some mineral surface); the emergence of protocells enabled a "habitat-shift" into bulk water. Second, the protocell stage started with a substage of "pseudo-protocells", with functional molecules catalyzing template-replication and metabolism, but still missing the function involved in the synthesis of membrane components, the emergence of which would lead to a subsequent "true-protocell" substage. Third, the initial unstable membrane, composed of prebiotically available fatty acids, should have been superseded quite early by a more stable membrane (e.g., composed of phospholipids, like modern cells). Additionally, the membrane-takeover probably occurred at the transition of the two substages of the protocells. The scenario described in the present study should correspond to an episode in early evolution, after the emergence of single "genes", but before the appearance of a "chromosome" with linked genes.     

Package models and the information crisis of prebiotic evolution

The coexistence between different types of templates has been the choice solution to the information crisis of prebiotic evolution, triggered by the finding that a single RNA-like template cannot carry enough information to code for any useful replicase. In principle, confining d distinct templates of length L in a package or protocell, whose survival depends on the coexistence of the templates it holds in, could resolve this crisis provided that d is made sufficiently large. Here we review the prototypical package model of Niesert et al. [1981. Origin of life between Scylla and Charybdis. J. Mol. Evol. 17, 348-353] which guarantees the greatest possible region of viability of the protocell population, and show that this model, and hence the entire package approach, does not resolve the information crisis. In particular, we show that the total information stored in a viable protocell (Ld) tends to a constant value that depends only on the spontaneous error rate per nucleotide of the template replication mechanism. As a result, an increase of d must be followed by a decrease of L, so that the net information gain is null.