this article, we used a 3D Mesh modeling to show the range of distribution of each separate group of Archaea as a function of pH, temperature, and salinity.
EVOLUTION OF ARCHAEA IN 3D MODELING Elena V. Pikuta,* Dragana Tankosic** and Rob Sheldon*** *
Astrobiology Lab., NSSTC/UAH, 320 Sparkman Dr., Huntsville AL 35805 USA ORAU/NASA/MSFC NSSTC, 320 Sparkman Dr., Huntsville AL 35805 USA *** NSSTC/GD, LLC 320 Sparkman Dr., Huntsville AL, 358 05 USA
**
ABSTRACT The analysis of all groups of Archaea performed in a two-dimension plot had demonstrated a specific distribution of Archaean species as a function of pH/temperature, temperature/salinity and pH/salinity. Work presented here is an extension of this analysis with a three dimensional (3D) modeling in logarithmic scale. As it was shown in 2D graphics, the “Rules of the Diagonal” have been expressed even more clearly in 3D modeling. In this article, we used a 3D Mesh modeling to show the range of distribution of each separate group of Archaea as a function of pH, temperature, and salinity. Visible overlap and links between different groups indicate a direction of evolution in Archaea. Specifics of the geometrical coordinates and distribution of separate groups of Archaea in 3 D scale were analyzed with a mathematical description of the functions. Based on the obtained data, a new model for the origin and evolution of life on Earth is proposed, the geometry of this model is described by a hyperboloid of one sheet. The major direction in ancestral life (vector of evolution) has been indicated: from high temperature, acidic, and low-salinity system towards low temperature, alkaline and high salinity systems. Conclusions of this research are consistent with previous results derived from the two-dimensional diagrams. This approach is suggested as a new method for analyzing any biological group in dependence upon its environmental parameters.
Key words: vector of evolution, ancestry, 3D computer graphics, primordial Ocean, hyperboloid
1.
INTRODUCTION
The previous analysis1 of validated and published species of all groups of Archaea in two-dimensional scale has demonstrated a specific distribution of the Archaean species within matrices pH/Temperature, Temperature/Salinity and pH/Salinity. The coordinates of Archaean species were distributed in a top corner of the graphic diagram. As a result, the conclusions about rules of the diagonal with consistent appearance of all groups of Archaea above the diagonal line crossing the plot were formulated and discussed. Present work is a continuation of the analysis of Archaea in 3D logarithmic scale with the same physico-chemical parameters (pH, salinity, temperature). As it was shown in previous study, “Rules of the Diagonal” has more obvious geometrical appearance in 3D scale as well. In this article, we applied 3D Mesh method (as an additional view of data) to describe the range and distribution (pH, temperature, and salinity) of each separate group in Archaea. A novel, theoretically useful information about co-evolution of the different groups of Archaea has been obtained and analyzed. The goal of this study was to investigate a distribution of separate groups of Archaea in 3 D scale, and analyze their evolution in space and time. In other words, we described their evolutionary development in relation to each other, and to environmental changes. As a result of this study, a universal model for the origin and distribution of life within the microbial world has been suggested, and the direction of adaptation to an environment for ancestral groups (vector of Evolution of life on Earth) had indicated and discussed. The major conclusions from this study are consistent with the previous results received on 2D diagrams. Described approach has been suggested as a method for analyzing any biological group. It is important to notice that each analysis in 2D and 3D has provided specific view and information, which cannot be observed just in one of them. Some information obviously seen in 2D could be completely hidden in 3D formate. This approach demonstrates a possibility for the evolution of life, and real history of the ecosystem's development on Earth. Three-dimensional model also predicts a possible existence of undiscovered groups of microorganisms, and/or indicates the area for extinct once.
2.
METHODS
For construction of 3D plots, the coordinates of each group of Archaea for (temperature, salinity, and pH), all physiological data from previous work1 (tables 1-14, not shown here) were transferred into logarithmic scale for the convenience of presentation and mathematical manipulation. In Sigma 3D plot (mash –modeling) the logarithms of physiological ranges were taken for graph construction. Methanoarchaea T, oC -0.3000 -0.3000 1.0000 1.0000 1.0000 1.3000 1.3000 1.6000 1.6000 1.6000 1.6000 1.6000 1.5000 1.7000 1.7000 1.8000 1.8500 1.8500 1.9000 1.9000 1.9000 1.9000 2.0000 2.0400
Halobacteria
pH 6.0000 8.0000 6.5000 9.0000 7.0000 5.5000 7.0000 7.0000 8.0000 7.0000 7.0000 9.0000 6.5000 7.0000 4.5000 9.4000 8.8000 8.0000 7.0000 8.5000 6.5000 5.5000 6.5000 6.0000
Salinity, % (w/v) -0.3000 0.7000 0.0000 0.7500 0.3000 -0.3000 0.3000 0.2000 0.5000 0.5000 1.5000 0.5000 0.9000 0.5000 0.0000 0.9500 -0.7000 0.6000 0.0000 0.7000 -0.2000 -0.7000 0.3000 0.6000
pH 5.5000 2.0000 3.0000 2.0000 6.0000 5.5000 6.0000 1.0000 3.0000 4.0000 7.0000 4.5000 5.0000 7.0000 1.0000 3.0000 0.3000 4.0000 6.0000 1.0000 5.0000
Salinity, % (w/v) 0.3000 -1.0000 0.2000 0.1000 -1.0000 0.0000 0.0000 0.0000 0.5000 -0.9500 0.6000 0.0000 0.5000 0.5000 0.7500 0.7000 -1.0000 -0.5000 0.6000 -1.0000 0.5000
pH 8.0000 5.5000 5.0000 7.0000 8.5000 8.0000 11.0000 5.0000 7.0000 8.0000 9.5000 10.5000 11.0000 8.5000 6.0000 11.0000 7.0000 11.0000
Salinity, % (w/v) 1.4000 1.1000 0.7000 1.1000 0.9000 1.6000 1.5000 1.5000 1.3000 1.4000 1.3000 1.2000 1.2000 1.5000 1.2000 1.5000 1.4000 1.3000
Thermal Euryarchaeota
Crenarchaeota T, oC 1.8500 1.7000 1.8000 1.8500 2.0000 1.8000 1.9000 1.9500 1.9500 1.9500 1.9500 2.0000 2.0000 2.0400 1.8500 1.9000 1.9500 1.7000 1.8000 1.8500 1.9000
T, oC 1.0000 1.1000 1.2000 1.3000 1.4000 1.5000 1.5000 1.5000 1.6000 1.6000 1.6000 1.6000 1.7000 1.8000 1.8000 1.8000 1.7000 1.7000
T, oC 1.6000 1.8000 1.8000 1.9500 2.0000 2.0000 1.8500 1.8000 1.2000 1.8000 1.7000 1.6000 1.9500 1.9500 2.0000 1.8000 2.0000
pH 1.7000 2.0000 2.0000 7.0000 7.0000 6.0000 1.8000 4.0000 0.0000 3.0000 2.0000 4.0000 8.0000 5.0000 9.0000 7.0000 9.0000
For Polygon-plot modeling the logarithms of optima were taken for the graph construction.
Salinity, % (w/v) 0.2000 -0.7000 0.3000 0.3000 0.5000 1.3000 0.0000 -0.1000 0.5000 0.3000 0.5000 -0.3000 0.6000 -0.1000 0.9000 0.5000 0.7000
3.
RESULTS
3.1 Three-dimensional view of physiological optima of different groups of Archaea 3.1.1 Optima in 3D Polygon view The graphic imaging of physiological optima of all Archaea constructed in coordinates x, y, z (temperature, pH, salinity) demonstrates a specific location and distribution for each group. In the figures 1,2 & 3, the green color indicates Halobacteria, blue - Methanoarchaea, purple - Thermophilic Euryarchaeota, and red – Crenarchaeota. In figure 1, the crossing point for all axes is located at 0, and physiological data are represented in logarithmic scale. For more expended viewing, in figure 2, the crossing point of axes x and y (temperature and pH) was moved to 1.5 and 7correspondently. This allows observe the diagonal distribution of two opposite groups (green and red) Halobacteria and Crenarchaeota. Methanoarchaea is the only group that expends to subzero temperatures.
Figure 1. Polygon view of Archaea (axes: abscissa – Temperature, ordinate – pH, height –salinity). The beginning of coordinates starts at 0.
Figure 2. Framed polygon of all group of Archaea (axes: abscissa –Temperature, ordinate – pH, height –salinity). The crossing point of axes is located at pH 7, temperature 1.5, and salinity 0). This view allows to demonstrate a separate location of two groups – Halobacteria and Crenarchaeota; These two groups are distant in coordinates temperature, salinity and pH, and have never been interacted. And opposite, Thermophilic Euryarchaeota had intensively coevolved with Crenarchaeota, as well as with Thermophilic Methanoarchaea: the crossing lines show ecological similarity at some coordinates of physiological optima. It is possible to see close contact between Halobacteria and some mesophilic groups of Methanoarchaea. This software demonstrates that Methanoarchaea is the latest group in evolutionary scale, since they have adapted to low temperatures and to high pH and salinity. The view shows an extension of Methanoarchaea (blue dots) to subzero temperatures; this is the only group of Archaea that carrying genes of lithoautotrophy in low temperature ecosystems. Halobacteria remains isolated from other Archaea, and restricted exclusively to organotrophy.
Figure 3. Polygon view of Archaea with connected coordinates of physiological optima to demonstrate interaction of groups (convergent evolution) or theirs isolation (divergent evolution).
3.1.2 View of physiological optima in 3D Sigma plot 3D Sigma plot view shown in figure 3 allows us to see a distribution of the physiological optima of all group of Archaea. However, changing the angle of view could give a wrong impression. So called illusionary effect applies in this case. For example, Halobacteria (shown in green) have an actual salinity at 1.6, but the rotation of the plot towards a viewer shows the values of salinity less than 1.0, and the optimum for haloalkaliphilic mesophilic Methanoarchaea looks higher, even so, it is actually lower. The diagonal cross section of 3D plot demonstrates the distribution of optima in space respectively of this cut. Crenarchaeota are located in lower corner of the plot, while Halobacteria have been raised in the upper corner.
Figure 3. Physiological optima of Archaea in 3D Sigma plot (pH/temperature/salinity).
3.2 Three Dimensional “Mash” models Viewing 3D Sigma plot with mash-modeling allows to visualize the position of different groups of Archaea with respect to each other, and also, to observe the areas of evolutionary co-existence and interaction along with an influence of environment. For this method the physiological ranges of each group of Archaea were taken for graphic work (see tables in Methods), the data were transferred in logarithms. 3.2.1 Crenarchaeota and Halobacteria are completely separated groups of Archaea that were chosen here as two opposite extremes for the 3D modeling in pH/temperature/Salinity graph. The position of both groups gives a diagonal slope location (see drown line) in opposite corners (top/bottom) of the matrix’s 3D plot cube. The corner, occupied by hyperthermophilic and extremely acidophilic Crenarchaeota (shown in red), stays oppositely to the upper diagonal’s corner, which is a zone of mesophilic halo-alkaliphilic organisms. No liaisons, or contacts, between these two groups are occurred. These groups were separated in time, and by the type of formed ecosystem. Halobacteria (shown in green) is the group, which characterized by aerobic/facultative anaerobic physiology and the growth requirement of high concentrations of salts in environment. This characteristic allows refer this group to the latest evolutionary development. Evaporite ecosystems for Halobacteria were evolved much later than ecosystems of Crenarchaeota. More precise, the conditions of modern volcanic thermo vents are approximately the same what was in Primordial Ocean. Approximately 3,950 million years separate these two types of evolutionary developed groups. Only in present time we could observe these two types of microorganisms on the planet at the same time. Of course, the clones or strains of modern species are not the same what had been left from the originals. Molecular studies of genome of Crenarchaeota will answer the questions: how much conservative and stable the DNA and replicative mechanism in comparison to the later groups – Halobacteria, halo-alkaliphilic methanoarchaea, and cyanobacteria. Members of Halobacteria are distributed within the highest values of salinity, which is 1.6. They do not have negative logarithms of salinity (0.7 is the lowest one), and the values of logarithm of temperature are occurred between 1 and 1.8. The pH minimum for this group starts from 5.5 and goes up to 11.
Figure 5. Geometry of mash for the Halobacteria.
2.0
(w/v))
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1.4 1.2 1.0 0.8
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Log (Salinity, %
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pH
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The mash of this group has a specific circular-symmetrical shape that reminds a flower with wavy on perimeter petals. Conically rising surface (hypersurface) at the center of mash is sloping into the lowest point forming a hyposurface. At the cross-section, it will provide a perfect hyperbolic paraboloid. The conical hypo-surface itself could be described as a paraboloid of revolution. This mash has also expressed the circular oscillation function as a geometrical effect. The perimeter of this mash clearly indicates a wave function from all four sides or directions. This mash represents a dead end of evolution, and a middle part of low branch of the hyperbola (fig. 12), where it’s right “shoulder” (mesophilic and extreme alkaline systems) is continuing by Cyanobacteria and bacterial haloalkaliphiles, and the left “shoulder” (region at low temperature) by psychrophilic methanoarchaea and Eubacteria. In 3D graph it would be the top “cup” of the hyperboloid of two sheets (fig. 13). Figure 6. Geometry of mash for the Crenarchaeota. Central rising area of the mash (in green) represents the main part of top branch of the hyperbola shown in 2D diagram (fig. 12). In 3D (figure 13) it would correspond to the bottom cup of the two-sheet hyperboloid. In figure 6, a gradually rising slope for pH and salinity at the lowest values of the temperature (logarithm 1.7 corresponds to the values of 80-85 oC) is shown. The oscillatory effect here could be observed at the higher pH area (6-7) only. The points of lowest pH (0-2) are pretty consistent (no oscillatory effect in geometry) that may indicate on the original point of the beginning of life itself precisely in this area, by other words, an initial point of the vector of evolution.
Members of Crenarchaeota are opposite to Halobacteria, grow at the lowest values of salinity, and therefore, located at the negative logarithms of salinity. The maximal logarithm of salinity in this group is 0.75. Crenarchaeota are spread within the region of high temperatures (logarithms 1.7-2.04). The pH for this group of Archaea is mostly acidic (pH 0-4, but spreads up to pH 6-7 where evolutionary latest representatives express wavy geometry – so called scintillatory effect – characteristics of adaptive behavior to new conditions).
3
Salinity
2
1
0
-1
2.0 re tu 1.8 era p
1.6 Tem
-2 10
1.4
8 6 2
pH
Halobacteria Crenarchaeota
Hyperboloid of two sheets
1.2
4 1.0
Figure 7. The diagonal location of mashes for the Halobacteria and Crenarchaeota in 3D (pH/temperature/salinity) Sigma plot indicates the hyperboloid of two sheets leaned with angle of 22.5 o according to the axes of temperature and pH. Stretched out axis of salinity would provide perfect view for the hyperboloid of two sheets.
3.2.2 Methanoarchaea & Hydrothermal Euryarchaeota
4
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1 -0.5 0.0 0.5
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Log (Salinity, %
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2.0 5
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2.5
ra t pe
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(T
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1.5
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Figure 8. Geometry of Mash for the Methanoarchaea.
Methanoarchaea are restricted to the neutral and alkaline pH; the lowest pH for this group is 4.5. Even so, the temperature characteristics express the presence of hyperthermophilic species, which are phylogenetically very distant from mesophilic majority of this group the adaptation to low temperatures in this group is obvious. The adaptation to highly mineralized (up to saturated solutions) buffer systems along with highly alkaline pH strongly indicates that this group has been continuing evolve at the latest geophysical and climatic changes on Earth. This group, as well as Halobacteria, contains the most halo- and alkali-tolerant species. The oscillation in this group is observed only at lower temperatures and high pH that indicates on the original pH around values of 4-5. Correlation between pH and increasing salinity here is clearly observed within mesophilic temperatures (here the horizontal gene transfer from Halobacteria is not excluded).
The paradox, or controversy, in this group is obligate anaerobiosis, which is observed along with the lowest red-ox potential requirements for growth of all species in this group, compare to other known biological species. If Figure 8. The shape of mash of so, they should be the most ancestral, but the minimal pH in this group occurs around 5, never lower. Does it mean Methanoarchaea. that extremely acidophilic species of methanoarchaea are completely extinct, or have never existed? Should they be searched on different buffer systems? Is the biochemistry of methanoarchaea absolutely restricted to the neutral and
alkaline pH? The only acidophilic species of methanoarchaea have been described from tundra’s pit ecosystems, where pH is slightly acidic (pH 3.5-4) due to the iron-containing waters, and could have a secondary acidic nature caused by incomplete cycle of decomposition of organic matter in cold climate. A rapid accumulation of organic acids produced by the primary anaerobes (sugar- and protein-lytics) due to a lower growth rate of the secondary anaerobes responsible for utilization of these acids is the main reason for low pH in cold ecosystems. Such an imbalance in speed of growth between primary and secondary anaerobes in cold ecosystems leads to the excess of organic acids, direct consequence of which is usually expressed in the predominance of fungal growth on micro- and macro- levels. Figure 9. Geometry of mash for the Hydrothermal Euryarchaea.
3
2
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2.0 1.9 1.8 1.7 1.6 1.5 1.4 1.3 1.2
ur e(
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Shape of the mash for Hydrothermal Euryarchaea is very specific and recognizable among of all Archaea. The absence of the oscillatory effect indicates that this group of microorganisms was close to the initial original point of the beginning of life. High probability for consideration of this group for a secondary stage of the evolution of life after appearance of the Crenarchaeota is quite adequate. In figure 10 the closest interaction and divergent co-evolution of these two groups (in purple and red) are shown. A correlation with increased salinity (direct dependence) is seen from both planes (axes pH and temperature) in this case. Salinity values in this group are reached of the logarithms 1.3 (corresponds to 8 %, even so some species of this group of Archaea do not require salinity at all.
3.3 Interaction and overlap between groups Analyzing all groups of Archaea, by putting the data from comparative tables into the 3D log-scale plot, it is possible to see a geometrical distribution of each group in coordinates x, y, and z. The boundaries of each group, overlaps between them, and bridges connecting the groups provide an additional information about that what may have happened in these groups during Evolution, and did they have points of cross-passes and experienced the same FigureFurthermore, 9. View of fortoThermal ecological pressure along with directed changes of geno- and phenotype? it ismash possible observe (central, on perimeter, or asymmetrically side-located) influence Euryarchaea. of physico-chemical extremes caused by environmental impact. Location and space distribution of the Hydrothermal Euryarchaeota (purple color) in 3D are very close to those of the Crenarchaeota, but the first is significantly more spread over the area of neutral and slightly alkaline pH (Fig. 10). This group is also not restricted to extremely high temperatures: it includes thermophilic and moderately thermophilic species. The percent of lithoautotrophy in this group has a significantly lower number compare to the Crenarchaeota. Finally, the range of salinity for Hydrothermal Euryarchaeota has been expanded to the logarithm 1.3, which has never been observed in Crenarchaeota (the maximum of salinity in this group had never exceeded 0.75). In figure 10, you could see an increase of salinity for the Crenarchaeota only at pH 4-5, whereas in Hydrotermal Euryarchaea, it appears at pH 6-7. pH range for the Hydrothermal Euryarchaea spreads up to 8-9, as well as the temperature minimum extends to 40 oC. Majorities of the Hydrothermal Euryarchaeota are marine species that require 2-3% NaCl for growth; the only exception is species of the genus Picrophilus. Within Crenarchaeota, there are only eight marine genera, other 17 genera have no, or require extremely low concentration of salts. Hyperthermophilic Methanoarchaea interacts with Hydrothermal Euryarchaeota starting at pH 4.5. The salinity in mesophilic species of Methanoarchaea reaches saturated concentrations, as well as the Halobacteria. Even so, these two groups are both coevolved within neutral and alkaline pH range, Methanoarchaea is strictly anaerobic, but Halobacteria experienced a shift in metabolism towards to aerobiosis. This clearly demonstrates a
secondary origin of the Halobacteria during Evolution. The physicochemical restriction (rule number 5)1 did not allow the development of halophilic psychrophilies within Halobacteria, but in Methanoarchaea we are observing a presence of psychrophilic species at neutral pH. As in the previous work for two dimensional plots,1 it is possible observe a diagonal slope distribution of Archaea under the diagonal cross section (within the bottom “wedge”, or a right-angle prism. This zone represents a life distribution, and the top prism represents a zone, which is not occupied by life. This geometry, or precisely trigonometry, was never discussed for life evolution before, and it definitely will contribute to the theoretical research in geology, geophysics, and paleontology. Additional physicochemical factors, such as redox potential, and oxygen concentration should contribute and improve this conclusion; that will be a next step in this research.
3
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1 0 -1 -2 0.0 0.5
e Temperatur
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2
6
4
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pH
Halobacteria Crenarchaeota Thermal Euryarchaeota Methanogens
3
Salinity
2 1 0
pH
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Figure 10. The profile view of the mashes for all groups of Archaea in 3D Sigma Plot (pH/temperature /salinity). The value of salinity and temperature are presented in logarithms. The top view of all mashes of Archaea demonstrates contact overlaps between Methanoarchaea and Halobacteria, as well as that for Crenarchaeota and Thermophilic Euryarchaeota. Methanoarchaea is the only group that had evolved into the area of low temperature along with strict anaerobiosis. In fig. 11, you could see that a region of temperature (logarithms of 1.5-1.0) had possibly provided good conditions for the horizontal gene transfer 12 between Halobacteria, some Thermophilic 10 Euryarchaeota, and Methanoarchaea. In zone 8 of temperature (logarithms 1.5-2.04) the same possibility for Crenarchaeota, Thermal 6 Euryarchaeota and Hyperthermophilic 4 Methanoarchaea are demonstrated too. 0.5 2 Hydrothermal Euryarchaeota and 1.0 1.5 0 Crenarchaeota interact and coevolved within Temp 2.0 eratur e the area pH of 0-3, and logarithms of temperatures of 1.7-1.8 (only at exclusively low salinity that means the beginning of life), see figure 10.
-2 0.0
Halobacteria Crenarchaeota Thermal Euryarchaeota Methanogens
Figure 11. Top view of mashes of all groups of Archaea in 3D. Data for salinity and temperature are presented in logarithms.
3.4 GEOMETRICAL MODELING OF EVOLUTION OF LIFE 3.4.1 The Model of Evolution for Archaea 3.4.1.1 Two-dimensional model For construction of the model of evolution of life, in a two-dimensional plot, the most distant groups of Archaea have been chosen, namely Crenarchaeota and Halobacteria. In figure 6, a plot of pH and temperature functions demonstrates the position of both these groups, where we could observe the hyperboloid geometry (hyperboloid of two sheets). In 3D mash modeling these two groups are located in an opposite corner of 3D plot, and they could be diagonally connected at the angle of ~22.5o (Fig. 7, 10). The distance between these two biological groups and space separation are function of time: ~0.5 million years are needed for formation of ecosystem for Crenarchaeota, and after that another ~3,950 million years for Halobacteria. So, 3.9 billions of years are between these two groups. By mathematical language, a hyperbola (in 2D plot), or two sheet hyperboloid (in 3DPlot) appears in this case.
100- T, oC Thermophilic Euryarchaeota and Eubacteria
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75 -
0
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50 37 -
Cyanobacteria Haloarchaea
25 Eubacterial mesophiles
Methanoarchaea Eubacterial psychrophiles 0-
Figure 12. Hyperbola function of the evolution for Crenarchaeota and Halobacteria, and parabola function for the Thermophilic Euryarchaeota and Thermoplasmata. Star shows the initial coordinates for worm-blooded animal buffer system (physiological solution 0.85 %), which appeared much earlier than saturated brines of Haloarchaea. Asymptote's connection of branches of the hyperbola (fig. 12) will give us a cross point at 63 oC and pH 5. The original drawing with a cross centre at pH 7 and temperature of 50 oC does not provide the symmetry of asymptotes. Does it have a mathematical/biological meaning for pH 5 and 63 oC? Was this point critical for some dramatic change within the buffer system of the ancient ocean that may be reflected on a biological level? Could it be also connected with formation of atmosphere or some critical accumulations, such as oxygen? These remain out of discussions of this article: we will leave this topic for future.
Evolution of members of the Class Thermoplasmata beautifully matches the function of parabola expending from Crenarchaeota (fig.12). In this case, a biologic linkage between Crenarchaeota and Euryarchaeota would be expected as currently existing groups, but not discovered yet, or as extinct microbial groups. Furthermore, the parabola’s function could be applied for the explanation of evolution of Eubacterial mesophiles in extreme acidic environments. The parabola could be applied only in 2D plot, but hyperboloid function, for the three-dimensional plot with symmetrical approximation, would provide a perfect view of the one-sheet hyperboloid for microbial evolution on Earth (fig. 13). Unfortunately, with Polygon software, it was impossible to insert hyperboloid with a diagonally inclined angle of 22.5o that would be consistent with the actual coordinate position (fig.7). 3.4.1.2 Three-dimensional model
a.
b. c. Figure 13. Hyperboloid of the evolution of life (based on Achaean’s data).
In three-dimensional polygon plot, the data from all groups of Archaea were inserted then the points of coordinates were connected by lines to demonstrate all possible interactions and co-evolution. Schematic image of two cups of the hyperboloid of two sheets was inserted to visualize the initial and final stages of the microbial evolution. The top cup has contact coordinates exclusively with halophilic Archaea, and the bottom cup is based on the points of the hyperthermophilic hyper-acidic Crenarchaeota. The net (shown in yellow) connecting these two cups unites all other representatives of Archaea, and itself represents the hyperboloid of one sheet. 3.4.2 Complete model of the Evolution of Life: Archaea, Eubacteria, and Eukaryotes In the beginning of work on the analysis of all groups of Archaea, the central primary goal was designing the evolution of Archaea. However, during this study, mathematical functions along with geometry of the obtained model led to the conclusions about continuous interaction and participation of other biological groups in the process of evolution. In figure 12, you could see that bottom branch of the hyperbola drawn for Halobacteria consist of three compounds. Only central part, which is almost flat, is occupied by halo-archaea, the coordinates of both shoulders of this branch are out of halo-archaean distribution; the evolution here continued on organisms belonging to different biological groups. Precisely, halo-alkaliphilic Eubacteria and Cyanobacteria are responsible for asymptote enclosure on the right shoulder, and psychrophilic Eubacteria and Methanoarchaea – for asymptote on the left side of bottom branch of the hyperbola. In other words, evolution for the alkali-tolerance continued in halo-alkaliphilic Eubacteria and Cyanobacteria, which are, indeed, found to be the toughest halo-alkaliphiles. Concerning psychrophiles, the lowest minimum temperatures within Archaea are known exclusively for mesophilic and psychrotolerant species of Methanoarchaea, and it much wider expressed in modern Eubacteria. In 3D diagram data for Cyanobacteria and Eubacteria were not inserted, since the subject of present work is limited to the Evolution of Archaea. In the 2D diagram (fig. 10), at the vertices of bottom branch (for Haloarchaea) of the hyperbola the star indicates an initial point, or the origin of a warm-blooded animal's buffer system with salinity 0.85 % (isotonic solution), which
occurred much before saturated solutions of the ecosystems for Haloarchaea. In figure 13c, the complete view of the model of evolution of life on Earth is presented; this model is described as a hyperboloid of one sheet. 3.5 Mathematical description of geometry In this study the modeling has been started with the choice of two radically opposite (by physiology and ecology) groups of Archaea. Therefore, a visualization of hyperbola and hyperboloid, in 2D and 3D graphic diagrams correspondently, had appeared exclusively empirically, and unexpected. A match of the distribution of physiological data of Archaea to such a model, consequently, led to the mathematical improvement in geometry of the model. In mathematics, a hyperbola is a curve, specifically a smooth curve that lies in a plane. This curve can be defined easier by its geometrical properties or by the equation: The hyperbola in figure 12, should have its conjugate hyperbola (not shown), both branches of which (in our case) should represent the environmental pressure squeezing life, and therefore, restricting a wider distribution of biological species. Hence, from definition, the conjugate hyperbola does not correspond to a 90 o rotation of the original (drown) hyperbola, the shape of the two hyperbola (in our case) are different. The formula for conjugative hyperbola representing ecological, or environmental, pressure is Hyperboloid is a quadric – a type of surface in three dimensions that is described by the equation (Hyperboloid of one sheet), or (Hyperboloid of two sheets). These are also called elliptical hyperboloids. Since, in our case, a ≠ b, it is not a hyperboloid of revolution, or a circular hyperboloid. A simple way of producing a hyperboloid is to rotate a hyperbola about the axis of its foci or about its symmetry axis perpendicular to the first axis; these rotations produce hyperboloids of two and one sheet, respectively. 4.0 DISCUSSION Three dimensional modeling of Archaea has clearly showed that the direction of evolution of life went from the low-pH, low-salinity, and high-temperature system to the high-pH and high-salinity cooled buffer system. Does it make sense from the point of view of geophysics? In literature, it is hard to find precise pH value of the Primordial Ocean. Hypothesis about original alkaline ocean have been discussed only for the later paleontological eras (Cambrian and latest Precambrian – Proterozoic Period). These periods already had photosynthetics, which alkalinized the environment by photolysis of water with consequent increased pH. What happened at the Archean Eonothem? Now no data, except for the isotope fractionation, is available. The excess of C13 in a ratio with C12 is widely accepted as indirect biomarker for earliest life. The opposite hypothesis about low pH Primordial Ocean does not provide an explanation for a reason of it, but roughly applies the analogy and extrapolation of a present day low pH volcanic water containing sulfuric acid to the first hydrosphere of Earth. Physics and radiochemistry would probably give some answers about the initial pH of water solution at the beginning of hydrosphere formation on Earth. Steam and vapor caught by the Earth’s gravity created a first condensate, which later was enlarged by precipitates from dusty clouds. Furthermore, participation of the bombardment by comets containing frozen water is commonly accepted now. The thermonuclear reactions during cooling and calming down geophysical processes on Early Earth would contribute significantly to the formation of H2, HD, D2, DT, HT, and T2. The products of dissociation of lasts should have increased the concentrations of H+ ions in a water solution, thereby greatly decreasing the pH of early water systems. At radiolysis, for example, the ionizing radiation (alpha particles, electrons, neutrons, X-rays, and gamma rays from radioactive materials) generates chemical reactions with energy transfer, and produces ions and excited species, which undergo further reaction. A particular feature of radiolysis is the formation of short-lived solvated ions in water or other polar solvents that may decrease the pH. Currently, in thermo-nuclear power plants, the water solution within a nuclear chamber with spent fuel rods is especially kept highly alkaline to prevent the corrosion caused by low pH. Along with the conclusion for the low-pH water system of Primordial Ocean, we are unavoidably facing another very important conclusion: obligate radiophilic nature of first living microorganisms. Commonly accepted point of view on radiation as an exclusively restricting and limiting factor for life needs to be changed. Currently,
the only microorganisms that tolerate 15-30 kGy levels of radiation are known.2 Work with isolation and description of truly radiophilic microorganisms would most likely require involvement of the top-operative systems and robotic machinery with different approaches, not yet developed in experimental microbiology. Now, radioecology and radiobiology are studying a level of natural and technogenic radiation, influence of it on living cells and tissues, the pathways of migration for radioactive isotopes in organism and ecosystems, accumulation of radiation in specific organs and materials. Back to the model of Archaea evolution, 3D modeling could be modified into 4D, and even 5D, by use of additional parameters, such as radiation, red-ox potential, length of wave (light – for photosynthetics), etc.… However, as practice shows, the dimensions of more than three are usually difficult to understand, and it would hide some obvious details visible in two- and three-dimensional viewing. In modeling for Paleontology, the time scale would be necessary to apply, where salinity and pH may be combined to the one scale. One of the most important messages in this article addresses the problem of biomarker of ancient life: traditional view of the fossilized remnants is actually possible only for much later life forms. Conditions for the formation of organic fossilized materials are exclusively restricted to the neutral and alkaline pH along with highly mineralized buffer systems that would stabilize organic remnants during the fossilization process. Furthermore, a specific temperature regime for the fossilization is required, and this excludes temperatures above 100 oC. Here we are emphasizing that all known fossilized organic remnants are work of Protezoic and late Archean eons. Fossilization would not work at pH 0-1 and temperatures above 100 oC. That means the earliest life forms have only indirect proofs of existence, such as a radio-isotope-fractionation. This probably could be changed if in Mineralogy, a radically new method will be introduced and developed. Evolution of antennas for catching electrons of different spectra of light (flavins, ferredoxins, and cytochromes) along with characteristics of wave length of light could be analyzed in 3D modeling to demonstrate evolution of photosynthetics on Earth.
5.0 CONCLUSIONS First time, the geometrical model of evolutionary development of the microbial world has been presented. Geometry of this model consists of the hyperboloid of one sheet. It was shown that separate physiological groups of Archaea were affected by numerous physicochemical factors of the Earth’s environment during ecological and climatic formations. The vector of this evolution was clearly indicated, and shown in two and three dimensions. The origin of initial (ancestral) and latest (by evolutionary development) physiological groups within the hyperboloid match the paleontological records of ecosystem formation on Earth: From the hyperthermophilic acidic systems towards the cold and halo-alkaline ones. This model may be used for prediction of missing physiological groups, among which there are extinct, and undiscovered existing microorganisms. Therefore, the search for new groups of microorganisms would be more comprehensive and easier. Application of this model as a guidepost, or map, for verifying a range of all possible combination of the physico-chemical parameters within the buffer system for synthetic growth media, would significantly increase the rate of successful in vitro cultivation. Furthermore, an application of molecular probes and attempts to cultivate microorganisms expected within a precise range of environmental parameters should be consistent in regards to other biological groups. For example, the following groups should be checked: 1. 2. 3. 4.
Thermophilic and moderately thermophilic Crenarchaeota at pH 0-2 are unknown. Are they extinct group or should be cultivated on different buffer systems; Thermophilic Euryarchaeota and Eubacteria should be checked on synthetic media with high pH buffers; Moderately thermophilic Halobacteria and halophilic Eubacteria should be checked on high salinity media with different buffer systems; Search for acidophilic organisms at meso- and low temperatures.
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2. 3. 4. 5.
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