# Prebiotic Competition between Information Variants, With Low Error Catastrophe Risks

^{1}

^{2}

^{*}

^{†}

## Abstract

**:**

## 1. Introduction

**Figure 1.**Diagram of a system containing two information variants (types of order or sub-systems) called Syst#1 and Syst#2 competing for building materials (BM) and free energy (W) in a BM-finite environment. These sub-systems have similar cyclomatic complexity (v = 3). “nf” = Natural forward rate. “nr” = Natural reverse rate. The two sub-systems can be given dissimilar energy-related performance. Q = Heat released during energy dissipation. The model assumes an infinite heat sink in the exterior and no temperature variation. During simulations, changes in ratio between A and B components occur, as well as changes in abundance between the two sub-systems. One sub-system is considered to be over-competed when its relative abundance changes from 50% to < 1% in a given timeframe (i.e., full length simulation). The arrow indicated by the Autocatalyzed path shows the positive feedback of B units on the A => B transformation.

- v = e − n + 2p, where: v = the cyclomatic number of a network or circuit (a measure of its complexity);
- e = the number of edges in a network (equivalent with the number of connections, or avenues of transformation, between the various types of components from inside the network);
- n = the number of vertices in a network (equivalent to the number of types of components);
- p = the number of externally connected components (i.e., 2p is the number of entries and exits connecting the network with the exterior).

## 2. Results and Discussion

#### 2.1. Series 1

^{−15}to ≈ 3×10

^{−3}J range), nine values for “EG_B2” (in the 1.2×10

^{−17}to ≈ 2.4×10

^{−16}J range) and six values for “Autocat_B2” (in the 1.1 ≈ 4.0 range). In this series, it is assumed that the range of EG is smaller than the range of energy availability in the environment. Simulations have shown that if “Autocat_B2” = “Autocat_B1” and “EG_B2” ≤ “EG_B1”, Syst#2 cannot over-compete Syst#1 for any given “free_E_input” (results not shown). This is because without changes in autocatalysis, only the cost of order influences competition, and the overall system (Syst#1 + Syst#2) evolves toward the state of lowest order and free energy content (i.e., according to the 2

^{nd}law of thermodynamics).

**Figure 2.**The evolution of competitive success of Syst#2 (“compet_success_2vs1”) in the model from Figure 1. The panels A through F represent variation for six values of autocatalytic activity of B2 components (“Autocat_B2”). “Autocat_B1” = 1 in all simulations. Each graph shows the effect of two variables: “free_E_input” (the availability of free energy in the exterior), and “EG_B2” (the free energy content per B2 component). The smallest value for EG used in these graphs (log(EG) = −16.92) corresponds with “EG_B2” = 1.2 × 10

^{−17}J. “EG_B1” = 6.6 × 10

^{−17}J in all simulations. A single value for the standard rates of transformation has been used: “Ro_A1_to_B1” = “Ro_A2_to_B2” = 1×10

^{−4}. Each graph summarizes results of 288 Stella simulations with 32,000 steps each (DT = 1). The vertical axis shows the competitive success of Syst#2 at the end of each simulation. When “compet_success_2vs1” = 0, the mass of Syst#2 equals that of Syst#1. When “compet_success_2vs1” = 1, Syst#1 is eliminated. The wireframe on the 3D graph and on the 2D map projection on the XY axis distinguishes various colors (where: dark blue = −1; green = mid values around 0; highest red values = 0.98–0.99 and white > 0.99). We have selected white for the peak in competitive success of Syst#2 in order to obtain maximum contrast on the 2D XY projection. The white area in the 2D map projection shows cases where Syst#1 has reached ≤ 1% at the end of simulations.

^{−11}to ≈ 10

^{−10}J) and when the energy cost of building B2 is large (log(EG) > −16.3). This phenomenon is due to autocatalysis not being sufficiently strong to favor the energy costly Syst#2 in an environment where energy availability is limiting. This phenomenon disappears when energy availability is very little (< 10

^{−11}J), because insufficient free energy exists to build up disequilibrium in either system and the low cost Syst#1 prevails. It is also absent when free energy becomes more abundant, because the autocatalytic capability of Syst#2 finds sufficient energy for growth. In this model, the threshold where “Autocat_B2” becomes relevant is approximately 1.5. When “Autocat_B2” = 1.5 efficient elimination of Syst#1 occurs, yet only within very narrow range of energy availability, i.e., “free_E_input” between 1 × 10

^{−10}and 2 × 10

^{−10}J (Figure 2; Panel B), and when the energy content of order “EG_B2” ≤ 10

^{−16.5}J.

^{−14}J (results not shown). This effect is due to high energy costs for building B2 entities relative to advantages of autocatalysis, and decreases at large energy availability.

#### 2.2. Series 2

^{−17}J was used, corresponding to “Irs” = 40 and “kG” = 3 × 10

^{−18}J/bit (this EG value is in the range from Series 1, Figure 2). Increase in the A⇔B rate is equivalent with the activity of a catalyst, and “Ro_Ax_to_Bx” modifications do not alter the A:B ratio at equilibrium, but shorten the time needed to reach it. Combining larger A⇔B rate with larger B2 autocatalysis is expected to increase the turnover time of building materials through the B2 reservoir and to also increase the energy cost of maintaining order afar from equilibrium. Faster A⇔B exchange can also be produced by increase in temperature, but this would also influence the BM⇔A exchange rate. In this series, only the A⇔B transformation rates are modified, not the BM⇔A rates as well. Very slow A⇔B rates are expected to diminish access of B structures to building materials before they are exchanged back between A and BM. Very fast A⇔B rates are expected to shorten the residence time of building materials in the B reservoir, giving competitors a chance to pick them up through the BM reservoir. Figure 3 summarizes results of 1,344 Stella simulations (each 32,000 steps long; DT = 1).

**Figure 3.**The evolution of competitive success of Syst#2 (“compet_success_2vs1”) in the model from Figure 1. Panels A through F represent variation for six values of autocatalytic activity of B2 components (“Autocat_B2”). “Autocat_B1” = 1 in all simulations. Each graph shows the effect of two variables: “free_E_input” (the exterior free energy availability), and the intrinsic rate of A⇔B transformations (“Ro_Ax_to_Bx”), representing the contribution of a catalyst of the A⇔B transformation. Panels A through F use the same range and values for “Autocat_B2” and “free_E_input” from Figure 2. The −5 value on the log(Ro_Ax_to_Bx) axis represents natural uncatalyzed transformation. All other graph notations and color code are similar to Figure 2.

#### 2.3. Series 3

^{® }(see Experimental Section for details), simulations (32,000 steps each) are shown in Figure 4. The general trend showing consequences of increasing “Autocat_B2” remains, but with a few differences. Unlike Figure 2, Panel A (“Autocat_B2” = 1.1), “compet_success_2vs1” never reaches negative values. At small autocatalytic efficiency the increased stability of B2 makes Syst#2 “lose less ground” relative to Syst#1 (Figure 4, Panel A). This shows that as ordered systems gain stability and autocatalytic capabilities, chances for success in competition improve and beneficial environmental niches can extend to broad range of energy availability. The stability of structures also plays an important role in competitive success. For example, increased stability of B2 entities led to improvement in competitive success of Syst#2 at lower energy levels than in Series 1. Increased stability of order also allowed small changes in autocatalysis influence the efficiency of information selection. When autocatalytic efficiency was large (“Autocat_B2” = 4) increase in the stability of order diminished the upper limit where excess energy availability has lowered the efficiency of Syst#2 (Figure 4, Panel F). This series of simulations shows how increased capacity of Syst#2 to sequester energy, and primarily the ability of a sub-system to adjust its energy dissipative activity to energy availability, can help eliminate competitors by starvation.

**Figure 4.**The evolution of competitive success of Syst#2 (“compet_success_2vs1”) in the model from Figure 1. Variables from each graph are similar to those from Figure 2, but in this series of simulations larger “EG_B2” value also increases the stability of order. Each graph summarizes the results of 256 Stella simulations with 32,000 steps each (DT = 1). All other graph notations and color code are similar to Figure 2.

## 3. Experimental Section

^{®}(http://www.iseesystems.com/softwares/Education/StellaSoftware.aspx), and the file (written in Stella) is available at www.ksg.ro/Entropy_simulation02.STM. Principles of BiADA modeling, the meaning of various parameters, equations, sequence of commands, model limitations and technical solutions have been previously published [19,20]. Next, we summarize BiADA principles and model parameters used in this study.

- (1)
- Each type of component in a BiADA model is characterized by two energy-related features, free energy content and heat content;
- (2)
- Each type of component is characterized by two information-related features: Residual information and Remanent information. Residual information is the unused information capacity in a system or the information capacity of the disordered part of the system. Remanent information is the information capacity removed due to ordering the system. The sum between Residual information and Remanent information is called Virtual information and represents the maximum information capacity of a system (or Shannon’s information capacity) in the fully disordered state.
- (3)
- The parameters representing free energy, heat content, Residual information and Remanent information are only given zero or positive values; and thermodynamic rules of transformation are obeyed.
- (4)
- All transformations are integer increments or decrements of building blocks and are expressed in units of transformation.
- (5)
- All transformations or transfer of materials and energy between internal components are uni-flows (i.e., forward and reverse transformations are analyzed separately). Natural and catalyzed flows are also analyzed separately. In BiADA models equilibrium is determined by differences between forward and reverse transformations.
- (6)
- The direction and equilibrium of a process is derived from differences between the net forward and net reverse transformations.

- “Init_BM_units”, “Init_A1_units”, “Init_B1_units”, “Init_A2_units” and “Init_B2_units” represent the amount of various components used in the model (BM, A1, B1, A2 and B2 respectively) at the beginning of a simulation.
- “BM”, “A1”, “B1”, “A2” and “B2” are the magnitude of the five stocks used in this model (Figure 1), expressed in mass units.
- “Irs_BM_units”, “Irs_A1_units”, “Irs_B1_units”, “Irs_A2_units” and “Irs_B2_units” are the residual information capacity of the entities “BM”, “A1”, “B1”, “A2” and “B2”, respectively. Irs represents the information capacity present in a system or structure after ordering has removed degrees of freedom. The capacity of Irs (expressed in bits) indicates the amount of information that can still be stored in the system by further ordering.
- “Irm_BM_units”, “Irm_A1_units”, “Irm_B1_units”, “Irm_A2_units” and “Irm_B2_units” are the remanent information content of the entities “BM”, “A1”, “B1”, “A2” and “B2” respectively. Irm, means information content and represents the amount of information capacity removed by ordering the system.
- “Ivt_BM_units”, “Ivt_A1_units”, “Ivt_B1_units”, “Ivt_A2_units” and “Ivt_B2_units” are the virtual information content of the entities “BM”, “A1”, “B1”, “A2” and “B2” respectively. Ivt is the information capacity of the system in fully disordered state, and Ivt = Irs + Irm.
- “kG_of_BM_J_per_bit_Irm”, “kG_of_A1_J_per_bit_Irm”, “kG_of_B1_J_per_bit_Irm”, “kG_of_ A2_J_per_bit_Irm” and “kG_of_B2_J_per_bit_Irm” are the free energy associated with one bit of Irm in the “BM”, “A1”, “B1”, “A2” and “B2” entities respectively. kG is variable, as free energy content relative to Irm varies among various ordered structures.
- “EG_BM_J_per_unit_transf”, “EG_A1_J_per_unit_transf”, “EG_B1_J_per_unit_transf”, “EG_A2_ J_per_unit_transf” and “EG_B2_J_per_unit_transf” are the free energy associated with units of transformation of “BM”, “A1”, “B1”, “A2” and “B2”, respectively. EG = kG × Irm. EG is equivalent to the free energy content of an organized structure. In the model, the value of EG of an organized structure can be modified by increasing the order of a structure (Irm) or its kG value.
- “free_E_input” is the availability of free energy in the environment.
- “Autocat_B1” and “Autocat_B2” are the autocatalytic capability of the entities B1 and B2 respectively. “Autocat” is ≥ 0. The rate of the Autocatalyzed path in Syst#1 from Figure 1 is proportional to the magnitude of the B1 stock at the power of “Autocat_B1”; same formula is used for the rate of the Autocatalyzed path in Syst#2.
- “Ro_BM_to_A1”, “Ro_A1_to_B1”, “Ro_BM_to_A2” and “Ro_A2_to_B2” are the intrinsic rates of forward transformations: “BM to A1”, “A1 to B1”, “BM to A2” and “A2 to B2”, respectively.
- “Ro_A1_to_BM”, “Ro_B1_to_A1”, “Ro_A2_to_BM” and “Ro_B2_to_A2” are the intrinsic rates of reverse transformations: “A1 to BM”, “B1 to A1”, “A2 to BM” and “B2 to A2”, respectively.
- “Compet_success_2vs1” = ((A2 + B2) − (A1 + B1))/(A1 + B1 + A2 + B2) measures the dominance of Syst#2 over Syst#1 during competition. Total elimination of Syst#1 is often not observed within reasonable timeframe (i.e., 32,000 simulation steps). An efficient competition-success threshold has been established as the ability of Syst#2 to reach 99% abundance during 32,000 step simulation for Delta Time (DT) = 1.

## 4. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References and Notes

- Popa, R. Between Necessity and Probability: Searching for the Definition and Origin of Life; Springer: Berlin, Germany, 2004. [Google Scholar]
- Shelley, D.C.; Smith, E.; Morowitz, H.J. The Origin of the RNA World: Co-evolution of Genes and Metabolism. Bioorgan. Chem.
**2007**, 35, 430–443. [Google Scholar] - Gilbert, W. Origin of Life: The RNA World. Nature
**1986**, 319, 618. [Google Scholar] [CrossRef] - Poole, A.M.; Jeffares, D.C.; Penny, D. The Path from the RNA World. J. Mol. Evol.
**1998**, 46, 1–17. [Google Scholar] [CrossRef] [PubMed] - Joyce, G.F. The Antiquity of RNA-Based Evolution. Nature
**2002**, 418, 214–221. [Google Scholar] [CrossRef] [PubMed] - Eigen, M. Self-organization of Matter and Evolution of Biological Macro-molecules. Naturwissenschaften.
**1971**, 58, 465–523. [Google Scholar] [CrossRef] [PubMed] - McCabe, T.J., Sr. A Complexity Measure. IEEE Trans. Softw. Eng.
**1976**, 4, 308–320. [Google Scholar] [CrossRef] - Dyson, F.J. A Model for the Origin of Life. J. Mol. Evol.
**1982**, 18, 344–350. [Google Scholar] [CrossRef] [PubMed] - Dyson, F.J. Origins of Life; Cambridge University Press: Cambridge, UK, 1999. [Google Scholar]
- Rosen, R. On the Dynamical Realization of (M, R)-Systems. Bull. Math. Biol.
**1973**, 35, 1–9. [Google Scholar] [PubMed] - Ray, T.S. Evolution and Optimization of Digital Organisms. In Scientific Excellence in Supercomputing: The IBM 1990 Contest Prize Papers; Billingsley, K.R., Derohanes, E., Brown, H., Eds.; Baldwin Press: Boston, MA, USA, 1991; pp. 489–531. [Google Scholar]
- Fontana, W.; Buss, L.W. What Would Be Conserved if the Tape Were Played Twice? Proc. Natl. Acad. Sci. USA
**1994**, 91, 757–761. [Google Scholar] [CrossRef] [PubMed] - Pargellis, A.N. The Evolution of Self-replicating Computer Organisms. Physica. D
**1996**, 98, 111–127. [Google Scholar] [CrossRef] - McMullin, B. SCL: An Artificial Chemistry in Swarm. Available online: http://samoa.santafe.edu/media/workingpapers/97-01-002.pdf (accessed on 23 July 2015).
- Adami, C. Introduction to Artificial Life; Springer: Berlin, Germany, 1997. [Google Scholar]
- Moran, F.; Moreno, A.; Minch, E.; Montero, F. Further Steps toward a Realistic Description of the Essence of Life. In Artificial Life V: Proceedings of the Fifth International Workshop on the Synthesis and Simulation of Living Systems (Complex Adaptive Systems); Langton, C.G., Shimonara, K., Eds.; MIT Press: Cambridge, MA, USA, 1997; pp. 255–263. [Google Scholar]
- Bedau, M.A.; McCaskill, J.S.; Packard, N.; Rasmussen, S.; Adami, C.; Green, D.G.; Ikegami, T.; Kaneko, K.; Ray, T.S. Open Problems in Artificial Life. Artif. Life
**2000**, 6, 363–376. [Google Scholar] [CrossRef] [PubMed] - Wilensky, U.; Rand, W. NetLogo 3.1: Low Threshold, no Ceiling. Available online: https://ccl.northwestern.edu/papers/2006/SoftwareDemo.pdf (accessed on 23 July 2015).
- Cimpoiasu, V.M.; Popa, R. Biotic Abstract Dual Automata (BIADA)−A Novel Tool for Studying the Evolution of Prebiotic Order (and the Origin of Life). Astrobiology
**2012**, 12, 1123–1134. [Google Scholar] [CrossRef] [PubMed] - Cimpoiasu, V.M.; Popa, R. Elimination of Less-Fit Information Variants during Competition between Low Complexity Dynamic Systems. Phys. AUC
**2014**, 24, 130–151. [Google Scholar] - Popa, R.; Cimpoiasu, V.M. Energy-Driven Evolution of Prebiotic Chiral Order (Lessons from Dynamic Systems Modeling). In Genesis—In the Beginning; Springer: Berlin, Germany, 2012; Volume 22, pp. 526–545. [Google Scholar]
- Popa, R.; Cimpoiasu, V.M. Analysis of Competition between Transformation Pathways in the Functioning of Biotic Abstract Dual Automata. Astrobiology
**2013**, 13, 454–464. [Google Scholar] [CrossRef] [PubMed] - Baltscheffsky, H. Major “Anastrophes” in the Origin and Early Evolution of Biological Energy Conversion. J. Theor. Biol.
**1997**, 187, 495–501. [Google Scholar] [CrossRef] [PubMed]

© 2015 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Popa, R.; Cimpoiasu, V.M.
Prebiotic Competition between Information Variants, With Low Error Catastrophe Risks. *Entropy* **2015**, *17*, 5274-5287.
https://doi.org/10.3390/e17085274

**AMA Style**

Popa R, Cimpoiasu VM.
Prebiotic Competition between Information Variants, With Low Error Catastrophe Risks. *Entropy*. 2015; 17(8):5274-5287.
https://doi.org/10.3390/e17085274

**Chicago/Turabian Style**

Popa, Radu, and Vily Marius Cimpoiasu.
2015. "Prebiotic Competition between Information Variants, With Low Error Catastrophe Risks" *Entropy* 17, no. 8: 5274-5287.
https://doi.org/10.3390/e17085274