Template and copy are either different (thin) or identical (bold) for complementary (top) and homologous pairing (bottom) due to strand polarity.

<p>Reverse (top left) and direct palindromes (bottom middle) yield two identical templates with complementary and homologous pairing, respectively, just like homologous pairing with parallel polarity. Note, that in case of reverse palindromes, it is not necessary for the sequence itself to be palindromic to make the two strands identical. Cases of complementary pairing with antiparallel polarity (top left and middle) and homologous pairing with parallel polarity (bottom right) are discussed in the main text; homologous pairing with antiparallel polarity (bottom left and middle) is discussed in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003193#pcbi.1003193.s009" target="_blank">Text S1</a>. The remaining case (top right) is not discussed here.</p

Dynamics of the chemoton with two different templates, <i>p</i>V and <i>p</i>W, when the main food molecule (X) has a low influx rate.

<p><i>k</i>_V6 = <i>k</i>_V7 = <i>k</i>_W6 = 1, critical T_m = 1000. Top row: the polymerization rate of V (<i>k</i>_V7) and W (<i>k</i>_W7) are identical. Middle row: k_W7 = 10. Bottom row: <i>k</i>_W7 = 100. In the last two cases, <i>k_V7</i> = 1. Volume and surface variables are omitted from the figure. Initial amounts: 100 A₁, 100 X, 100 <i>p</i>V(0), 100 <i>p</i>W(0), 100 T_m and 1 Growth. Influx rate of X is 10; Z₁ and Z₂ are still constant.</p

Analysis of coexistence of complementary pairs of sequences of length according to method M1.

<p>Second column shows the number of scanned sequences (and the amount as a fraction of the whole combined sequence space). The third column shows the fraction of coexisting sequences in the scanned domain, i.e. the probability of coexistence of random sequence groups of size with a given parameter set. (S) indicates that all cases of coexistence are locally asymptotically stable. The fourth column shows the average of the leading eigenvalues (if there is coexistence) as a measure of stability. For parameters, see <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003193#pcbi.1003193.s009" target="_blank">Text S1</a>.</p

Split plot of the coexistence of two complementary sequence pairs with antiparallel strand polarity (4 sequences per pair) of length .

<p>Lower left half: coexistence is marked by green, extinction of the first sequence pair by red and extinction of the second sequence pair by blue. Upper right half: stability of coexistence according to the leading eigenvalue (red indicates more stable, blue indicates less stable coexistence, white indicates extinction of one of the sequence pairs). The upper triangle shows the stability measures of the sequences pairs from the lower one (mirrored and rotated ). From the point of view of coexistence two pairs (e.g. -, -) and their reverse (-, -) are not fully equivalent. The reason for this is that the degradation rates are assigned to sequences, always in the same order within a set (this means that the same rates are assigned to e.g. and in the two cases, respectively). Despite this difference the plot is almost symmetrical since degradation rates are taken from a narrow distribution. For details, see main text, for parameters, see <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003193#pcbi.1003193.s009" target="_blank">Text S1</a>.</p

Dynamics of the chemoton with two different templates, <i>p</i>V and <i>p</i>W, when the concentration of food molecules is constant.

<p><i>k</i>_V6 = <i>k</i>_V7 = <i>k</i>_W6 = 1, critical T_m = 1000. Top row: the polymerization rate of V (<i>k</i>_V7) and W (<i>k</i>_W7) are identical (1). Middle row: <i>k</i>_W7 = 10. Bottom row: <i>k</i>_W7 = 100. In the last two cases, <i>k</i>_V7 = 1. Volume and surface variables are omitted from the figure. Initial amounts: 100 A₁, 100 <i>p</i>V(0), 100 <i>p</i>W(0), 100 T_m and 1 Growth. X has constant amount at 20, Z₁ and Z₂ at 10. Note that since division is set to a 100 times slower than in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0021380#pone-0021380-g002" target="_blank">Figures 2</a> and <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0021380#pone-0021380-g004" target="_blank">4</a>, removal of molecules is actually slower than growth. This has no effect on the outcome of the simulation, as the removal process is deterministic. ∑A<i>_i</i> stands for the total amount of all metabolites, ∑<i>p</i>V<i>_i</i> and ∑<i>p</i>W<i>_j</i> for the total amount of all <i>p</i>V and <i>p</i>W polymer stages, respectively.</p

Analysis of coexistence of two sequences of length according to method M3.

<p>Second column shows the number of scanned sequences (the whole combined sequence space for all investigated ). The third column shows the fraction of coexisting sequences, i.e. the probability of coexistence of two sequences with a given parameter set (see <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003193#pcbi.1003193.s009" target="_blank">Text S1</a>). (S) indicates that all cases of coexistence are locally asymptotically stable. The fourth column shows the average of the leading eigenvalues (if coexistence exists) as a measure of stability.</p

Coexistence plots of pairs of double-stranded sequences of length (upper panel) and (lower panel) using two monomers (, ) in case of uniform degradation and identical elongation rate constants and non-complementary pairing.

<p>The green indicates stable coexistence, grey indicates structurally unstable coexistence, i.e. compositional identity (no coexistence in a biological sense), while pink indicates that there is no coexistence possible. Sequences along the axes are arranged first according to Hamming distance and secondly according to lexicographic ordering from more (top and left) to more (bottom and right). For parameters, see <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003193#pcbi.1003193.s009" target="_blank">Text S1</a>.</p

Additional file 1 of Cue-driven microbial cooperation and communication: evolving quorum sensing with honest signaling

Additional file 1: Appendix 1, Mean-field model, Fig. S1; Appendix 2, Configuration-field model, Figs. S2-S5; Appendix 3. Individual-based lattice model, Fig. S6

Comparison of different metabolic subsystems.

<p>The chemoton on the left consists of a 5-member metabolic cycle (A₁ to A₅), while the chemoton on the right harbors a 12-strong metabolism (A₁ to A₁₂). The extra metabolites feed on X and the previous metabolite, and produce the next metabolite in the cycle. The larger number of metabolic partners slightly decreases the total amount of metabolites, ∑A<i>_i</i>. This is a phenomenon that is supported directly by the numerical results of deterministic models: the larger the number of intermediates in the metabolic cycle the less the total amount of metabolic molecules is in a splitting equilibrium. It is a consequence of the relative position where T_m is produced in the cycle: the earlier it is generated (i.e. the more metabolites are in the cycle after T_m is generated), the less the total amount of metabolites will be, as T_m defines the critical value for splitting.</p

Chemoton with two templates.

<p>T_m…T_m+k represent the boundary subsystem, A₁…A₅ represent the metabolic subsystem and pV(0)…pV(n−1) and pW(0)…pW(n−1) represent two different template polymerization cycles (informational subsystems), T₁ and T₂. Z₁, Z₂ and X are food molecules. See text for further details.</p