PMC

Average entropy of specific post-translational modification sites in each of the MEME blocks is demonstrated using boxplot. (A) Average entropy of potential CKII phosphorylation sites in the MEME blocks. Blocks 1, 5 and 9 have zero entropy at all CKII sites. The majority of MEME blocks 2 and 7 CKII sites have nonzero entropy. One of the MEME block 2 CKII sites (amino acid 205) has the largest entropy (1.24) among all of CKII's sites. The average entropy over MEME block 7 and 2 CKII sites is therefore higher than for any other block. MEME block 1 has a wider boxplot than the others, indicating more CKII sites in this block. (B) Average entropy of potential PKC phosphorylation site in the MEME blocks. MEME block 1 and 4 have zero entropy at all their PKC sites. The highest PKC entropy values were observed in MEME block 2 (amino acid 205) and MEME block 7 (amino acid 160) with 1.2 entropy values. MEME block 5, 7 and 11 are unusual in that very few of their PKC sites have zero entropy. MEME block 11 then 7 PKC sites have the highest average entropy. The width of the boxplots indicates that more PKC sites are observed in MEME sites 2, 3 and 7 respectively. (C) Average entropy of potential N-glycosylation site in the MEME blocks. MEME blocks 4 and 5 have zero entropy at all of their ASN sites. MEME block 2, 6 and 9 have nonzero entropy at the majority of their ASN sites. One of the ASN sites (amino acid 99) from MEME block 1 has the highest entropy (1.003) among all ASN sites. The width of the boxplots indicates that more N-glycosylation sites are observed in MEME sites 2 and 7 respectively (D) Average entropy of potential N-myristylation site in the MEME blocks. MEME blocks 1, 2, 4, and 9 have the majority of their myristylation sites possessing zero entropy. The highest myristylation sites entropy is at MEME block 9 and 7 (Amino acid 78 and 160 respectively) with an approximate entropy value of 1.2. MEME block 1 and 7 have more N-myristylation sites than any other block, although MEME block 2 also has a fairly large number of myristylation sites.

Entropy production in a probe bath that is kept at zero temperature and is coupled to a two-level system depicted in . The entropy is the sum of two parts: the incoherent and the coherent parts. (a) the incoherent part of entropy is nothing new and can be determined by standard correlations. It is positive by the convention that entropy enters from a higher temperature bath (via the two-level system); (b) the coherent part of entropy is a previously unknown part as it comes from the informational correlations between different replicas. This part depends quadratically on the off diagonal density. Quite nontrivially, this part of entropy is negative and summing it with the incoherent part will result in a positive flow yet with much smaller magnitude for entropy at small driving amplitudes.

a The normalized conditional entropy S_u∣u−1 (equivalent to the entropy rate under a steady state). b the normalized conditional entropy of the reverse dynamics . c The normalized entropy production at a steady state. d Horizontal sections of the entropy production (ΔH = 0.2, 0.4, 0.6, 0.8, 1.0, and 1.2). It peaks at the critical line. e A vertical section of the entropy production at zero temperature (β → ∞). All plots are based on a model with fixed parameters J₀ = 1, ΔJ = 0.2 and variable ΔH and β.

Entropy of a variable X which takes the value one with probability p and the value zero with probability .