Maximum mutational robustness in genotype-phenotype maps follows a self-similar blancmange-like curve.

Phenotype robustness, defined as the average mutational robustness of all the genotypes that map to a given phenotype, plays a key role in facilitating neutral exploration of novel phenotypic variation by an evolving population. By applying results from coding theory, we prove that the maximum phenotype robustness occurs when genotypes are organized as bricklayer's graphs, so-called because they resemble the way in which a bricklayer would fill in a Hamming graph. The value of the maximal robustness is given by a fractal continuous everywhere but differentiable nowhere sums-of-digits function from number theory. Interestingly, genotype-phenotype maps for RNA secondary structure and the hydrophobic-polar (HP) model for protein folding can exhibit phenotype robustness that exactly attains this upper bound. By exploiting properties of the sums-of-digits function, we prove a lower bound on the deviation of the maximum robustness of phenotypes with multiple neutral components from the bricklayer's graph bound, and show that RNA secondary structure phenotypes obey this bound. Finally, we show how robustness changes when phenotypes are coarse-grained and derive a formula and associated bounds for the transition probabilities between such phenotypes.

Random and Natural Non-Coding RNA Have Similar Structural Motif Patterns but Differ in Bulge, Loop, and Bond Counts.

An important question in evolutionary biology is whether (and in what ways) genotype-phenotype (GP) map biases can influence evolutionary trajectories. Untangling the relative roles of natural selection and biases (and other factors) in shaping phenotypes can be difficult. Because the RNA secondary structure (SS) can be analyzed in detail mathematically and computationally, is biologically relevant, and a wealth of bioinformatic data are available, it offers a good model system for studying the role of bias. For quite short RNA (length L≤126), it has recently been shown that natural and random RNA types are structurally very similar, suggesting that bias strongly constrains evolutionary dynamics. Here, we extend these results with emphasis on much larger RNA with lengths up to 3000 nucleotides. By examining both abstract shapes and structural motif frequencies (i.e., the number of helices, bonds, bulges, junctions, and loops), we find that large natural and random structures are also very similar, especially when contrasted to typical structures sampled from the spaces of all possible RNA structures. Our motif frequency study yields another result, where the frequencies of different motifs can be used in machine learning algorithms to classify random and natural RNA with high accuracy, especially for longer RNA (e.g., ROC AUC 0.86 for L = 1000). The most important motifs for classification are the number of bulges, loops, and bonds. This finding may be useful in using SS to detect candidates for functional RNA within 'junk' DNA regions.

Quantitative analyses of cytokine profiles reveal hormone-mediated modulation of cytokine profiles in recurrent spontaneous miscarriage.

PURPOSE: Cytokines play important roles in pregnancy complications. Some hormones such as estrogen, progesterone, and dydrogesterone have been shown to alter cytokine profiles. Understanding how cytokine profiles are affected by these hormones is therefore an important step towards immunomodulatory therapies for pregnancy complications. We analyse previously published data on the effects of estrogen, progesterone, and dydrogesterone on cytokine balances in women having recurrent spontaneous miscarriages. MATERIALS AND METHODS: Levels of eight cytokines (IFN-γ, IL-2, IL-6, IL-10, IL-13, IL-17, IL-23, TNF-α) from n = 22 women presenting unexplained recurrent spontaneous miscarriages were studied. Cytokine values were recorded after in vitro exposure of peripheral blood cells to estrogen, progesterone, and dydrogesterone. We expand on earlier analysis of the dataset by employing different statistical techniques including effect sizes for individual cytokine values, a more powerful statistical test, and adjusting p-values for multiple comparisons. We employ multivariate analysis methods, including to determine the relative magnitude of the effects of the hormone therapies on cytokines. A new statistical method is introduced based on pairwise distances able to accommodate complex relations in cytokine profiles. RESULTS: We report several statistically significant differences in individual cytokine values between the control group and each hormone treated group, with estrogen affecting the fewest cytokines, and progesterone and dydrogesterone both affecting seven out of eight cytokines. Exposure to estrogen produces no large effects sizes however, while IFN-γ and IL-17 show large effect sizes for both progesterone and dydrogesterone, among other cytokines. Our new method for identifying which collections (i.e. subsets) of cytokines best distinguish contrasting groups identifies IFN-γ, IL-10 and IL-23 as especially noteworthy for both progesterone and dydrogesterone treatments. CONCLUSIONS: While some statistically significant differences in cytokine levels after exposure to estrogen are found, these have small effect sizes and are unlikely to be clinically relevant. Progesterone and dydrogesterone both induce statistically significant and large effect-size differences in cytokine levels, hence therapy with these two progestogens is more likely to be clinically relevant. Univariate and multivariate methods for identifying cytokine importances provide insight into which groups of cytokines are most affected and in what ways by therapies.

Predicting phenotype transition probabilities via conditional algorithmic probability approximations.

Unravelling the structure of genotype-phenotype (GP) maps is an important problem in biology. Recently, arguments inspired by algorithmic information theory (AIT) and Kolmogorov complexity have been invoked to uncover simplicity bias in GP maps, an exponentially decaying upper bound in phenotype probability with the increasing phenotype descriptional complexity. This means that phenotypes with many genotypes assigned via the GP map must be simple, while complex phenotypes must have few genotypes assigned. Here, we use similar arguments to bound the probability P(x → y) that phenotype x, upon random genetic mutation, transitions to phenotype y. The bound is [Formula: see text], where [Formula: see text] is the estimated conditional complexity of y given x, quantifying how much extra information is required to make y given access to x. This upper bound is related to the conditional form of algorithmic probability from AIT. We demonstrate the practical applicability of our derived bound by predicting phenotype transition probabilities (and other related quantities) in simulations of RNA and protein secondary structures. Our work contributes to a general mathematical understanding of GP maps and may facilitate the prediction of transition probabilities directly from examining phenotype themselves, without utilizing detailed knowledge of the GP map.

Symmetry and simplicity spontaneously emerge from the algorithmic nature of evolution.

SignificanceWhy does evolution favor symmetric structures when they only represent a minute subset of all possible forms? Just as monkeys randomly typing into a computer language will preferentially produce outputs that can be generated by shorter algorithms, so the coding theorem from algorithmic information theory predicts that random mutations, when decoded by the process of development, preferentially produce phenotypes with shorter algorithmic descriptions. Since symmetric structures need less information to encode, they are much more likely to appear as potential variation. Combined with an arrival-of-the-frequent mechanism, this algorithmic bias predicts a much higher prevalence of low-complexity (high-symmetry) phenotypes than follows from natural selection alone and also explains patterns observed in protein complexes, RNA secondary structures, and a gene regulatory network.

Phenotype Bias Determines How Natural RNA Structures Occupy the Morphospace of All Possible Shapes.

Morphospaces-representations of phenotypic characteristics-are often populated unevenly, leaving large parts unoccupied. Such patterns are typically ascribed to contingency, or else to natural selection disfavoring certain parts of the morphospace. The extent to which developmental bias, the tendency of certain phenotypes to preferentially appear as potential variation, also explains these patterns is hotly debated. Here we demonstrate quantitatively that developmental bias is the primary explanation for the occupation of the morphospace of RNA secondary structure (SS) shapes. Upon random mutations, some RNA SS shapes (the frequent ones) are much more likely to appear than others. By using the RNAshapes method to define coarse-grained SS classes, we can directly compare the frequencies that noncoding RNA SS shapes appear in the RNAcentral database to frequencies obtained upon a random sampling of sequences. We show that: 1) only the most frequent structures appear in nature; the vast majority of possible structures in the morphospace have not yet been explored; 2) remarkably small numbers of random sequences are needed to produce all the RNA SS shapes found in nature so far; and 3) perhaps most surprisingly, the natural frequencies are accurately predicted, over several orders of magnitude in variation, by the likelihood that structures appear upon a uniform random sampling of sequences. The ultimate cause of these patterns is not natural selection, but rather a strong phenotype bias in the RNA genotype-phenotype map, a type of developmental bias or "findability constraint," which limits evolutionary dynamics to a hugely reduced subset of structures that are easy to "find."

CytokineExplore: An Online Tool for Statistical Analysis of Cytokine Concentration Datasets.

PURPOSE: Cytokine data sets are increasing both in the number of different cytokines measured and the number of samples assayed. Further, typically data from different groups may be contrasted, eg, normal vs complication subjects. Many univariate and multivariate statistical techniques exist to study such cytokine datasets, but the ability to implement these techniques may be lacking for some practitioners, or may not be available quickly and conveniently. Here, we introduce CytokineExplore, an online tool for multi-cytokine and multi-group data analysis of user-provided Microsoft Excel data files. MATERIALS AND METHODS: In order to illustrate the tool features, we use data from intrauterine growth retardation (IUGR), a pregnancy complication, and normal healthy subjects as a control. The dataset contains levels for 10 cytokines, namely: IL-4, IL-6, IL-8, IL-10, IL-12, IL-13, IL-18, IL-23, interferon-gamma (IFN-γ) and tumour necrosis-alpha (TNF-α), obtained from 34 women with IUGR (further divided into 17 symmetric and 17 asymmetric cases) and 24 gestationally age-matched normal controls. RESULTS: The online tool automatically generates box-plots, histograms, PCA and PLSDA plots, t-tests and Mann-Whitney statistical tests, cytokine importance values for separating two groups, heatmaps for comparing multiple groups, and other functionalities. Figures generated can be directly downloaded for use in presentations or journal articles. CONCLUSION: The tool facilitates quick and easy numerical exploration and multivariate analysis of cytokine datasets, to aid basic understanding and hypothesis generation.

Generic predictions of output probability based on complexities of inputs and outputs.

For a broad class of input-output maps, arguments based on the coding theorem from algorithmic information theory (AIT) predict that simple (low Kolmogorov complexity) outputs are exponentially more likely to occur upon uniform random sampling of inputs than complex outputs are. Here, we derive probability bounds that are based on the complexities of the inputs as well as the outputs, rather than just on the complexities of the outputs. The more that outputs deviate from the coding theorem bound, the lower the complexity of their inputs. Since the number of low complexity inputs is limited, this behaviour leads to an effective lower bound on the probability. Our new bounds are tested for an RNA sequence to structure map, a finite state transducer and a perceptron. The success of these new methods opens avenues for AIT to be more widely used.

Multivariate Comparison of Cytokine Profiles for Normal- and Low-Bone-Density Subjects.

Osteoporosis is a serious worldwide public health concern. The role of the immune system in the onset of osteoporosis in postmenopausal women is an area of current research. Here we study data from a panel of 10 cytokines obtained from postmenopausal women, with both normal and low bone mineral density (BMD). Normal- and low-BMD groups are compared and contrasted, and further low-BMD participants are sub-classified into osteopenic and osteoporotic based on BMD levels, and compared to each other. Via the use of multivariate statistical tools, we examine contrasting groups in relation to: (a) the presence of subgroups/clusters; (b) whether groups have statistically different multivariate distributions; (c) how strongly groups differ (if at all), which relates to the practical/clinical significant of any differences; and (d) which cytokines contribute most to any differences between groups. We find that the normal- vs. low-BMD groups are markedly different (p-value = 0.00013), with IL-23, IL-12, TNF-α, IL-4 and IL-6 being the most important differentiating cytokines. No significant difference between the osteopenic and osteoporotic groups is found (p-value = 0.81). These findings may aid the development of cytokine therapies for osteoporosis, and suggest the use of certain cytokine profiles as biomarkers for osteoporosis risk factors, and ways to quantify the progress of treatment therapies.

Input-output maps are strongly biased towards simple outputs.

Many systems in nature can be described using discrete input-output maps. Without knowing details about a map, there may seem to be no a priori reason to expect that a randomly chosen input would be more likely to generate one output over another. Here, by extending fundamental results from algorithmic information theory, we show instead that for many real-world maps, the a priori probability P(x) that randomly sampled inputs generate a particular output x decays exponentially with the approximate Kolmogorov complexity [Formula: see text] of that output. These input-output maps are biased towards simplicity. We derive an upper bound P(x) ≲ [Formula: see text], which is tight for most inputs. The constants a and b, as well as many properties of  P(x), can be predicted with minimal knowledge of the map. We explore this strong bias towards simple outputs in systems ranging from the folding of RNA secondary structures to systems of coupled ordinary differential equations to a stochastic financial trading model.

Multivariate analysis of cytokine profiles in pregnancy complications.

PROBLEM: The immunoregulation to tolerate the semiallogeneic fetus during pregnancy includes a harmonious dynamic balance between anti- and pro-inflammatory cytokines. Several earlier studies reported significantly different levels and/or ratios of several cytokines in complicated pregnancy as compared to normal pregnancy. However, as cytokines operate in networks with potentially complex interactions, it is also interesting to compare groups with multi-cytokine data sets, with multivariate analysis. Such analysis will further examine how great the differences are, and which cytokines are more different than others. METHODS: Various multivariate statistical tools, such as Cramer test, classification and regression trees, partial least squares regression figures, 2-dimensional Kolmogorov-Smirmov test, principal component analysis and gap statistic, were used to compare cytokine data of normal vs anomalous groups of different pregnancy complications. RESULTS: Multivariate analysis assisted in examining if the groups were different, how strongly they differed, in what ways they differed and further reported evidence for subgroups in 1 group (pregnancy-induced hypertension), possibly indicating multiple causes for the complication. CONCLUSION: This work contributes to a better understanding of cytokines interaction and may have important implications on targeting cytokine balance modulation or design of future medications or interventions that best direct management or prevention from an immunological approach.

Patterns of circulatory and peripheral blood mononuclear cytokines in rheumatoid arthritis.

An imbalance in pro- and anti-inflammatory cytokines is suggested to contribute to tissue damage in rheumatoid arthritis (RA). This study was aimed at investigating profiles of cytokines in circulation and cytokines produced by mitogen-stimulated peripheral blood mononuclear cells (PBMC) in RA patients and healthy controls, and to explore correlations of cytokines with disease activity. Our aim was to identify patterns of cytokine expression as possible indicators of disease activity. Levels of plasma cytokines and PBMC-secreted cytokines were estimated in 26 female RA patients and 28 controls. Five pro-inflammatory cytokines (IFN-γ, TNF-α, IL-6, IL-17, IL-12) and three anti-inflammatory cytokines (IL-4, IL-10, IL-13) were assayed in a multiplex ELISA. RA patients had significantly higher plasma levels of TNF-α, IL-12, and IL-4 compared to healthy controls. On the other hand, mitogen-activated PBMC secreted significantly higher levels of the pro-inflammatory cytokines TNF-α, IFN-γ, IL-17, and IL-12, but lower levels of the anti-inflammatory cytokine IL-10 in RA compared to healthy subjects. The ratios TNF-α/IL-10, IFN-γ/IL-10, IL-17/IL-10, IL-12/IL-10, and IFN-γ/IL-13 were significantly higher in RA patients compared to healthy controls. The range and expression of cytokines were higher in PBMC than in the plasma in all the groups studied. Multivariate pattern analysis of eight cytokines revealed a prediction accuracy of 69% in differentiating RA patients from healthy controls, and of 73% in classifying patients as in remission or active RA. Our data suggest that it is worthwhile to explore ratios of pro- to anti-inflammatory cytokines produced by mitogen-stimulated PBMC in RA, and the use of multivariate cytokine pattern and algorithms for better delineation of this condition.

Association of self-reported symptoms with serum levels of vitamin D and multivariate cytokine profile in healthy women.

BACKGROUND: Although a large number of studies have investigated possible relationships among serum levels of vitamin D or cytokines with disease progress and prognosis, similar studies on self-reported symptoms are still controversial. The overall objective of this study was to look into the association between serum levels of vitamin D or cytokines with self-reported symptoms related to musculoskeletal pain, sleep disorders, and premenstrual syndrome (PMS) in healthy adult women. SUBJECTS AND METHODS: Venous blood samples were collected from 117 healthy adult women, and serum levels of vitamin D, pro-inflammatory cytokines (IL-1ß, IL-6, IL-8, IL-17, IFN-γ, and TNF-α) and anti-inflammatory cytokines (IL-4, IL-10, and IL-13) were measured. Groups were tested for differences in single parameters, pro-:anti-inflammatory cytokine ratios, and differences in multivariate patterns. RESULTS: There were no significant associations between serum levels of vitamin D and any of the self-reported symptoms studied. However, serum levels of certain pro-inflammatory cytokines were significantly higher in subjects with musculoskeletal pain (IL-8, P=0.008), sleep disorders (IFN-γ, P=0.02), and PMS (IL-8 and TNF-α, P=0.009 and 0.002, respectively) compared to subjects who reported no symptoms. The pro-:anti-inflammatory cytokine ratios showed pro-inflammatory cytokine dominance in subjects with self-reported symptoms, particularly in the groups with deficient levels of vitamin D. However, the multivariate cytokine-pattern analysis was significantly different between PMS groups only. CONCLUSION: These data point to a possible role of pro-inflammatory cytokines as a contributing factor in self-reported symptoms related to musculoskeletal pain, sleep disorders, and PMS.

The structure of the genotype-phenotype map strongly constrains the evolution of non-coding RNA.

The prevalence of neutral mutations implies that biological systems typically have many more genotypes than phenotypes. But, can the way that genotypes are distributed over phenotypes determine evolutionary outcomes? Answering such questions is difficult, in part because the number of genotypes can be hyper-astronomically large. By solving the genotype-phenotype (GP) map for RNA secondary structure (SS) for systems up to length L = 126 nucleotides (where the set of all possible RNA strands would weigh more than the mass of the visible universe), we show that the GP map strongly constrains the evolution of non-coding RNA (ncRNA). Simple random sampling over genotypes predicts the distribution of properties such as the mutational robustness or the number of stems per SS found in naturally occurring ncRNA with surprising accuracy. Because we ignore natural selection, this strikingly close correspondence with the mapping suggests that structures allowing for functionality are easily discovered, despite the enormous size of the genetic spaces. The mapping is extremely biased: the majority of genotypes map to an exponentially small portion of the morphospace of all biophysically possible structures. Such strong constraints provide a non-adaptive explanation for the convergent evolution of structures such as the hammerhead ribozyme. These results present a particularly clear example of bias in the arrival of variation strongly shaping evolutionary outcomes and may be relevant to Mayr's distinction between proximate and ultimate causes in evolutionary biology.