We present a novel method for analyzing the folding of intrinsically disordered proteins (IDPs), such as Tau and phosphorylated Tau (pTau), in solution. Using cross-linking mass spectrometry (XL-MS) combined with a new downstream analysis framework, we construct weighted interaction networks from cross-link-derived residue pairs without relying on predefined secondary structure assumptions. Structural differences between protein conformations are quantified by comparing the organization of loop structures within their cross-link networks. Validation with bovine serum albumin (BSA) in native and denatured states shows that at least 500 cross-links-requiring 5-10 replicate measurements-are needed for reliable detection of structural divergence. Leave-one-out analysis confirms that structural transitions are global, highlighting the importance of comprehensive cross-link datasets. The coverage of unique cross-links was evaluated using accumulation curves from randomized permutations. Saturation levels were found to be 9.7%, 5.0%, and 6.2% of the total 528 and 10,731 possible cross-links after 30, 84, and 62 technical replicates, respectively, for myoglobin, native BSA, and denatured BSA. For Tau and pTau, coverage reached 10.8% and 5.5% of the upper limit (8,256). Finally, applying our structural analysis to Tau and pTau during arachidonic acid-induced aggregation revealed distinct patterns of structural evolution between the two proteins.

Clustering is a central approach for unsupervised learning. After clustering is applied, the most fundamental analysis is to quantitatively compare clusterings. Such comparisons are crucial for the evaluation of clustering methods as well as other tasks such as consensus clustering. It is often argued that, in order to establish a baseline, clustering similarity should be assessed in the context of a random ensemble of clusterings. The prevailing assumption for the random clustering ensemble is the permutation model in which the number and sizes of clusters are fixed. However, this assumption does not necessarily hold in practice; for example, multiple runs of K-means clustering reurns clusterings with a fixed number of clusters, while the cluster size distribution varies greatly. Here, we derive corrected variants of two clustering similarity measures (the Rand index and Mutual Information) in the context of two random clustering ensembles in which the number and sizes of clusters vary. In addition, we study the impact of one-sided comparisons in the scenario with a reference clustering. The consequences of different random models are illustrated using synthetic examples, handwriting recognition, and gene expression data. We demonstrate that the choice of random model can have a drastic impact on the ranking of similar clustering pairs, and the evaluation of a clustering method with respect to a random baseline; thus, the choice of random clustering model should be carefully justified.

Emergent individuals are often characterized with respect to their viability: their ability to maintain themselves and persist in variable environments. As such individuals interact with an environment, they undergo sequences of structural changes that correspond to their ontogenies. Ultimately, individuals that adapt to their environment, and increase their chances of survival, persist. This article provides an initial step towards a more formal treatment of these concepts. A network of possible ontogenies is uncovered by subjecting a model protocell to sequential perturbations and mapping the resulting structural configurations. The analysis of this network reveals trends in how the protocell can move between configurations, how its morphology changes, and how the role of the environment varies throughout. Viability is defined as expected life span given an initial configuration. This leads to two notions of adaptivity: a local adaptivity that addresses how viability changes in plastic transitions, and a global adaptivity that looks at longer-term tendencies for increased viability. To demonstrate how different protocell-environment pairings produce different patterns of ontogenic change, we generate and analyze a second ontogenic network for the same protocell in a different environment. Finally, the mechanisms of a minimal adaptive transition are analyzed, and it is shown that these rely on distributed spatial processes rather than an explicit regulatory mechanism. The combination of this model and analytical techniques provides a foundation for studying the emergence of viability, ontogeny, and adaptivity in more biologically realistic systems.

We introduce a spatial model of concentration dynamics that supports the emergence of spatiotemporal inhomogeneities that engage in metabolism-boundary co-construction. These configurations exhibit disintegration following some perturbations, and self-repair in response to others. We define robustness as a viable configuration's tendency to return to its prior configuration in response to perturbations, and plasticity as a viable configuration's tendency to change to other viable configurations. These properties are demonstrated and quantified in the model, allowing us to map a space of viable configurations and their possible transitions. Combining robustness and plasticity provides a measure of viability as the average expected survival time under ongoing perturbation, and allows us to measure how viability is affected as the configuration undergoes transitions. The framework introduced here is independent of the specific model we used, and is applicable for quantifying robustness, plasticity, and viability in any computational model of artificial life that demonstrates the conditions for viability that we promote.

We introduce a spatial model of autopoiesis that demonstrates boundary-metabolism co-construction, disintegration following harsh perturbations, and self-repair in response to lighter perturbations. The system’s continued maintenance is equated with robustness and quantitatively investigated. This investigation highlights several important operational dependencies for robustness including spatiality, identity, stability, and appropriate specification of perturbations in the types of environments to which an entity must be robust.

Complex systems are typically understood as large nonlinear multivariate systems. Their organization and behavior are commonly modeled by representations such as graphs and automata networks. Graphs, where nodes representing variables lack intrinsic dynamics, capture the structure or organization of complex systems. The simplest way to study multi-variate dynamics, is to allow network nodes to have states and update them with automata; for instance, Boolean networks (BN) are canonical models of complex systems and exhibit a wide range of dynamical behaviors [1].