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Quantitative mass spectrometry has revolutionized proteomics by enabling simultaneous quantification of thousands of proteins. Pooling patient-derived data from multiple institutions enhances statistical power but raises significant privacy concerns. Here we introduce FedProt, the first privacy-preserving tool for collaborative differential protein abundance analysis of distributed data, which utilizes federated learning and additive secret sharing. In the absence of a multicenter patient-derived dataset for evaluation, we created two, one at five centers from LFQ E.coli experiments and one at three centers from TMT human serum. Evaluations using these datasets confirm that FedProt achieves accuracy equivalent to DEqMS applied to pooled data, with completely negligible absolute differences no greater than $\text{$4 \times 10^{-12}$}$. In contrast, -log10(p-values) computed by the most accurate meta-analysis methods diverged from the centralized analysis results by up to 25-27. FedProt is available as a web tool with detailed documentation as a FeatureCloud App., Comment: 52 pages, 16 figures, 12 tables. Last two authors listed are joint last authors

Chromatin is a highly compact and dynamic nuclear structure that consists of DNA and associated proteins. The main organizational unit is the nucleosome, which consists of a histone octamer with DNA wrapped around it. Histone proteins are implicated in the regulation of eukaryote genes and they carry numerous reversible post-translational modifications that control DNA-protein interactions and the recruitment of chromatin binding proteins. Heterochromatin, the transcriptionally inactive part of the genome, is densely packed and contains histone H3 that is methylated at Lys 9 (H3K9me). The propagation of H3K9me in nucleosomes along the DNA in chromatin is antagonizing by methylation of H3 Lysine 4 (H3K4me) and acetylations of several lysines, which is related to euchromatin and active genes. We show that the related histone modifications form antagonized domains on a coarse scale. These histone marks are assumed to be initiated within distinct nucleation sites in the DNA and to propagate bi-directionally. We propose a simple computer model that simulates the distribution of heterochromatin in human chromosomes. The simulations are in agreement with previously reported experimental observations from two different human cell lines. We reproduced different types of barriers between heterochromatin and euchromatin providing a unified model for their function. The effect of changes in the nucleation site distribution and of propagation rates were studied. The former occurs mainly with the aim of (de-)activation of single genes or gene groups and the latter has the power of controlling the transcriptional programs of entire chromosomes. Generally, the regulatory program of gene transcription is controlled by the distribution of nucleation sites along the DNA string., Comment: 24 pages,9 figures, 1 table + supplementary material

Microbiological systems evolve to fulfill their tasks with maximal efficiency. The immune system is a remarkable example, where self-non self distinction is accomplished by means of molecular interaction between self proteins and antigens, triggering affinity-dependent systemic actions. Specificity of this binding and the infinitude of potential antigenic patterns call for novel mechanisms to generate antibody diversity. Inspired by this problem, we develop a genetic algorithm where agents evolve their strings in the presence of random antigenic strings and reproduce with affinity-dependent rates. We ask what is the best strategy to generate diversity if agents can rearrange their strings a finite number of times. We find that endowing each agent with an inheritable cellular automaton rule for performing rearrangements makes the system more efficient in pattern-matching than if transformations are totally random. In the former implementation, the population evolves to a stationary state where agents with different automata rules coexist., Comment: 12 pages, 7 figures

Fuzzy c-means clustering is widely used to identify cluster structures in high-dimensional data sets, such as those obtained in DNA microarray and quantitative proteomics experiments. One of its main limitations is the lack of a computationally fast method to determine the two parameters fuzzifier and cluster number. Wrong parameter values may either lead to the inclusion of purely random fluctuations in the results or ignore potentially important data. The optimal solution has parameter values for which the clustering does not yield any results for a purely random data set but which detects cluster formation with maximum resolution on the edge of randomness. Estimation of the optimal parameter values is achieved by evaluation of the results of the clustering procedure applied to randomized data sets. In this case, the optimal value of the fuzzifier follows common rules that depend only on the main properties of the data set. Taking the dimension of the set and the number of objects as input values instead of evaluating the entire data set allows us to propose a functional relationship determining its value directly. This result speaks strongly against setting the fuzzifier equal to 2 as typically done in many previous studies. Validation indices are generally used for the estimation of the optimal number of clusters. A comparison shows that the minimum distance between the centroids provides results that are at least equivalent or better than those obtained by other computationally more expensive indices., Comment: 9 pages, 9 figures

The stability of $q$-Gaussian distributions as particular solutions of the linear diffusion equation and its generalized nonlinear form, $\pderiv{P(x,t)}{t} = D \pderiv{^2 [P(x,t)]^{2-q}}{x^2}$, the \emph{porous-medium equation}, is investigated through both numerical and analytical approaches. It is shown that an \emph{initial} $q$-Gaussian, characterized by an index $q_i$, approaches the \emph{final}, asymptotic solution, characterized by an index $q$, in such a way that the relaxation rule for the kurtosis evolves in time according to a $q$-exponential, with a \emph{relaxation} index $q_{\rm rel} \equiv q_{\rm rel}(q)$. In some cases, particularly when one attempts to transform an infinite-variance distribution ($q_i \ge 5/3$) into a finite-variance one ($q<5/3$), the relaxation towards the asymptotic solution may occur very slowly in time. This fact might shed some light on the slow relaxation, for some long-range-interacting many-body Hamiltonian systems, from long-standing quasi-stationary states to the ultimate thermal equilibrium state., Comment: 20 pages, 6 figures

Barchan dunes emerge as a collective phenomena involving the generation of thousands of them in so called barchan dune fields. By measuring the size and position of dunes in Moroccan barchan dune fields, we find that these dunes tend to distribute uniformly in space and follow an unique size distribution function. We introduce an analyticalmean-field approach to show that this empirical size distribution emerges from the interplay of dune collisions and sand flux balance, the two simplest mechanisms for size selection. The analytical model also predicts a scaling relation between the fundamental macroscopic properties characterizing a dune field, namely the inter-dune spacing and the first and second moments of the dune size distribution., Comment: 6 pages, 4 figures. Submitted for publication

Barchans are isolated mobile dunes often organized in large dune fields. Dune fields seem to present a characteristic dune size and spacing, which suggests a cooperative behavior based on dune interaction. In Duran et al. (2009), we propose that the redistribution of sand by collisions between dunes is a key element for the stability and size selection of barchan dune fields. This approach was based on a mean-field model ignoring the spatial distribution of dune fields. Here, we present a simplified dune field model that includes the spatial evolution of individual dunes as well as their interaction through sand exchange and binary collisions. As a result, the dune field evolves towards a steady state that depends on the boundary conditions. Comparing our results with measurements of Moroccan dune fields, we find that the simulated fields have the same dune size distribution as in real fields but fail to reproduce their homogeneity along the wind direction., Comment: 12 pages and 15 figures. Submitted for publication

We investigate the macroscopic effects of the ingredients that drive the origin of species through sympatric speciation. In our model, sympatric speciation is obtained as we tune up the strength of competition between individuals with different phenotypes. As a function of this control parameter, we can characterize, through the behavior of a macroscopic order parameter, a phase transition from a non-speciation to a speciation state of the system. The behavior of the first derivative of the order parameter with respect to the control parameter is consistent with a phase transition and exhibits a sharp peak at the transition point. For different resources distribution, the transition point is shifted, an effect similar to pressure in PVT system. The inverse of the parameter related to sexual selection strength behaves like an external field in the system and, as thus, is also a control parameter. The macroscopic effects of the biological parameters used in our model reveal thus fingerprints typical of thermodynamic quantities in a phase transition of an equilibrium physical system., Comment: 4 pages and 10 figures

Recently, individual-based models originally used for biological purposes revealed interesting insights into processes of the competition of languages. Within this new field of population dynamics a model considering sexual populations with ageing is presented. The agents are situated on a lattice and each one speaks one of two languages or both. The stability and quantitative structure of an interface between two regions, initially speaking different languages, is studied. We find that individuals speaking both languages do not prefer any of these regions and have a different age structure than individuals speaking only one language., Comment: submitted to International Journal of Modern Physics C

The Penna model is a strategy to simulate the genetic dynamics of age-structured populations, in which the individuals genomes are represented by bit-strings. It provides a simple metaphor for the evolutionary process in terms of the mutation accumulation theory. In its original version, an individual dies due to inherited diseases when its current number of accumulated mutations, n, reaches a threshold value, T. Since the number of accumulated diseases increases with age, the probability to die is zero for very young ages (n < T) and equals 1 for the old ones (n >= T). Here, instead of using a step function to determine the genetic death age, we test several other functions that may or may not slightly increase the death probability at young ages (n < T), but that decreases this probability at old ones. Our purpose is to study the oldest old effect, that is, a plateau in the mortality curves at advanced ages. Imposing certain conditions, it has been possible to obtain a clear plateau using the Penna model. However, a more realistic one appears when a modified version, that keeps the population size fixed without fluctuations, is used. We also find a relation between the birth rate, the age-structure of the population and the death probability., Comment: submitted to Phys. Rev. E

Transverse dunes appear in regions of mainly unidirectional wind and high sand availability. A dune model is extended to two dimensional calculation of the shear stress. It is applied to simulate dynamics and morphology of transverse dunes which seem to reach translational invariance and do not stop growing. Hence, simulations of two dimensional dune fields have been performed. Characteristic laws were found for the time evolution of transverse dunes. Bagnold's law of the dune velocity is modified and reproduced. The interaction between transverse dunes led to interesting results which conclude that small dunes can pass through bigger ones., Comment: Submitted to Earth Surface Processes and Landforms