Related papers: Maximum entropy models for antibody diversity
We demonstrate and characterize a first-principles approach to modeling the mass action dynamics of metabolism. Starting from a basic definition of entropy expressed as a multinomial probability density using Boltzmann probabilities with…
The adaptive immune system recognizes antigens via an immense array of antigen-binding antibodies and T-cell receptors, the immune repertoire. The interrogation of immune repertoires is of high relevance for understanding the adaptive…
In most of the recent immunological literature the differences across antigen receptor populations are examined via non-parametric statistical measures of species overlap and diversity borrowed from ecological studies. While this approach…
Bounds on the entropy of patterns of sequences generated by independently identically distributed (i.i.d.) sources are derived. A pattern is a sequence of indices that contains all consecutive integer indices in increasing order of first…
The joint probability distribution of many degrees of freedom in biological systems, such as firing patterns in neural networks or antibody sequence composition in zebrafish, often follow Zipf's law, where a power law is observed on a…
The multiple sequence alignment (MSA) of a protein family provides a wealth of information in terms of the conservation pattern of amino acid residues not only at each alignment site but also between distant sites. In order to statistically…
The field of complex networks studies a wide variety of interacting systems by representing them as networks. To understand their properties and mutual relations, the randomisation of network connections is a commonly used tool. However,…
Mathematical modeling of disease outbreaks can infer the future trajectory of an epidemic, which can inform policy decisions. Another task is inferring the origin of a disease, which is relatively difficult with current mathematical models.…
The diversity of the immune repertoire is initially generated by random rearrangements of the receptor gene during early T and B cell development. Rearrangement scenarios are composed of random events -- choices of gene templates, base pair…
Maximum entropy models are the least structured probability distributions that exactly reproduce a chosen set of statistics measured in an interacting network. Here we use this principle to construct probabilistic models which describe the…
Protein sequences serve as a natural record of the evolutionary constraints that shape their functional structures. We show that it is possible to use only sequence information to go beyond predicting native structures and global stability…
The maximum entropy principle (MEP) is a method for obtaining the most likely distribution functions of observables from statistical systems, by maximizing entropy under constraints. The MEP has found hundreds of applications in ergodic and…
Eukaryote genomes contain excessively introns, inter-genic and other non-genic sequences that appear to have no vital functional role or phenotype manifestation. Their existence, a long-standing puzzle, is viewed from the principle of…
The twenty protein coding amino acids are found in proteomes with different relative abundances. The most abundant amino acid, leucine, is nearly an order of magnitude more prevalent than the least abundant amino acid, cysteine. Amino acid…
Complex natural and technological systems can be considered, on a coarse-grained level, as assemblies of elementary components: for example, genomes as sets of genes, or texts as sets of words. On one hand, the joint occurrence of…
Maximum entropy models provide the least constrained probability distributions that reproduce statistical properties of experimental datasets. In this work we characterize the learning dynamics that maximizes the log-likelihood in the case…
Fundamental to quantitative characterization of the B cell receptor repertoire is clonal diversity - the number of distinct somatically recombined receptors present in the repertoire and their relative abundances, defining the search space…
We introduce a protein language model for determining the complete sequence of a peptide based on measurement of a limited set of amino acids. To date, protein sequencing relies on mass spectrometry, with some novel edman degregation based…
We study a class of dynamical systems generated by random substitutions, which contains both intrinsically ergodic systems and instances with several measures of maximal entropy. In this class, we show that the measures of maximal entropy…
Predicting the binding free energy between antibodies and antigens is a key challenge in structure-aware biomolecular modeling, with direct implications for antibody design. Most existing methods either rely solely on sequence embeddings or…