Related papers: Parameter identifiability for a profile mixture mo…
Understanding the relationships between protein sequence, structure and function is a long-standing biological challenge with manifold implications from drug design to our understanding of evolution. Recently, protein language models have…
Recent work has shown that finite mixture models with $m$ components are identifiable, while making no assumptions on the mixture components, so long as one has access to groups of samples of size $2m-1$ which are known to come from the…
Predictive constructions are a powerful way of characterizing the probability law of stochastic processes with certain forms of invariance, such as exchangeability or Markov exchangeability. When de Finetti-like representation theorems are…
Mathematical models are routinely applied to interpret biological data, with common goals that include both prediction and parameter estimation. A challenge in mathematical biology, in particular, is that models are often complex and…
A phylogenetic birth-and-death model is a probabilistic graphical model for a so-called phylogenetic profile, i.e., the size distribution for a homolog gene family at the terminal nodes of a phylogeny. Profile datasets are used in…
Phylogenetic comparative methods (PCMs) are widely used to study trait evolution. However, many evolutionary histories involve reticulate evolutionary scenarios, such as hybridization, that violate core assumptions of these methods. In this…
During their evolution, proteins explore sequence space via an interplay between random mutations and phenotypic selection. Here we build upon recent progress in reconstructing data-driven fitness landscapes for families of homologous…
Identifiability is a desirable property of a statistical model: it implies that the true model parameters may be estimated to any desired precision, given sufficient computational resources and data. We study identifiability in the context…
Protein is linked to almost every life process. Therefore, analyzing the biological structure and property of protein sequences is critical to the exploration of life, as well as disease detection and drug discovery. Traditional protein…
We consider the estimation of the mixing distribution of a normal distribution where both the shift and scale are unobserved random variables. We argue that in general, the model is not identifiable. We give an elegant non-constructive…
Generative modeling has become a central paradigm in protein research, extending machine learning beyond structure prediction toward sequence design, backbone generation, inverse folding, and biomolecular interaction modeling. However, the…
Protein activity is a significant characteristic for recombinant proteins which can be used as biocatalysts. High activity of proteins reduces the cost of biocatalysts. A model that can predict protein activity from amino acid sequence is…
The observed correlations between pairs of homologous protein sequences are typically explained in terms of a Markovian dynamic of amino acid substitution. This model assumes that every location on the protein sequence has the same…
We address phylogenetic reconstruction when the data is generated from a mixture distribution. Such topics have gained considerable attention in the biological community with the clear evidence of heterogeneity of mutation rates. In our…
A parameter of a mathematical model is structurally identifiable if it can be determined from noiseless experimental data. Here, we examine the identifiability properties of two important classes of linear compartmental models:…
One of the outstanding challenges in comparative genomics is to interpret the evolutionary importance of regulatory variation between species. Rigorous molecular evolution-based methods to infer evidence for natural selection from…
Networks are widely used in the biological, physical, and social sciences as a concise mathematical representation of the topology of systems of interacting components. Understanding the structure of these networks is one of the outstanding…
Functional protein-protein interactions are crucial in most cellular processes. They enable multi-protein complexes to assemble and to remain stable, and they allow signal transduction in various pathways. Functional interactions between…
We propose a model that explains the hierarchical organization of proteins in fold families. The model, which is based on the evolutionary selection of proteins by their native state stability, reproduces patterns of amino acids conserved…
Observability is a modelling property that describes the possibility of inferring the internal state of a system from observations of its output. A related property, structural identifiability, refers to the theoretical possibility of…