Bayesian inference for duplication-mutation with complementarity network models

Biocode: A Data-Driven Procedure to Learn the Growth of Biological Networks

Probabilistic biological network growth models have been utilized for many tasks including but not limited to capturing mechanism and dynamics of biological growth activities, null model representation, capturing anomalies, etc. Well-known examples of these probabilistic models are Kronecker model, preferential attachment model, and duplication-based model. However, we should frequently keep developing new models to better fit and explain the observed network features while new networks are being observed. Additionally, it is difficult to develop a growth model each time we study a new network. In this paper, we propose Biocode, a framework to automatically discover novel biological growth models matching user-specified graph attributes in directed and undirected biological graphs. Biocode designs a basic set of instructions which are common enough to model a number of well-known biological graph growth models. We combine such instruction-wise representation with a genetic algorithm based optimization procedure to encode models for various biological networks. We mainly evaluate the performance of Biocode in discovering models for biological collaboration networks, gene regulatory networks, and protein interaction networks which features such as assortativity, clustering coefficient, degree distribution closely match with the true ones in the corresponding real biological networks.

Estimating Distributions of Parameters in Nonlinear State Space Models with Replica Exchange Particle Marginal Metropolis–Hastings Method

Extracting latent nonlinear dynamics from observed time-series data is important for understanding a dynamic system against the background of the observed data. A state space model is a probabilistic graphical model for time-series data, which describes the probabilistic dependence between latent variables at subsequent times and between latent variables and observations. Since, in many situations, the values of the parameters in the state space model are unknown, estimating the parameters from observations is an important task. The particle marginal Metropolis–Hastings (PMMH) method is a method for estimating the marginal posterior distribution of parameters obtained by marginalization over the distribution of latent variables in the state space model. Although, in principle, we can estimate the marginal posterior distribution of parameters by iterating this method infinitely, the estimated result depends on the initial values for a finite number of times in practice. In this paper, we propose a replica exchange particle marginal Metropolis–Hastings (REPMMH) method as a method to improve this problem by combining the PMMH method with the replica exchange method. By using the proposed method, we simultaneously realize a global search at a high temperature and a local fine search at a low temperature. We evaluate the proposed method using simulated data obtained from the Izhikevich neuron model and Lévy-driven stochastic volatility model, and we show that the proposed REPMMH method improves the problem of the initial value dependence in the PMMH method, and realizes efficient sampling of parameters in the state space models compared with existing methods.

Maximum likelihood reconstruction of ancestral networks by integer linear programming

MOTIVATION

The study of the evolutionary history of biological networks enables deep functional understanding of various bio-molecular processes. Network growth models, such as the Duplication-Mutation with Complementarity (DMC) model, provide a principled approach to characterizing the evolution of protein-protein interactions (PPIs) based on duplication and divergence. Current methods for model-based ancestral network reconstruction primarily use greedy heuristics and yield sub-optimal solutions.

RESULTS

We present a new Integer Linear Programming (ILP) solution for maximum likelihood reconstruction of ancestral PPI networks using the DMC model. We prove the correctness of our solution that is designed to find the optimal solution. It can also use efficient heuristics from general-purpose ILP solvers to obtain multiple optimal and near-optimal solutions that may be useful in many applications. Experiments on synthetic data show that our ILP obtains solutions with higher likelihood than those from previous methods, and is robust to noise and model mismatch. We evaluate our algorithm on two real PPI networks, with proteins from the families of bZIP transcription factors and the Commander complex. On both the networks, solutions from our ILP have higher likelihood and are in better agreement with independent biological evidence from other studies.

AVAILABILITY AND IMPLEMENTATION

A Python implementation is available at https://bitbucket.org/cdal/network-reconstruction.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Bayesian estimation of scaled mutation rate under the coalescent: a sequential Monte Carlo approach

BACKGROUND

Samples of molecular sequence data of a locus obtained from random individuals in a population are often related by an unknown genealogy. More importantly, population genetics parameters, for instance, the scaled population mutation rate Θ=4N _e μ for diploids or Θ=2N _e μ for haploids (where N _e is the effective population size and μ is the mutation rate per site per generation), which explains some of the evolutionary history and past qualities of the population that the samples are obtained from, is of significant interest.

RESULTS

In this paper, we present the evolution of sequence data in a Bayesian framework and the approximation of the posterior distributions of the unknown parameters of the model, which include Θ via the sequential Monte Carlo (SMC) samplers for static models. Specifically, we approximate the posterior distributions of the unknown parameters with a set of weighted samples i.e., the set of highly probable genealogies out of the infinite set of possible genealogies that describe the sampled sequences. The proposed SMC algorithm is evaluated on simulated DNA sequence datasets under different mutational models and real biological sequences. In terms of the accuracy of the estimates, the proposed SMC method shows a comparable and sometimes, better performance than the state-of-the-art MCMC algorithms.

CONCLUSIONS

We showed that the SMC algorithm for static model is a promising alternative to the state-of-the-art approach for simulating from the posterior distributions of population genetics parameters.