Deterministic mathematical models of the cAMP pathway in Saccharomyces cerevisiae

Background  

Cyclic adenosine monophosphate (cAMP) has a key signaling role in all eukaryotic organisms. In Saccharomyces cerevisiae, it is the second messenger in the Ras/PKA pathway which regulates nutrient sensing, stress responses, growth, cell cycle progression, morphogenesis, and cell wall biosynthesis. A stochastic model of the pathway has been reported.     

Reconstruction of cell population dynamics using CFSE

Background  

Quantifying cell division and death is central to many studies in the biological sciences. The fluorescent dye CFSE allows the tracking of cell division in vitro and in vivo and provides a rich source of information with which to test models of cell kinetics. Cell division and death have a stochastic component at the single-cell level, and the probabilities of these occurring in any given time interval may also undergo systematic variation at a population level. This gives rise to heterogeneity in proliferating cell populations. Branching processes provide a natural means of describing this behaviour.     

Probability distributed time delays: integrating spatial effects into temporal models

Background  

In order to provide insights into the complex biochemical processes inside a cell, modelling approaches must find a balance between achieving an adequate representation of the physical phenomena and keeping the associated computational cost within reasonable limits. This issue is particularly stressed when spatial inhomogeneities have a significant effect on system's behaviour. In such cases, a spatially-resolved stochastic method can better portray the biological reality, but the corresponding computer simulations can in turn be prohibitively expensive.     

Bayesian inference of biochemical kinetic parameters using the linear noise approximation

Background  

Fluorescent and luminescent gene reporters allow us to dynamically quantify changes in molecular species concentration over time on the single cell level. The mathematical modeling of their interaction through multivariate dynamical models requires the deveopment of effective statistical methods to calibrate such models against available data. Given the prevalence of stochasticity and noise in biochemical systems inference for stochastic models is of special interest. In this paper we present a simple and computationally efficient algorithm for the estimation of biochemical kinetic parameters from gene reporter data.     

Global parameter estimation methods for stochastic biochemical systems

Background  

The importance of stochasticity in cellular processes having low number of molecules has resulted in the development of stochastic models such as chemical master equation. As in other modelling frameworks, the accompanying rate constants are important for the end-applications like analyzing system properties (e.g. robustness) or predicting the effects of genetic perturbations. Prior knowledge of kinetic constants is usually limited and the model identification routine typically includes parameter estimation from experimental data. Although the subject of parameter estimation is well-established for deterministic models, it is not yet routine for the chemical master equation. In addition, recent advances in measurement technology have made the quantification of genetic substrates possible to single molecular levels. Thus, the purpose of this work is to develop practical and effective methods for estimating kinetic model parameters in the chemical master equation and other stochastic models from single cell and cell population experimental data.     

Parameter estimation and inference for stochastic reaction-diffusion systems: application to morphogenesis in D. melanogaster

Background  

Reaction-diffusion systems are frequently used in systems biology to model developmental and signalling processes. In many applications, count numbers of the diffusing molecular species are very low, leading to the need to explicitly model the inherent variability using stochastic methods. Despite their importance and frequent use, parameter estimation for both deterministic and stochastic reaction-diffusion systems is still a challenging problem.     

Quantifying the threat of extinction from Muller's ratchet in the diploid Amazon molly (<Emphasis Type="Italic">Poecilia formosa</Emphasis>)

Background  

The Amazon molly (Poecilia formosa) is a small unisexual fish that has been suspected of being threatened by extinction from the stochastic accumulation of slightly deleterious mutations that is caused by Muller's ratchet in non-recombining populations. However, no detailed quantification of the extent of this threat is available.     

A new stochastic and state space model of human colon cancer incorporating multiple pathways

Background and Purpose  

Studies by molecular biologists and geneticists have shown that tumors of human colon cancer are developed from colon stem cells through two mechanisms: The chromosomal instability and the micro-satellite instability. The purpose of this paper is therefore to develop a new stochastic and state space model for carcinogenesis of human colon cancer incorporating these biological mechanisms.     

A hybrid multiscale Monte Carlo algorithm (HyMSMC) to cope with disparity in time scales and species populations in intracellular networks

Background  

The fundamental role that intrinsic stochasticity plays in cellular functions has been shown via numerous computational and experimental studies. In the face of such evidence, it is important that intracellular networks are simulated with stochastic algorithms that can capture molecular fluctuations. However, separation of time scales and disparity in species population, two common features of intracellular networks, make stochastic simulation of such networks computationally prohibitive. While recent work has addressed each of these challenges separately, a generic algorithm that can simultaneously tackle disparity in time scales and population scales in stochastic systems is currently lacking. In this paper, we propose the hybrid, multiscale Monte Carlo (HyMSMC) method that fills in this void.     

A probabilistic model for the evolution of RNA structure

Background  

For the purposes of finding and aligning noncoding RNA gene- and cis-regulatory elements in multiple-genome datasets, it is useful to be able to derive multi-sequence stochastic grammars (and hence multiple alignment algorithms) systematically, starting from hypotheses about the various kinds of random mutation event and their rates.     

Parameter inference for discretely observed stochastic kinetic models using stochastic gradient descent

Background  

Stochastic effects can be important for the behavior of processes involving small population numbers, so the study of stochastic models has become an important topic in the burgeoning field of computational systems biology. However analysis techniques for stochastic models have tended to lag behind their deterministic cousins due to the heavier computational demands of the statistical approaches for fitting the models to experimental data. There is a continuing need for more effective and efficient algorithms. In this article we focus on the parameter inference problem for stochastic kinetic models of biochemical reactions given discrete time-course observations of either some or all of the molecular species.     

FERN – a Java framework for stochastic simulation and evaluation of reaction networks

Background  

Stochastic simulation can be used to illustrate the development of biological systems over time and the stochastic nature of these processes. Currently available programs for stochastic simulation, however, are limited in that they either a) do not provide the most efficient simulation algorithms and are difficult to extend, b) cannot be easily integrated into other applications or c) do not allow to monitor and intervene during the simulation process in an easy and intuitive way. Thus, in order to use stochastic simulation in innovative high-level modeling and analysis approaches more flexible tools are necessary.     

XRate: a fast prototyping, training and annotation tool for phylo-grammars

Background  

Recent years have seen the emergence of genome annotation methods based on the phylo-grammar, a probabilistic model combining continuous-time Markov chains and stochastic grammars. Previously, phylo-grammars have required considerable effort to implement, limiting their adoption by computational biologists.     

Complex inter‐island colonization and peripatric founder speciation promote diversification of flightless Pachyrhynchus weevils in the Taiwan–Luzon volcanic belt

Aim

We investigated the spatial and temporal patterns of diversification among colourful and flightless weevils, the Pachyrhynchus orbifer complex, to test the stepping‐stone hypothesis of colonization across the Taiwan–Luzon volcanic belt.

Location

Southeast Asia.

Methods

The phylogeny of the P. orbifer complex was reconstructed from a multi‐locus data set of mitochondrial and nuclear genes using maximum likelihood in RAxML and Bayesian inference in MRBAYES. Likelihood‐based tests in CONSEL were used to evaluate alternative tree topologies. Divergence times were estimated in beast based on a range of mutation rates. Ancestral range and biogeographical history were reconstructed using Bayesian binary MCMC (BBM) methods in RASP and in BioGeoBEARS. Demographic histories were inferred using the extended Bayesian skyline plot (EBSP). Species boundaries were tested using BPP.

Results

The phylogeny of the P. orbifer complex indicated strong support for seven reciprocally monophyletic lineages grouped by current island boundaries (Camiguin, Fuga, Dalupiri, Calayan, Babuyan, Orchid and Yaeyama Islands), except for a sister Green + Itbayat lineage. Complex and stochastic colonization of P. orbifer was inferred to have involved both northward and southward directions with short‐ and long‐distance dispersal events, which are strongly inconsistent with the strict stepping‐stone hypothesis. Divergence time estimates for all extant island lineages (<1 Myr of Middle Pleistocene) are much more recent than the geological ages (22.4–1.7 Myr) and subaerial existence (c. 3 Myr) of the islands. The statistically delimited seven cryptic species imply that the diversity of Pachyrhynchus from small peripheral islands continues to be largely under‐estimated.

Main conclusions

The non‐linear, more complex spatial and temporal settings of the archipelago and stochastic dispersal were probable key factors shaping the colonization history of the P. orbifer complex. Speciation of the P. orbifer complex may have occurred only between islands, indicating that peripatric speciation through the founders of stochastic dispersals was the major evolutionary driver.     

Insertions and the emergence of novel protein structure: a structure-based phylogenetic study of insertions

Background  

In protein evolution, the mechanism of the emergence of novel protein domain is still an open question. The incremental growth of protein variable regions, which was produced by stochastic insertions, has the potential to generate large and complex sub-structures. In this study, a deterministic methodology is proposed to reconstruct phylogenies from protein structures, and to infer insertion events in protein evolution. The analysis was performed on a broad range of SCOP domain families.     

Safe uses of Hill's model: an exact comparison with the Adair-Klotz model

Background  

The Hill function and the related Hill model are used frequently to study processes in the living cell. There are very few studies investigating the situations in which the model can be safely used. For example, it has been shown, at the mean field level, that the dose response curve obtained from a Hill model agrees well with the dose response curves obtained from a more complicated Adair-Klotz model, provided that the parameters of the Adair-Klotz model describe strongly cooperative binding. However, it has not been established whether such findings can be extended to other properties and non-mean field (stochastic) versions of the same, or other, models.