Dataset Information

Potential landscape of high dimensional nonlinear stochastic dynamics with large noise.

ABSTRACT: Quantifying stochastic processes is essential to understand many natural phenomena, particularly in biology, including the cell-fate decision in developmental processes as well as the genesis and progression of cancers. While various attempts have been made to construct potential landscape in high dimensional systems and to estimate transition rates, they are practically limited to the cases where either noise is small or detailed balance condition holds. A general and practical approach to investigate real-world nonequilibrium systems, which are typically high-dimensional and subject to large multiplicative noise and the breakdown of detailed balance, remains elusive. Here, we formulate a computational framework that can directly compute the relative probabilities between locally stable states of such systems based on a least action method, without the necessity of simulating the steady-state distribution. The method can be applied to systems with arbitrary noise intensities through A-type stochastic integration, which preserves the dynamical structure of the deterministic counterpart dynamics. We demonstrate our approach in a numerically accurate manner through solvable examples. We further apply the method to investigate the role of noise on tumor heterogeneity in a 38-dimensional network model for prostate cancer, and provide a new strategy on controlling cell populations by manipulating noise strength.

SUBMITTER: Tang Y

PROVIDER: S-EPMC5693902 | biostudies-other | 2017 Nov

REPOSITORIES: biostudies-other

ACCESS DATA

Publications

Potential landscape of high dimensional nonlinear stochastic dynamics with large noise.

Tang Ying Y Yuan Ruoshi R Wang Gaowei G Zhu Xiaomei X Ao Ping P

Scientific reports 20171117 1

Quantifying stochastic processes is essential to understand many natural phenomena, particularly in biology, including the cell-fate decision in developmental processes as well as the genesis and progression of cancers. While various attempts have been made to construct potential landscape in high dimensional systems and to estimate transition rates, they are practically limited to the cases where either noise is small or detailed balance condition holds. A general and practical approach to inve ...[more]

PMID: 29150680

Similar Datasets

Project description:Optimal control simulations have shown that both musculoskeletal dynamics and physiological noise are important determinants of movement. However, due to the limited efficiency of available computational tools, deterministic simulations of movement focus on accurately modelling the musculoskeletal system while neglecting physiological noise, and stochastic simulations account for noise while simplifying the dynamics. We took advantage of recent approaches where stochastic optimal control problems are approximated using deterministic optimal control problems, which can be solved efficiently using direct collocation. We were thus able to extend predictions of stochastic optimal control as a theory of motor coordination to include muscle coordination and movement patterns emerging from non-linear musculoskeletal dynamics. In stochastic optimal control simulations of human standing balance, we demonstrated that the inclusion of muscle dynamics can predict muscle co-contraction as minimal effort strategy that complements sensorimotor feedback control in the presence of sensory noise. In simulations of reaching, we demonstrated that nonlinear multi-segment musculoskeletal dynamics enables complex perturbed and unperturbed reach trajectories under a variety of task conditions to be predicted. In both behaviors, we demonstrated how interactions between task constraint, sensory noise, and the intrinsic properties of muscle influence optimal muscle coordination patterns, including muscle co-contraction, and the resulting movement trajectories. Our approach enables a true minimum effort solution to be identified as task constraints, such as movement accuracy, can be explicitly imposed, rather than being approximated using penalty terms in the cost function. Our approximate stochastic optimal control framework predicts complex features, not captured by previous simulation approaches, providing a generalizable and valuable tool to study how musculoskeletal dynamics and physiological noise may alter neural control of movement in both healthy and pathological movements.

Project description:Existing sensitivity analysis approaches are not able to handle efficiently stochastic reaction networks with a large number of parameters and species, which are typical in the modeling and simulation of complex biochemical phenomena. In this paper, a two-step strategy for parametric sensitivity analysis for such systems is proposed, exploiting advantages and synergies between two recently proposed sensitivity analysis methodologies for stochastic dynamics. The first method performs sensitivity analysis of the stochastic dynamics by means of the Fisher Information Matrix on the underlying distribution of the trajectories; the second method is a reduced-variance, finite-difference, gradient-type sensitivity approach relying on stochastic coupling techniques for variance reduction. Here we demonstrate that these two methods can be combined and deployed together by means of a new sensitivity bound which incorporates the variance of the quantity of interest as well as the Fisher Information Matrix estimated from the first method. The first step of the proposed strategy labels sensitivities using the bound and screens out the insensitive parameters in a controlled manner. In the second step of the proposed strategy, a finite-difference method is applied only for the sensitivity estimation of the (potentially) sensitive parameters that have not been screened out in the first step. Results on an epidermal growth factor network with fifty parameters and on a protein homeostasis with eighty parameters demonstrate that the proposed strategy is able to quickly discover and discard the insensitive parameters and in the remaining potentially sensitive parameters it accurately estimates the sensitivities. The new sensitivity strategy can be several times faster than current state-of-the-art approaches that test all parameters, especially in "sloppy" systems. In particular, the computational acceleration is quantified by the ratio between the total number of parameters over the number of the sensitive parameters.

Project description:BackgroundThe rapid and accurate identification of a minimal-size core set of representative microbial species plays an important role in the clustering of microbial community data and interpretation of clustering results. However, the huge dimensionality of microbial metagenomics datasets is a major challenge for the existing methods such as Dirichlet multinomial mixture (DMM) models. In the approach of the existing methods, the computational burden of identifying a small number of representative species from a large number of observed species remains a challenge.ResultsWe propose a novel approach to improve the performance of the widely used DMM approach by combining three ideas: (i) we propose an indicator variable to identify representative operational taxonomic units that substantially contribute to the differentiation among clusters; (ii) to address the computational burden of high-dimensional microbiome data, we propose a stochastic variational inference, which approximates the posterior distribution using a controllable distribution called variational distribution, and stochastic optimization algorithms for fast computation; and (iii) we extend the finite DMM model to an infinite case by considering Dirichlet process mixtures and estimating the number of clusters as a variational parameter. Using the proposed method, stochastic variational variable selection (SVVS), we analyzed the root microbiome data collected in our soybean field experiment, the human gut microbiome data from three published datasets of large-scale case-control studies and the healthy human microbiome data from the Human Microbiome Project.ConclusionsSVVS demonstrates a better performance and significantly faster computation than those of the existing methods in all cases of testing datasets. In particular, SVVS is the only method that can analyze massive high-dimensional microbial data with more than 50,000 microbial species and 1000 samples. Furthermore, a core set of representative microbial species is identified using SVVS that can improve the interpretability of Bayesian mixture models for a wide range of microbiome studies. Video Abstract.

Dataset Information

Potential landscape of high dimensional nonlinear stochastic dynamics with large noise.

Publications

Potential landscape of high dimensional nonlinear stochastic dynamics with large noise.

Similar Datasets

OmicsDI is part of the ELIXIR infrastructure

Tweets