Dataset Information

Mixtures of Gaussian Wells: Theory, Computation, and Application.

ABSTRACT: A primary challenge in unsupervised clustering using mixture models is the selection of a family of basis distributions flexible enough to succinctly represent the distributions of the target subpopulations. In this paper we introduce a new family of Gaussian Well distributions (GWDs) for clustering applications where the target subpopulations are characterized by hollow [hyper-]elliptical structures. We develop the primary theory pertaining to the GWD, including mixtures of GWDs, selection of prior distributions, and computationally efficient inference strategies using Markov chain Monte Carlo. We demonstrate the utility of our approach, as compared to standard Gaussian mixture methods on a synthetic dataset, and exemplify its applicability on an example from immunofluorescence imaging, emphasizing the improved interpretability and parsimony of the GWD-based model.

SUBMITTER: Manolopoulou I

PROVIDER: S-EPMC3384503 | biostudies-literature | 2012 Dec

REPOSITORIES: biostudies-literature

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Mixtures of Gaussian Wells: Theory, Computation, and Application.

Manolopoulou Ioanna I Kepler Thomas B TB Merl Daniel M DM

Computational statistics & data analysis 20120521 12

A primary challenge in unsupervised clustering using mixture models is the selection of a family of basis distributions flexible enough to succinctly represent the distributions of the target subpopulations. In this paper we introduce a new family of Gaussian Well distributions (GWDs) for clustering applications where the target subpopulations are characterized by hollow [hyper-]elliptical structures. We develop the primary theory pertaining to the GWD, including mixtures of GWDs, selection of p ...[more]

PMID: 22754052

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Project description:We present a hybrid computational methodology to predict multiple energetically accessible conformations for G protein-coupled receptors (GPCRs) that might play a role in binding to ligands and different signaling partners. To our knowledge, this method, termed ActiveGEnSeMBLE, enables the first quantitative energy profile for GPCR activation that is consistent with the qualitative profile deduced from experiments. ActiveGEnSeMBLE starts with a systematic coarse grid sampling of helix tilts/rotations (?13 trillion transmembrane-domain conformations) and selects the conformational landscape based on energy. This profile identifies multiple potential active-state energy wells, with the TM3-TM6 intracellular distance as an approximate activation coordinate. These energy wells are then sampled locally using a finer grid to find locally minimized conformation in each energy well. We validate this strategy using the inactive and active experimental structures of ?2 adrenergic receptor (h?2AR) and M2 muscarinic acetylcholine receptor. Structures of membrane-embedded h?2AR along its activation coordinate are subjected to molecular-dynamics simulations for relaxation and interaction energy analysis to generate a quantitative energy landscape for h?2AR activation. This landscape reveals several metastable states along this coordinate, indicating that for h?2AR, the agonist alone is not enough to stabilize the active state and that the G protein is necessary, consistent with experimental observations. The method's application to somatostatin receptor SSTR5 (no experimental structure available) shows that to predict an active conformation it is better to start from an inactive structure template based on a close homolog than to start from an active template based on a distant homolog. The energy landscape for hSSTR5 activation is consistent with h?2AR in the role of the G protein. These results demonstrate the utility of the ActiveGEnSeMBLE method for predicting multiple conformations along the pathways for activating GPCRs and the corresponding energy landscapes, thereby providing detailed structural insights into the initial molecular events of GPCR function that are not easily accessible by experiments.

Project description:Although there has been tremendous progress in understanding the mechanics of the nervous system, there has not been a general theory of its computational function. Here I present a theory that relates the established biophysical properties of single generic neurons to principles of Bayesian probability theory, reinforcement learning and efficient coding. I suggest that this theory addresses the general computational problem facing the nervous system. Each neuron is proposed to mirror the function of the whole system in learning to predict aspects of the world related to future reward. According to the model, a typical neuron receives current information about the state of the world from a subset of its excitatory synaptic inputs, and prior information from its other inputs. Prior information would be contributed by synaptic inputs representing distinct regions of space, and by different types of non-synaptic, voltage-regulated channels representing distinct periods of the past. The neuron's membrane voltage is proposed to signal the difference between current and prior information ("prediction error" or "surprise"). A neuron would apply a Hebbian plasticity rule to select those excitatory inputs that are the most closely correlated with reward but are the least predictable, since unpredictable inputs provide the neuron with the most "new" information about future reward. To minimize the error in its predictions and to respond only when excitation is "new and surprising," the neuron selects amongst its prior information sources through an anti-Hebbian rule. The unique inputs of a mature neuron would therefore result from learning about spatial and temporal patterns in its local environment, and by extension, the external world. Thus the theory describes how the structure of the mature nervous system could reflect the structure of the external world, and how the complexity and intelligence of the system might develop from a population of undifferentiated neurons, each implementing similar learning algorithms.

Dataset Information

Mixtures of Gaussian Wells: Theory, Computation, and Application.

Publications

Mixtures of Gaussian Wells: Theory, Computation, and Application.

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