P-Splines Using Derivative Information

Calderon, Christopher P.; Martinez, Josue G.; Carroll, Raymond J.; Sorensen, Danny C.

doi:10.1137/090768102

Cited by 13 publications

(46 citation statements)

References 34 publications

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“…Accounting for (and detecting) time changing parameters characterizing 2D and/or 3D SDE models, e.g., effective measurement noise that is changing significantly over time for a single trajectory, is another contribution of this work (other numerical approaches for quantifying effective continuous parameter changes in single-molecule trajectories are discussed in Ref. 53 ).…”

Section: Theoretical Methodsmentioning

confidence: 99%

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Quantifying Transient 3D Dynamical Phenomena of Single mRNA Particles in Live Yeast Cell Measurements

et al. 2013

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Single-particle tracking (SPT) has been extensively used to obtain information about diffusion and directed motion in a wide range of biological applications. Recently, new methods have appeared for obtaining precise (10s of nm) spatial information in three dimensions (3D) with high temporal resolution (measurements obtained every 4ms), which promise to more accurately sense the true dynamical behavior in the natural 3D cellular environment. Despite the quantitative 3D tracking information, the range of mathematical methods for extracting information about the underlying system has been limited mostly to mean-squared displacement analysis and other techniques not accounting for complex 3D kinetic interactions. There is a great need for new analysis tools aiming to more fully extract the biological information content from in vivo SPT measurements. High-resolution SPT experimental data has enormous potential to objectively scrutinize various proposed mechanistic schemes arising from theoretical biophysics and cell biology. At the same time, methods for rigorously checking the statistical consistency of both model assumptions and estimated parameters against observed experimental data (i.e. goodness-of-fit tests) have not received great attention. We demonstrate methods enabling (1) estimation of the parameters of 3D stochastic differential equation (SDE) models of the underlying dynamics given only one trajectory; and (2) construction of hypothesis tests checking the consistency of the fitted model with the observed trajectory so that extracted parameters are not over-interpreted (the tools are applicable to linear or nonlinear SDEs calibrated from non-stationary time series data). The approach is demonstrated on high-resolution 3D trajectories of single ARG3 mRNA particles in yeast cells in order to show the power of the methods in detecting signatures of transient directed transport. The methods presented are generally relevant to a wide variety of 2D and 3D SPT tracking applications.

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Section: Theoretical Methodsmentioning

confidence: 99%

“…The equations above were inspired by models in statistical physics 49,53 . For example, k B T represents Boltzmann’s constant multiplied by the system temperature.…”

Section: Theoretical Methodsmentioning

confidence: 99%

Quantifying Transient 3D Dynamical Phenomena of Single mRNA Particles in Live Yeast Cell Measurements

et al. 2013

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“…The funding sources listed for Raymond J. Carroll were incorrect in the original publication [1]. Prof. Carroll's corrected financial acknowledgment should read: "RJC's research was supported by a grant from the National Cancer Institute (CA57030).…”

Section: Doi 101137/100809921mentioning

confidence: 99%

Erratum: P-Splines Using Derivative Information

Calderon¹,

Martinez²,

Carroll³

et al. 2010

Multiscale Model. Simul.

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Abstract. This is a correction to the author's article [Multiscale Model. Simul., 8 (2010), pp. 1562-1580. DOI. 10.1137/100809921The funding sources listed for Raymond J. Carroll were incorrect in the original publication [1]. Prof. Carroll's corrected financial acknowledgment should read: "RJC's research was supported by a grant from the National Cancer Institute (CA57030)."The grant listed above was printed as shown in the original article but another was removed.

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“…Our main contributions to this type of endeavor are associated with showing how modern time series analysis tools can be used to help in quantitatively determining some “coarse-graining” parameters and also determine the goodness-of-fit of surrogate models in a pathwise fasion. We also demonstrate how a collection of low-dimensional models can be used to study various all-atom simulations and single-molecule experiments where certain collective degrees of freedom are associated with slow time-scales and influence the estimated surrogate models 30,31,61,62. The motivation for using a collection of simple low-dimensional models as opposed to more complicated high-dimensional models as surrogates is discussed in detail in Ref.…”

Section: Theoretical Backgroundmentioning

confidence: 99%

“…The motivation for using a collection of simple low-dimensional models as opposed to more complicated high-dimensional models as surrogates is discussed in detail in Ref. [61] and in the Conclusions.…”

Section: Theoretical Backgroundmentioning

confidence: 99%

Extracting Kinetic and Stationary Distribution Information from Short MD Trajectories via a Collection of Surrogate Diffusion Models

Calderon

Arora

2008

J. Chem. Theory Comput.

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Low-dimensional stochastic models can summarize dynamical information and make long time predictions associated with observables of complex atomistic systems. Maximum likelihood based techniques for estimating low-dimensional surrogate diffusion models from relatively short time series are presented. It is found that a heterogeneous population of slowly evolving conformational degrees of freedom modulates the dynamics. This underlying heterogeneity results in a collection of estimated low-dimensional diffusion models. Numerical techniques for exploiting this finding to approximate skewed histograms associated with the simulation are presented. In addition, statistical tests are also used to assess the validity of the models and determine physically relevant sampling information, e.g. the maximum sampling frequency at which one can discretely sample from an atomistic time series and have a surrogate diffusion model pass goodness-of-fit tests. The information extracted from such analyses can possibly be used to assist umbrella sampling computations as well as help in approximating effective diffusion coefficients. The techniques are demonstrated on simulations of Adenylate Kinase.

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P-Splines Using Derivative Information

Cited by 13 publications

References 34 publications

Quantifying Transient 3D Dynamical Phenomena of Single mRNA Particles in Live Yeast Cell Measurements

Quantifying Transient 3D Dynamical Phenomena of Single mRNA Particles in Live Yeast Cell Measurements

Erratum: P-Splines Using Derivative Information

Extracting Kinetic and Stationary Distribution Information from Short MD Trajectories via a Collection of Surrogate Diffusion Models

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