Algebraic statistical model for biochemical network dynamics inference

Linder, Daniel F.; Rempała, Grzegorz A.

doi:10.1166/jcsmd.2013.1032

Cited by 6 publications

(7 citation statements)

References 13 publications

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“…where Σ is the limiting covariance, see the literature. 17,29 The normality of̂allows to express the synthetic likelihood for the j th trajectory (replicate) as…”

Section: Proposition 1 the Statisticŝ Of Equations (3) And (5) Comentioning

confidence: 99%

“…Given the partially observed trajectory, X j , we denote by

{\overset{bold-italicβ}{true}}_{j}

the solution of either () or (). In the mass action setting, the ODE coefficients β are linear combinations of the reaction rates and can be written as β = Q κ where Q is a d × r matrix (see, e.g., Linder and Rempała 29 ). Some specific examples of β and Q are given in Section 4 below.…”

Section: Synthetic Likelihoodmentioning

confidence: 99%

“…The empirical patterns of the position of the LSE‐type estimates within these regions are then the basis for the multinomial likelihood and resulting parameter inference. To facilitate the comparison, we reanalyze a dataset introduced in Linder and Rempała 29 and consisting of the longitudinal RNA‐seq measurements from the retinal tissue in the zebrafish ( Danio rerio ). The study was performed to probe the regenerative properties of the zebrafish retina after it sustained cell‐specific damage.…”

Section: Data Examplesmentioning

confidence: 99%

“…One interest of the study was in analyzing a particular subsystem, consisting of the following species: heat shock protein transcription factor (Hsp70), signal transducer and activator of transcription 3 (Stat3), and the suppressor of cytokine signaling 3 (Socs3). For more details on the experiment, see Linder and Rempała 29 . The network of interest has the form

\begin{matrix} right & left Ø \to_{}^{κ_{1}} S t a t 3 S t a t 3 \to_{}^{κ_{4}} 2 S t a t 3 & right \\ right & left Ø \to_{}^{κ_{2}} S o c s 3 b S t a t 3 \to_{}^{κ_{5}} S o c s 3 b \\ right & left Ø \to_{}^{κ_{3}} h s p 70 S t a t 3 \to_{}^{κ_{6}} h s p 70 \\ right & left S t a t 3 + S o c s 3 b \to_{}^{κ_{7}} S o c s 3 b \\ right & left S t a t 3 \to_{}^{κ_{8}} Ø \\ right & left S o c s 3 b \to_{}^{κ_{9}} Ø \\ right & left h s p 70 \to_{}^{κ_{10}} Ø . \end{matrix}

…”

Section: Data Examplesmentioning

confidence: 99%

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Synthetic likelihood method for reaction network inference

Linder

Rempała

2020

Math Methods in App Sciences

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We propose a novel Markov chain Monte-Carlo (MCMC) method for reverse engineering the topological structure of stochastic reaction networks, a notoriously challenging problem that is relevant in many modern areas of research, like discovering gene regulatory networks or analyzing epidemic spread. The method relies on projecting the original time series trajectories, from the stochastic data generating process, onto information rich summary statistics and constructing the appropriate synthetic likelihood function to estimate reaction rates. The resulting estimates are consistent in the large volume limit and are obtained without employing complicated tuning strategies and expensive resampling as typically used by likelihood-free MCMC and approximate Bayesian methods. To illustrate the method, we apply it in two real data examples: the molecular pathway analysis with RNA-seq and the famous incidence data from 1665 plague outbreak at Eyam, England.

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“…where Σ is the limiting covariance, see the literature. 17,29 The normality of̂allows to express the synthetic likelihood for the j th trajectory (replicate) as…”

Section: Proposition 1 the Statisticŝ Of Equations (3) And (5) Comentioning

confidence: 99%

“…Given the partially observed trajectory, X j , we denote by

{\overset{bold-italicβ}{true}}_{j}

Section: Synthetic Likelihoodmentioning

confidence: 99%

Section: Data Examplesmentioning

confidence: 99%

\begin{matrix} right & left Ø \to_{}^{κ_{1}} S t a t 3 S t a t 3 \to_{}^{κ_{4}} 2 S t a t 3 & right \\ right & left Ø \to_{}^{κ_{2}} S o c s 3 b S t a t 3 \to_{}^{κ_{5}} S o c s 3 b \\ right & left Ø \to_{}^{κ_{3}} h s p 70 S t a t 3 \to_{}^{κ_{6}} h s p 70 \\ right & left S t a t 3 + S o c s 3 b \to_{}^{κ_{7}} S o c s 3 b \\ right & left S t a t 3 \to_{}^{κ_{8}} Ø \\ right & left S o c s 3 b \to_{}^{κ_{9}} Ø \\ right & left h s p 70 \to_{}^{κ_{10}} Ø . \end{matrix}

…”

Section: Data Examplesmentioning

confidence: 99%

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Synthetic likelihood method for reaction network inference

Linder

Rempała

2020

Math Methods in App Sciences

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“…Dinamika molekuler (30)(31)(32)(33)(34)(35)(36)(37)(38) merupakan suatu metode untuk menyelidiki struktur dari zat padat (41) , cair dan gas. Dinamika molekuler (42) pada umumnya menggunakan teknik persamaan hukum newton (43)(44)(45)(46)(47) dan mekanika klasik.…”

Section: Pendahuluanunclassified

Calcium Chloride (CaCl2) : Characteristics and Molecular Interaction in Solution

Alfionita¹,

Zainul²

2019

Preprint

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Kalsium klorida merupakan senyawa anorganik dengan rumus kimia CaCl2 berupa padatan kristal yang tak berwarna pada suhu kamar dan sangat larut dalam air. Dalam analisis struktur molekul Kalsium Klorida (CaCl2), riset ini bertujuan mengetahui karakteristik molekul, struktur, sifat, permukaan, jari-jari molekul, energi stabiliti dan MM2 molekul tersebut. Metoda yang digunakan yaitu penelusuran literatur dengan Endnote X7, metode pemodelan dengan menggunakan software ChemOffice 15.0, dan juga perhitungan matematis. Pada dasarnya untuk menemukan literasi jurnal yang bagus digunakanlah aplikasi Endnote X7 yang dijelaskan melalui fishbone state of art. Senyawa ini juga mempunyai total energi dan juga jari-jari molekul CaCl2 yang hasilnya bisa diketahui dengan menggunakan chemoffice 15.0 yaitu sebesar 526,865 kcal/mol dan 2.730 Å Kemudian untuk mengetahui kecepatan hanyut, konduktiviti, gerakan ion, viskositas, kelarutan dan bilangan transpor digunakan perhitungan matematis dari review jurnal mengenai kalsium klorida. Dimana kalsium klorida mempunyai kapasitas kalor (C), entropi molar standar (So), entalpi pembentukan standar (∆fH) dan energi bebas gibbs (∆fG) yang masing-masingnya mempunyai nilai C 72,89 J/molK, So 108,4 J/molK, ∆fH 795,42 kJ/mol, dan ∆fG -748,81nkJ/mol. Serta nilai kecepatan hanyut didapatkan sebesar 4,5125 V/cm setelah dilakukan perhitungan dengan menggunakan rumus. Nilai viskositas pada suhu 10oC sebesar 1.20, suhu 20oC sebesar 1.02, dan pada suhu 30oC sebesar 0,79. Nilai konduktiviti yang beragam tergantung dari suhu dan spesinya. Dimana nilai konduktiviti pada suhu 25oC sebesar 0.0617 jika nilai molarnya 0.3857 mole/L, 0.1289 jika nilai molarnya 0.905 mole/L.Hasil dari viskositas dan konduktiviti ini dituangkan dalam bentuk grafik

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Estimation of Dynamic Systems for Gene Regulatory Networks from Dependent Time-Course Data

Kim

2018

Journal of Computational Biology

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Dynamic system consisting of ordinary differential equations (ODEs) is a well-known tool for describing dynamic nature of gene regulatory networks (GRNs), and the dynamic features of GRNs are usually captured through time-course gene expression data. Owing to high-throughput technologies, time-course gene expression data have complex structures such as heteroscedasticity, correlations between genes, and time dependence. Since gene experiments typically yield highly noisy data with small sample size, for a more accurate prediction of the dynamics, the complex structures should be taken into account in ODE models. Hence, this study proposes an ODE model considering such data structures and a fast and stable estimation method for the ODE parameters based on the generalized profiling approach with data smoothing techniques. The proposed method also provides statistical inference for the ODE estimator and it is applied to a zebrafish retina cell network.

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Algebraic statistical model for biochemical network dynamics inference

Cited by 6 publications

References 13 publications

Synthetic likelihood method for reaction network inference

Synthetic likelihood method for reaction network inference

Calcium Chloride (CaCl2) : Characteristics and Molecular Interaction in Solution

Estimation of Dynamic Systems for Gene Regulatory Networks from Dependent Time-Course Data

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