scholarly journals DeepCME: A deep learning framework for computing solution statistics of the chemical master equation

2021 ◽  
Vol 17 (12) ◽  
pp. e1009623
Author(s):  
Ankit Gupta ◽  
Christoph Schwab ◽  
Mustafa Khammash
Keyword(s):  
Deep Learning ◽  
Master Equation ◽  
State Vector ◽  
Stochastic Dynamics ◽  
Chemical Master Equation ◽  
Stochastic Simulations ◽  
Chemical System ◽  
High Dimensional ◽  
Future Research ◽  
Copy Numbers

Stochastic models of biomolecular reaction networks are commonly employed in systems and synthetic biology to study the effects of stochastic fluctuations emanating from reactions involving species with low copy-numbers. For such models, the Kolmogorov’s forward equation is called the chemical master equation (CME), and it is a fundamental system of linear ordinary differential equations (ODEs) that describes the evolution of the probability distribution of the random state-vector representing the copy-numbers of all the reacting species. The size of this system is given by the number of states that are accessible by the chemical system, and for most examples of interest this number is either very large or infinite. Moreover, approximations that reduce the size of the system by retaining only a finite number of important chemical states (e.g. those with non-negligible probability) result in high-dimensional ODE systems, even when the number of reacting species is small. Consequently, accurate numerical solution of the CME is very challenging, despite the linear nature of the underlying ODEs. One often resorts to estimating the solutions via computationally intensive stochastic simulations. The goal of the present paper is to develop a novel deep-learning approach for computing solution statistics of high-dimensional CMEs by reformulating the stochastic dynamics using Kolmogorov’s backward equation. The proposed method leverages superior approximation properties of Deep Neural Networks (DNNs) to reliably estimate expectations under the CME solution for several user-defined functions of the state-vector. This method is algorithmically based on reinforcement learning and it only requires a moderate number of stochastic simulations (in comparison to typical simulation-based approaches) to train the “policy function”. This allows not just the numerical approximation of various expectations for the CME solution but also of its sensitivities with respect to all the reaction network parameters (e.g. rate constants). We provide four examples to illustrate our methodology and provide several directions for future research.

scholarly journals DeepCME: A deep learning framework for solving the Chemical Master Equation

2021 ◽  
Author(s):  
Ankit Gupta ◽  
Christoph Schwab ◽  
Mustafa Khammash
Keyword(s):  
Deep Learning ◽  
Master Equation ◽  
Stochastic Dynamics ◽  
Chemical Master Equation ◽  
Stochastic Simulations ◽  
Chemical System ◽  
High Dimensional ◽  
Future Research ◽  
Approximation Properties ◽  
Copy Numbers

Stochastic models of biomolecular reaction networks are commonly employed in systems and synthetic biology to study the effects of stochastic fluctuations emanating from reactions involving species with low copy-numbers. For such models, the Kolmogorov's forward equation is called the chemical master equation (CME), and it is a fundamental system of linear ordinary differential equations (ODEs) that describes the evolution of the probability distribution of the random state-vector representing the copy-numbers of all the reacting species. The size of this system is given by the number of states that are accessible by the chemical system, and for most examples of interest this number is either very large or infinite. Moreover, approximations that reduce the size of the system by retaining only a finite number of important chemical states (e.g. those with non-negligible probability) result in high-dimensional ODE systems, even when the number of reacting species is small. Consequently, accurate numerical solution of the CME is very challenging, despite the linear nature of the underlying ODEs. One often resorts to estimating the solutions via computationally intensive stochastic simulations. The goal of the present paper is to develop a novel deep-learning approach for solving high-dimensional CMEs by reformulating the stochastic dynamics using Kolmogorov's backward equation. The proposed method leverages superior approximation properties of Deep Neural Networks (DNNs) and is algorithmically based on reinforcement learning. It only requires a moderate number of stochastic simulations (in comparison to typical simulation-based approaches) to train the "policy function". This allows not just the numerical approximation of the CME solution but also of its sensitivities to all the reaction network parameters (e.g. rate constants). We provide four examples to illustrate our methodology and provide several directions for future research.

scholarly journals Role of periodic forcing on the stochastic dynamics of a biomolecular clock

2020 ◽  
Author(s):  
Zhanhao Zhang ◽  
Supravat Dey ◽  
Abhyudai Singh
Keyword(s):  
Copy Number ◽  
Stochastic Dynamics ◽  
Stochastic Simulations ◽  
External Signal ◽  
Periodic Forcing ◽  
Diurnal Cycles ◽  
Oscillatory Systems ◽  
Sustained Oscillations ◽  
Copy Numbers ◽  
Goodwin Oscillator

AbstractBiomolecular clocks produce sustained oscillations in mRNA/protein copy numbers that are subject to inherent copy-number fluctuations with important implications for proper cellular timekeeping. These random fluctuations embedded within periodic variations in copy numbers make the quantification of noise particularly challenging in stochastic gene oscillatory systems, unlike other non-oscillatory circuits. Motivated by diurnal cycles driving circadian clocks, we investigate the noise properties in the well-known Goodwin oscillator in the presence and absence of a periodic driving signal. We use two approaches to compute the noise as a function of time: (i) solving the moment dynamics derived from the linear noise approximation (LNA) assuming fluctuations are small relative to the mean and (ii) analyzing trajectories obtained from exact stochastic simulations of the Goodwin oscillator. Our results demonstrate that the LNA can predict the noise behavior quite accurately when the system shows damped oscillations or in the presence of external periodic forcing. However, the LNA could be misleading in the case of sustained oscillations without an external signal due to the propagation of large noise. Finally, we study the effect of random bursting of gene products on the clock stochastic dynamics. Our analysis reveals that the burst of mRNAs enhances the noise in the copy number regardless of the presence of external forcing, although the extent of fluctuations becomes less due to the forcing.

scholarly journals On the Properties of the Reaction Counts Chemical Master Equation

Entropy ◽  
2019 ◽  
Vol 21 (6) ◽  
pp. 607
Author(s):  
Sunkara
Keyword(s):  
Master Equation ◽  
State Space ◽  
Continuous Time ◽  
A Priori ◽  
Chemical Master Equation ◽  
The State ◽  
High Dimensional ◽  
Population Counts ◽  
Theoretical Results ◽  
Over Time

The reaction counts chemical master equation (CME) is a high-dimensional variant ofthe classical population counts CME. In the reaction counts CME setting, we count the reactionswhich have fired over time rather than monitoring the population state over time. Since a reactioneither fires or not, the reaction counts CME transitions are only forward stepping. Typically thereare more reactions in a system than species, this results in the reaction counts CME being higher indimension, but simpler in dynamics. In this work, we revisit the reaction counts CME frameworkand its key theoretical results. Then we will extend the theory by exploiting the reactions counts’forward stepping feature, by decomposing the state space into independent continuous-time Markovchains (CTMC). We extend the reaction counts CME theory to derive analytical forms and estimatesfor the CTMC decomposition of the CME. This new theory gives new insights into solving hittingtimes-, rare events-, and a priori domain construction problems.

Modeling Stochastic Gene Regulatory Networks Using Direct Solutions of Chemical Master Equation and Rare Event Sampling

2016 ◽  
pp. 80-122
Author(s):  
Youfang Cao ◽  
Anna Terebus ◽  
Jie Liang
Keyword(s):  
Master Equation ◽  
Gene Regulatory Networks ◽  
Biological Networks ◽  
Regulatory Networks ◽  
Rare Event ◽  
Planck Equation ◽  
Chemical Master Equation ◽  
Copy Numbers ◽  
Finite State ◽  
Gene Regulatory

Stochasticity plays important roles in many biological networks. A fundamental framework for studying the full stochasticity is the Discrete Chemical Master Equation (dCME). Under this framework, the combination of copy numbers of molecular species defines the microstate of the molecular interactions in the network. The probability distribution over these microstates provide a full description of the properties of a stochastic molecular network. However, it is challenging to solve a dCME. In this chapter, we will first discuss how to derive approximation methods including Fokker-Planck equation and the chemical Langevin equation from the dCME. We also discuss the widely used stochastic simulation method. After that, we focus on the direct solutions to the dCME. We first discuss the Finite State Projection (FSP) method, and then introduce the recently developed finite buffer method (fb-dCME) for directly solving both steady state and time-evolving probability landscape of dCME. We show the advantages of the fb-dCME method using two realistic gene regulatory networks.

Feature Selection Techniques in High Dimensional Data With Machine Learning and Deep Learning

2021 ◽  
pp. 17-37
Author(s):  
Bhanu Chander
Keyword(s):  
Machine Learning ◽  
Feature Selection ◽  
Deep Learning ◽  
High Dimensional Data ◽  
Complete Information ◽  
High Dimensional ◽  
Future Research ◽  
Future Research Directions ◽  
Class Labels ◽  
Feature Selection Techniques

High-dimensional data inspection is one of the major disputes for researchers plus engineers in domains of deep learning (DL), machine learning (ML), as well as data mining. Feature selection (FS) endows with proficient manner to determine these difficulties through eradicating unrelated and outdated data, which be capable of reducing calculation time, progress learns precision, and smooth the progress of an enhanced understanding of the learning representation or information. To eradicate an inappropriate feature, an FS standard was essential, which can determine the significance of every feature in the company of the output class/labels. Filter schemes employ variable status procedure as the standard criterion for variable collection by means of ordering. Ranking schemes utilized since their straightforwardness and high-quality accomplishment are detailed for handy appliances. The goal of this chapter is to produce complete information on FS approaches, its applications, and future research directions.

Review of the Applications of Deep Learning in Bioinformatics

2021 ◽  
Vol 15 (8) ◽  
pp. 898-911
Author(s):  
Yongqing Zhang ◽  
Jianrong Yan ◽  
Siyu Chen ◽  
Meiqin Gong ◽  
Dongrui Gao ◽  
...  
Keyword(s):  
Deep Learning ◽  
Drug Discovery ◽  
Biomedical Imaging ◽  
State Of The Art ◽  
Black Box ◽  
Medical Data ◽  
Biological Data ◽  
High Dimensional ◽  
Biological Research ◽  
Process Data

Rapid advances in biological research over recent years have significantly enriched biological and medical data resources. Deep learning-based techniques have been successfully utilized to process data in this field, and they have exhibited state-of-the-art performances even on high-dimensional, nonstructural, and black-box biological data. The aim of the current study is to provide an overview of the deep learning-based techniques used in biology and medicine and their state-of-the-art applications. In particular, we introduce the fundamentals of deep learning and then review the success of applying such methods to bioinformatics, biomedical imaging, biomedicine, and drug discovery. We also discuss the challenges and limitations of this field, and outline possible directions for further research.

Android Malware Detection Techniques: A Literature Review

2020 ◽  
Vol 14 ◽  
Author(s):  
Meghna Dhalaria ◽  
Ekta Gandotra
Keyword(s):  
Machine Learning ◽  
Deep Learning ◽  
Malware Detection ◽  
Future Research ◽  
Android Malware ◽  
Detection Techniques ◽  
Android Malware Detection ◽  
Future Research Directions ◽  
To Come ◽  
Tools And Techniques

Purpose: This paper provides the basics of Android malware, its evolution and tools and techniques for malware analysis. Its main aim is to present a review of the literature on Android malware detection using machine learning and deep learning and identify the research gaps. It provides the insights obtained through literature and future research directions which could help researchers to come up with robust and accurate techniques for classification of Android malware. Design/Methodology/Approach: This paper provides a review of the basics of Android malware, its evolution timeline and detection techniques. It includes the tools and techniques for analyzing the Android malware statically and dynamically for extracting features and finally classifying these using machine learning and deep learning algorithms. Findings: The number of Android users is expanding very fast due to the popularity of Android devices. As a result, there are more risks to Android users due to the exponential growth of Android malware. On-going research aims to overcome the constraints of earlier approaches for malware detection. As the evolving malware are complex and sophisticated, earlier approaches like signature based and machine learning based are not able to identify these timely and accurately. The findings from the review shows various limitations of earlier techniques i.e. requires more detection time, high false positive and false negative rate, low accuracy in detecting sophisticated malware and less flexible. Originality/value: This paper provides a systematic and comprehensive review on the tools and techniques being employed for analysis, classification and identification of Android malicious applications. It includes the timeline of Android malware evolution, tools and techniques for analyzing these statically and dynamically for the purpose of extracting features and finally using these features for their detection and classification using machine learning and deep learning algorithms. On the basis of the detailed literature review, various research gaps are listed. The paper also provides future research directions and insights which could help researchers to come up with innovative and robust techniques for detecting and classifying the Android malware.

scholarly journals Application of deep learning in detecting neurological disorders from magnetic resonance images: a survey on the detection of Alzheimer’s disease, Parkinson’s disease and schizophrenia

2020 ◽  
Vol 7 (1) ◽  
Author(s):  
Manan Binth Taj Noor ◽  
Nusrat Zerin Zenia ◽  
M Shamim Kaiser ◽  
Shamim Al Mamun ◽  
Mufti Mahmud
Keyword(s):  
Alzheimer’S Disease ◽  
Parkinson’S Disease ◽  
Alzheimer's Disease ◽  
Parkinson's Disease ◽  
Deep Learning ◽  
Magnetic Resonance ◽  
Neurological Disorders ◽  
Magnetic Resonance Images ◽  
Future Research ◽  
Comparative Performance

Abstract Neuroimaging, in particular magnetic resonance imaging (MRI), has been playing an important role in understanding brain functionalities and its disorders during the last couple of decades. These cutting-edge MRI scans, supported by high-performance computational tools and novel ML techniques, have opened up possibilities to unprecedentedly identify neurological disorders. However, similarities in disease phenotypes make it very difficult to detect such disorders accurately from the acquired neuroimaging data. This article critically examines and compares performances of the existing deep learning (DL)-based methods to detect neurological disorders—focusing on Alzheimer’s disease, Parkinson’s disease and schizophrenia—from MRI data acquired using different modalities including functional and structural MRI. The comparative performance analysis of various DL architectures across different disorders and imaging modalities suggests that the Convolutional Neural Network outperforms other methods in detecting neurological disorders. Towards the end, a number of current research challenges are indicated and some possible future research directions are provided.

scholarly journals Neural network aided approximation and parameter inference of non-Markovian models of gene expression

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Qingchao Jiang ◽  
Xiaoming Fu ◽  
Shifu Yan ◽  
Runlai Li ◽  
Wenli Du ◽  
...  
Keyword(s):  
Neural Network ◽  
Stochastic Dynamics ◽  
Stochastic Simulations ◽  
Parameter Inference ◽  
Biochemical Processes ◽  
Markovian Models ◽  
The Neural Network ◽  
Large Numbers ◽  
Small Set ◽  
Noisy Measurements

AbstractNon-Markovian models of stochastic biochemical kinetics often incorporate explicit time delays to effectively model large numbers of intermediate biochemical processes. Analysis and simulation of these models, as well as the inference of their parameters from data, are fraught with difficulties because the dynamics depends on the system’s history. Here we use an artificial neural network to approximate the time-dependent distributions of non-Markovian models by the solutions of much simpler time-inhomogeneous Markovian models; the approximation does not increase the dimensionality of the model and simultaneously leads to inference of the kinetic parameters. The training of the neural network uses a relatively small set of noisy measurements generated by experimental data or stochastic simulations of the non-Markovian model. We show using a variety of models, where the delays stem from transcriptional processes and feedback control, that the Markovian models learnt by the neural network accurately reflect the stochastic dynamics across parameter space.

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