Non-Markovian processes

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Table of contents

1 Introduction 
2 Stochastic processes and simulation methods 
2.1 Stochastic processes in statistical mechanics
2.1.1 Markov processes
2.1.2 Jump processes and the Master equation
2.1.3 Transition matrices
2.1.4 Langevin equations
2.1.5 The Fokker-Planck equation: expanding the Master equation
2.1.6 From Langevin to Fokker-Planck
2.1.7 Boundary conditions
2.1.8 The old problem of Itô and Stratonovitch
2.1.9 In and out of equilibrium
2.1.10 About non-Markovian processes
2.1.11 Correlation, covariance, and autocorrelation functions
2.2 Computational methods
2.2.1 Simulating random population models: Gillespie method and fixed time step methods
2.2.2 Numerical solutions to partial differential equations (PDEs)
2.2.3 Optimization and Maximum Likelihood estimation
2.2.4 The example of least squares
3 Introduction to immunology 
3.1 The immune system
3.1.1 The role of the immune system
3.1.2 Actors of the immune system
3.1.3 B cells and T cells
3.1.4 The adaptive immune system and the immune response
3.1.5 The naive and memory pool
3.1.6 Immune systems across species
3.2 Experimental clone size distributions
3.3 Models of the immune system
3.3.1 Why model the immune system?
3.3.2 A model of antigenic stimuli
3.3.3 Current models of the immune system
4 Fitness shapes clone size distributions of immune repertoires 
4.1 Significance
4.2 Abstract
4.3 Introduction
4.4 Results
4.4.1 Clone dynamics in a fluctuating antigenic landscape
4.4.2 Simplified models and the origin of the power law
4.4.3 A model of fluctuating phenotypic fitness
4.5 Discussion
5 Random networks of immune systems: structure and selection 
5.1 Selection and fitness change with de novo mutations
5.1.1 Introduction
5.1.2 From biology to model
5.1.3 Model of a niche
5.1.4 The dynamics of the winners’ pool
5.1.5 The case of independent niches
5.1.6 Prospects and discussion
5.2 Fine structure of networks and clone size distributions
5.2.1 Modeling competition: antigens and lymphocytes
5.2.2 Dynamics of the system
5.3 Clone size distributions in limits of the niche structure
5.3.1 Degenerated cases: fully specific and nonspecific models
5.3.2 Perturbation, global effects and fitness change
5.3.3 Fokker-Planck equation
5.3.4 Interclonal and intraclonal competition
6 Development in Drosophila embryos 
6.1 Patterning in early embryos
6.2 Development in fly embryos: Bicoid and hunchback
6.3 The Berg and Purcell limit
6.4 Experimental methods
6.4.1 RNA FISH
6.4.2 Live fluorescent Imaging
6.4.3 The importance of the construct
6.4.4 On the dynamics of hunchback activation
6.5 Motivation for autocorrelation method
7 Precision of readout at the hunchback gene 
7.1 Abstract
7.2 Introduction
7.3 Results
7.3.1 Characterizing the time traces
7.3.2 Promoter switching models
7.3.3 Autocorrelation approach
7.3.4 Simulated data
7.3.5 Fly trace data analysis
7.3.6 Accuracy of the transcriptional process
7.4 Discussion
7.5 Materials and Methods
7.5.1 Constructs
7.5.2 Live Imaging
7.5.3 Image analysis
7.5.4 Trace preprocessing
7.5.5 The two state model
7.5.6 The cycle model
7.5.7 The ! waiting time model
7.5.8 Finite cell cycle length correction to the connected autocorrelation function101
7.5.9 Inference
8 Conclusions 
8.1 About models in biophysics
8.2 Future work
A Fitness shapes clone size distributions of immune repertoires: supplementary information
A.1 Simple birth-death process with no fitness fluctuations, and its continuous limit
A.2 Effects of explicit global homeostasis
A.3 Details of noise partition do not influence the clone size distribution function
A.4 Model of temporally correlated clone-specific fitness fluctuations
A.5 The Ornstein Uhlenbeck process and maximum entropy
A.6 Model solution for white-noise clone-specific fitness fluctuations
A.7 Data analysis
A.8 Cell specific simulations
A.9 Model of cell-specific fitness fluctuations, and its limit of no heritability
A.10 Model solutions for cell-specific fitness fluctuations in the limit of no heritability
A.11 Dynamics of naive and memory cells
A.12 Effects of hypermutations
A.13 Time dependent source terms and aging
B Precision of readout at the hunchback gene: supplementary information
B.1 Basic setup and data preprocessing
B.2 The two state model
B.3 Computing out of steady state
B.4 Multiple off states
B.5 Generalized multi step model
B.6 The autocorrelation of a Poisson polymerase firing model
B.7 Numerical simulations
B.8 Correction to the autocorrelation function for finite trace lengths
B.9 Correction to the autocorrelation function from correlations in the variance
B.10 Cross-correlation
B.11 Precision of the translational process