Models of Switching in Biophysical Contexts
|
|
- Angel Harper
- 8 years ago
- Views:
Transcription
1 Models of Switching in Biophysical Contexts Martin R. Evans SUPA, School of Physics and Astronomy, University of Edinburgh, U.K. March 7, 2011 Collaborators: Paolo Visco (MSC, Paris) Rosalind J. Allen (Edinburgh) Satya N. Majumdar (LPTMS, Paris)
2 Plan Plan I Thoughts on biophysical modelling II Switching between states III Microscopic dynamics: model linear feedback switch IV Macroscopic dynamics: population growth in a catastrophic environment References: P. Visco, R. J. Allen, M. R. Evans, Phys. Rev. Lett. 2008, Phys. Rev. E 2009 P. Visco, R. J. Allen, S. N. Majumdar, M. R. Evans, Biophysical Journal 2010
3 Physics vs Biology Physics vs Biology Physics Unifying Principles Effective Theories; minimal models Mathematical proof e.g. Free energy minimisation Biology System details Models with many parameters to fit data Argumentation e.g. Evolutionary pressures
4 What can physicists bring to biophysical modelling? Ideas from (statistical) physics many particle behaviour non equilibrium phenomena fluctuations and stochastic effects idea of scales Model building savoir faire minimal models exact solutions; good approximations
5 What can physicists bring to biophysical modelling? Ideas from (statistical) physics many particle behaviour non equilibrium phenomena fluctuations and stochastic effects idea of scales Model building savoir faire minimal models exact solutions; good approximations What physicists shouldn t bring Arrogance and ignorance
6 Plan Plan I Thoughts on biophysical modelling II Switching between states III Microscopic dynamics: model linear feedback switch IV Macroscopic dynamics: population growth in a catastrophic environment References: P. Visco, R. J. Allen, M. R. Evans, Phys. Rev. Lett. 2008, Phys. Rev. E 2009 P. Visco, R. J. Allen, S. N. Majumdar, M. R. Evans, Biophysical Journal 2010
7 II Switching: Basic Biology for Physicists Gene Stretch of DNA 1000 base pairs long Transcription by RNAp mrna Translation amino acids production of proteins... Phenotype Regulation regulatory sites at ends of gene known as operators gene switched off/on by binding of repressors/enhancers known as Transcription factors genes can produce transcription factors for themselves or other genes genetic network
8 Heterogeneity Populations of bacteria are often heterogeneous even if environmentally and genetically identical Happens when bacteria frequently switches between different states: Multistable genetic switches Stochastic oscillation between different states It represents a strategy against environmental changes and stresses Examples: Bacterial persistence Phase variation (e.g.: fimbriae)
9 Example: Bacterial persistence Non persistent state Persistent state Vulnerable to antibiotics Resists against antibiotics Fast growth Very slow growth Balaban, Merrin, Chait, Kowalik, Leibler, Science, 2004
10 Examples of population strategies Bet Hedging small fraction of population in unfit persistor state which can survive catastrophes e.g. antibiotics Once and for all Population splits into groups with long lived phenotypes i.e. bistability Defence against immune response small fraction of population in fit state since too successful a population would evoke an immune response
11 Models of genetic switches Existing models for bistable gene regulatory networks Mutually repressing genes Positive feedback loop Typically: bistable systems effective potential But this is not how the most common bacterial phase variation systems work! state state 1 state 2
12 Example: Uropathogenic E.Coli Urinary tract Attached, fimbriated Detached, fimbriated Detached, non fimbriated Attached vulnerable to immune system Detached vulnerable to flushing
13 Example: Uropathogenic E. Coli Non fimbriated state Fimbriated state M. R. Evans Models of Switching in Biophysical Contexts
14 The fim switch DNA inversion switch fim system controls production of fimbriae short piece of DNA can be inserted in two orientations in one orientation fimbrial genes transcribed and fimbriae produced ( on state ) inversion of DNA element mediated by recombinase enzymes FimE recombinase which flips the switch on to off is produced more strongly in the on state orientational control
15 III Model of stochastic linear feedback switch Reaction network k R 1 1 k S 2 on Son + R 1 k S on + R on 3 1 S off + R 1 k 4 S on k4 S off R 1 variations switching reactions Reaction rates k 1 k 2 k on R 1 decay R 1 production 3 R 1 mediated switching (only on to off) k 4 spontaneous switching (both directions)
16 III Model of stochastic linear feedback switch Reaction network k R 1 1 k S 2 on Son + R 1 k S on + R on 3 1 S off + R 1 k 4 S on k4 S off R 1 variations switching reactions In the on state: dn dt = k 2 k 1 n
17 III Model of stochastic linear feedback switch Reaction network k R 1 1 k S 2 on Son + R 1 k S on + R on 3 1 S off + R 1 k 4 S on k4 S off R 1 variations switching reactions In the on state: n(t) = k 2 k 1 [1 exp( k 1 t)] n k 2 k 1 t
18 III Model of stochastic linear feedback switch Reaction network k R 1 1 k S 2 on Son + R 1 k S on + R on 3 1 S off + R 1 k 4 S on k4 S off R 1 variations switching reactions In the off state: dn dt = k 1 n n k 2 k 1 t
19 III Model of stochastic linear feedback switch Reaction network k R 1 1 k S 2 on Son + R 1 k S on + R on 3 1 S off + R 1 k 4 S on k4 S off R 1 variations switching reactions In the off state: n(t) = n 0 exp( k 1 t) n k 2 k 1 t
20 Scales k 2 k 1 0 n τ R τ on Three timescales τ off t τ R relaxation time of n: 1/k 1 τ on on to off switching time: 1/( n on k3 on + k on τ off off to on switching time: 1/k4 off Two n scales n on asymptotic value of n in the on state: k 2 /k 1 n off asymptotic value of n in the off state: 0 4 )
21 Some examples τ R τ S τ R τ S τ R τ S
22 Statistical description Define p s (n, t) probability that there are n enzymes and the switch is in position s {on, off} at time t. Master equation dp s (n) dt = k 1 [(n + 1)p s (n + 1) np s (n)] + k s 2 [p s(n 1) p s (n)] + n[k 1 s 3 p 1 s (n) k s 3 p s(n)] + k 4 [p 1 s (n) p s (n)] Removal of R 1 Production of R 1 (if the switch is on) R 1 mediated switching spontaneous switching
23 Steady state: two coupled equations (n + 1)k 1 p on (n + 1) + k 2 p on (n 1) + k 4 p off (n) (n + 1)k 1 p off (n + 1) + nk on 3 p on(n) + k 4 p on (n) = (nk 1 + k 2 + nk on 3 + k 4)p on (n) = (nk 1 + k 4 )p off (n) Exact solution p on (n) = a 0 (u 1 u 0 ) n n! (η) n (ζ) n 1F 1 (η + n, ζ + n, u 0 ) p off (n) = κδ n,0 + k 2 p on (n 1) p on (n) k 1 n where u 1, u 0, η, ζ are combinations of the reaction rates and κ, a 0 are normalising constants
24 Test against simulations Plot of p(n) = p on (n) + p off (n) Perfect agreement
25 Flipping time distribution Flipping time distribution F on (t)dt probability that the switch flips at time t t + dt Compare with mean first passage times and persistence distributions of stochastic processes We would like to see peak around typical time to be in on-state F(t) m t Can the model achieve this? require df(t) dt > 0 t=0
26 Measurement ensemble F (T ) depends on the initial condition of n i Two choices: Switch change ensemble SCE Steady state ensemble SSE Initial distribution W (n i ) defines the ensemble
27 Relation between ensembles on switch position T T 1 T 2 off Probability that t is an interval T : Prob(T )dt = t time T F SCE (T )dt 0 T F SCE (T )dt Prob(T 2 T )dt = θ(t T 2)dT T (uniform) F SSE (T 2 ) = T 2 Prob(T 2 T )Prob(T )dt = T 2 0 F SCE (T )dt TF SCE (T )dt General relation from renewal theory: df SSE dt = FSCE (T ) T SCE
28 Peak in the distribution never a peak in SSE in SCE require k 2 k on 3 (k 4) 2 k on 3 (k 1 + 2k 4 ) n W (k on 3 )2 n 2 W > 0 k k 2 = k 2 = k3 on Visco, Allen, Evans, PRL (2008);
29 IV Population dynamics in changing environments Consider whether switching rate to a less fit state is advantageous for the population Previous studies Thattai and Van Oudenaarden, Genetics environments, 2 phenotypes, Poissonian environmental changes Kussell and Leibler, Science 2005 many environments and phenotypes, different phentotypes have preferred environment Random switching between phenotypes good strategy when environmental changes unpredictable
30 General scenario Single environment Population of bacteria, say, with two possibles states for individuals: Fit state has fast growth Unfit (persistor) state has slow growth but withstands catastrophes Catastrophes occur stochastically, coupled to growth of population Question: what is best strategy of population to maximise growth?
31 Model Deterministic growth Two subpopulations n A and n B. Exponential growth rates γ A > γ B Individuals switch states with rates k A, k B dn A dt dn B dt = γ A n A + k B n B k A n A, = γ B n B + k A n A k B n B. Stochastic catastrophes Catastrophe rate β(n A, n B ) β is the environmental response function When a catastrophe occurs n A n A < n A, with probability density ν(n A n A ). ν is the catastrophe strength distribution
32 Fitness Biological definition: instantaneous growth rate of population Here f is fraction of population in fit state dn dt Deterministic growth: n A f = n A + n B = γ A n A + γ B n B = (γ B + γf )n df dt = v(f ) = γ(f + f )(f f ), where γ = γ A γ B and f ± are the roots of ( f 2 1 k ) A + k B f k B γ γ = 0.
33 Typical trajectory log(n A ) log(n B ) f + f(t) t Piecewise Deterministic Markov Processes - used extensively in context of queueing theory
34 Catastrophe rate Threshold sigmoid function Catastrophes triggered when a threshold is reached Our choice: β λ (f ) = ξ 2 ( 1 + ) f f λ2 + (f f ) 2 parameters ξ plateau value f threshold value βλ(f) 1 λ = 0.01 λ = 0.1 λ = 1 λ = 10 λ sharpness of the transition f
35 Catastrophe strength n A n A = u n A, where 0 < u < 1 is a random number sampled from: P(u) = (α + 1)u α α > 1 n ν(n n) α = 0.5 α = 0 α = 1 α = 10 1 < α < 0 strong catastrophes α > 0 weak catastrophes n /n To each jump n A n A corresponds a jump f f Catastrophe strengh distribution µ(f f ), where µ(f f ) = Θ(f f ) d m(f ) df m(f ) with m(f ) = ( f ) 1+α 1 f
36 Exact Solution for Stationary State Constant flux condition v(f ) 0 f f f f + β(f )µ(f f ) Recall df dt = v(f ) µ(f f ) = d m(f ) df m(f ) ( ) 1+α f m(f ) = 1 f p(f )v(f ) = f+ f df df p(f )β(f )µ(f f ) f 0
37 Exact Solution for Stationary State Constant flux condition v(f ) 0 f f f f + β(f )µ(f f ) Recall df dt = v(f ) µ(f f ) = d m(f ) df m(f ) ( ) 1+α f m(f ) = 1 f p(f )v(f ) = f+ f df p(f )β(f ) m(f ) f df 0 d df m(f )
38 Exact Solution for Stationary State Constant flux condition v(f ) 0 f f f f + β(f )µ(f f ) Recall df dt = v(f ) µ(f f ) = d m(f ) df m(f ) ( ) 1+α f m(f ) = 1 f p(f )v(f ) m(f ) = f+ f df p(f )β(f ) m(f )
39 Exact Solution for Stationary State Constant flux condition v(f ) 0 f f f f + β(f )µ(f f ) Recall df dt = v(f ) µ(f f ) = d m(f ) df m(f ) ( ) 1+α f m(f ) = 1 f d p(f )v(f ) p(f )β(f ) = df m(f ) m(f )
40 Exact Solution for Stationary State Constant flux condition v(f ) 0 f f f f + β(f )µ(f f ) Recall df dt = v(f ) µ(f f ) = d m(f ) df m(f ) ( ) 1+α f m(f ) = 1 f d p(f )v(f ) p(f )β(f ) = df m(f ) m(f ) p(f ) = C m(f ) ( ) β(f ) v(f ) exp v(f )
41 Examples 1.5 (a) (b) p(f/f+) (c) (d) p(f/f+) f /f f /f +
42 Optimal strategies We characterise the population strategy by the value of k A, which is the control parameter for the population balance. We define Optimal Strategies as the values of k A which maximise the average fitness f in the stationary state. Two optimal strategies emerge: f λ = 10 λ = 1 λ = 0.1 λ = k A
43 Optimal strategies cont. Two possible optimal strategies 1 k A = 0 (no switching to unfit state) 2 k A ka where ka yields f + = f (saturation fitness = response threshold) f(t) 1 no switching switching t t
44 Conclusions for population dynamics in changing environments New kind of environments Catastrophic Responsive Switching can be a good strategy Threshold mechanism (different from bet hedging) Two main strategies: no switching: grow faster oblivious to catastrophes switching: grow slower but try not to get caught Outlook: Generalise to saturating populations
45 Summary Plan I Thoughts on biophysical modelling II Switching between states III Microscopic dynamics: model linear feedback switch IV Macroscopic dynamics: population growth in a catastrophic environment References: P. Visco, R. J. Allen, M.R. Evans, Phys. Rev. Lett 2008, Phys. Rev. E 2009 P. Visco, R. J. Allen, S. N. Majumdar, M.R. Evans, Biophysical Journal 2010
Supplement to Call Centers with Delay Information: Models and Insights
Supplement to Call Centers with Delay Information: Models and Insights Oualid Jouini 1 Zeynep Akşin 2 Yves Dallery 1 1 Laboratoire Genie Industriel, Ecole Centrale Paris, Grande Voie des Vignes, 92290
More informationStochastic Gene Expression in Prokaryotes: A Point Process Approach
Stochastic Gene Expression in Prokaryotes: A Point Process Approach Emanuele LEONCINI INRIA Rocquencourt - INRA Jouy-en-Josas Mathematical Modeling in Cell Biology March 27 th 2013 Emanuele LEONCINI (INRIA)
More informationA Mathematical Model of a Synthetically Constructed Genetic Toggle Switch
BENG 221 Mathematical Methods in Bioengineering Project Report A Mathematical Model of a Synthetically Constructed Genetic Toggle Switch Nick Csicsery & Ricky O Laughlin October 15, 2013 1 TABLE OF CONTENTS
More informationChapter 6: Biological Networks
Chapter 6: Biological Networks 6.4 Engineering Synthetic Networks Prof. Yechiam Yemini (YY) Computer Science Department Columbia University Overview Constructing regulatory gates A genetic toggle switch;
More informationStochastic Gene Expression in Prokaryotes: A Point Process Approach
Stochastic Gene Expression in Prokaryotes: A Point Process Approach Emanuele LEONCINI INRIA Rocquencourt - INRA Jouy-en-Josas ASMDA Mataró June 28 th 2013 Emanuele LEONCINI (INRIA) Stochastic Gene Expression
More informationHydrodynamic Limits of Randomized Load Balancing Networks
Hydrodynamic Limits of Randomized Load Balancing Networks Kavita Ramanan and Mohammadreza Aghajani Brown University Stochastic Networks and Stochastic Geometry a conference in honour of François Baccelli
More informationThe search process for small targets in cellular microdomains! Jürgen Reingruber
The search process for small targets in cellular microdomains! Jürgen Reingruber Department of Computational Biology Ecole Normale Supérieure Paris, France Outline 1. Search processes in cellular biology
More informationEquation-free analysis of two-component system signalling model reveals the emergence of co-existing phenotypes in the absence of multistationarity
1 Equation-free analysis of two-component system signalling model reveals the emergence of co-existing phenotypes in the absence of multistationarity Rebecca B. Hoyle 1,, Daniele Avitabile 2, Andrzej M.
More informationPositive Feedback and Bistable Systems. Copyright 2008: Sauro
Positive Feedback and Bistable Systems 1 Copyright 2008: Sauro Non-Hysteretic Switches; Ultrasensitivity; Memoryless Switches Output These systems have no memory, that is, once the input signal is removed,
More informationAdditional Modeling Information
1 Additional Modeling Information Temperature Control of Fimbriation Circuit Switch in Uropathogenic Escherichia coli: Quantitative Analysis via Automated Model Abstraction Hiroyuki Kuwahara, Chris J.
More informationBrownian Motion and Stochastic Flow Systems. J.M Harrison
Brownian Motion and Stochastic Flow Systems 1 J.M Harrison Report written by Siva K. Gorantla I. INTRODUCTION Brownian motion is the seemingly random movement of particles suspended in a fluid or a mathematical
More informationPlanning And Scheduling Maintenance Resources In A Complex System
Planning And Scheduling Maintenance Resources In A Complex System Martin Newby School of Engineering and Mathematical Sciences City University of London London m.j.newbycity.ac.uk Colin Barker QuaRCQ Group
More informationLecture 1 MODULE 3 GENE EXPRESSION AND REGULATION OF GENE EXPRESSION. Professor Bharat Patel Office: Science 2, 2.36 Email: b.patel@griffith.edu.
Lecture 1 MODULE 3 GENE EXPRESSION AND REGULATION OF GENE EXPRESSION Professor Bharat Patel Office: Science 2, 2.36 Email: b.patel@griffith.edu.au What is Gene Expression & Gene Regulation? 1. Gene Expression
More informationA Uniform Asymptotic Estimate for Discounted Aggregate Claims with Subexponential Tails
12th International Congress on Insurance: Mathematics and Economics July 16-18, 2008 A Uniform Asymptotic Estimate for Discounted Aggregate Claims with Subexponential Tails XUEMIAO HAO (Based on a joint
More informationDNA Insertions and Deletions in the Human Genome. Philipp W. Messer
DNA Insertions and Deletions in the Human Genome Philipp W. Messer Genetic Variation CGACAATAGCGCTCTTACTACGTGTATCG : : CGACAATGGCGCT---ACTACGTGCATCG 1. Nucleotide mutations 2. Genomic rearrangements 3.
More informationQualitative modeling of biological systems
Qualitative modeling of biological systems The functional form of regulatory relationships and kinetic parameters are often unknown Increasing evidence for robustness to changes in kinetic parameters.
More informationQualitative analysis of regulatory networks
Qualitative analsis of regulator networks Denis THIEFFRY (LGPD-IBDM, Marseille, France) Introduction Formal tools for the analsis of gene networks Graph-based representation of regulator networks Dnamical
More informationα α λ α = = λ λ α ψ = = α α α λ λ ψ α = + β = > θ θ β > β β θ θ θ β θ β γ θ β = γ θ > β > γ θ β γ = θ β = θ β = θ β = β θ = β β θ = = = β β θ = + α α α α α = = λ λ λ λ λ λ λ = λ λ α α α α λ ψ + α =
More informationRNA & Protein Synthesis
RNA & Protein Synthesis Genes send messages to cellular machinery RNA Plays a major role in process Process has three phases (Genetic) Transcription (Genetic) Translation Protein Synthesis RNA Synthesis
More informationSome stability results of parameter identification in a jump diffusion model
Some stability results of parameter identification in a jump diffusion model D. Düvelmeyer Technische Universität Chemnitz, Fakultät für Mathematik, 09107 Chemnitz, Germany Abstract In this paper we discuss
More informationLocalised Sex, Contingency and Mutator Genes. Bacterial Genetics as a Metaphor for Computing Systems
Localised Sex, Contingency and Mutator Genes Bacterial Genetics as a Metaphor for Computing Systems Outline Living Systems as metaphors Evolutionary mechanisms Mutation Sex and Localized sex Contingent
More informationCellLine, a stochastic cell lineage simulator: Manual
CellLine, a stochastic cell lineage simulator: Manual Andre S. Ribeiro, Daniel A. Charlebois, Jason Lloyd-Price July 23, 2007 1 Introduction This document explains how to work with the CellLine modules
More informationTrading activity as driven Poisson process: comparison with empirical data
Trading activity as driven Poisson process: comparison with empirical data V. Gontis, B. Kaulakys, J. Ruseckas Institute of Theoretical Physics and Astronomy of Vilnius University, A. Goštauto 2, LT-008
More informationViscoelasticity of Polymer Fluids.
Viscoelasticity of Polymer Fluids. Main Properties of Polymer Fluids. Entangled polymer fluids are polymer melts and concentrated or semidilute (above the concentration c) solutions. In these systems polymer
More informationFinal Mathematics 5010, Section 1, Fall 2004 Instructor: D.A. Levin
Final Mathematics 51, Section 1, Fall 24 Instructor: D.A. Levin Name YOU MUST SHOW YOUR WORK TO RECEIVE CREDIT. A CORRECT ANSWER WITHOUT SHOWING YOUR REASONING WILL NOT RECEIVE CREDIT. Problem Points Possible
More informationDynamics of Biological Systems
Dynamics of Biological Systems Part I - Biological background and mathematical modelling Paolo Milazzo (Università di Pisa) Dynamics of biological systems 1 / 53 Introduction The recent developments in
More informationSemi-Markov model for market microstructure and HF trading
Semi-Markov model for market microstructure and HF trading LPMA, University Paris Diderot and JVN Institute, VNU, Ho-Chi-Minh City NUS-UTokyo Workshop on Quantitative Finance Singapore, 26-27 september
More informationComputation of Switch Time Distributions in Stochastic Gene Regulatory Networks
Computation of Switch Time Distributions in Stochastic Gene Regulatory Networks Brian Munsky and Mustafa Khammash Center for Control, Dynamical Systems and Computation University of California Santa Barbara,
More informationSelf-Organization in Nonequilibrium Systems
Self-Organization in Nonequilibrium Systems From Dissipative Structures to Order through Fluctuations G. Nicolis Universite Libre de Bruxelles Belgium I. Prigogine Universite Libre de Bruxelles Belgium
More informationSupporting Material to Crowding of molecular motors determines microtubule depolymerization
Supporting Material to Crowding of molecular motors determines microtubule depolymerization Louis Reese Anna Melbinger Erwin Frey Arnold Sommerfeld Center for Theoretical Physics and Center for NanoScience,
More informationConsensus and Polarization in a Three-State Constrained Voter Model
Consensus and Polarization in a Three-State Constrained Voter Model Department of Applied Mathematics University of Leeds The Unexpected Conference, Paris 14-16/11/2011 Big questions Outline Talk based
More informationThe Exponential Distribution
21 The Exponential Distribution From Discrete-Time to Continuous-Time: In Chapter 6 of the text we will be considering Markov processes in continuous time. In a sense, we already have a very good understanding
More informationEXIT TIME PROBLEMS AND ESCAPE FROM A POTENTIAL WELL
EXIT TIME PROBLEMS AND ESCAPE FROM A POTENTIAL WELL Exit Time problems and Escape from a Potential Well Escape From a Potential Well There are many systems in physics, chemistry and biology that exist
More information2038-20. Conference: From DNA-Inspired Physics to Physics-Inspired Biology. 1-5 June 2009. How Proteins Find Their Targets on DNA
2038-20 Conference: From DNA-Inspired Physics to Physics-Inspired Biology 1-5 June 2009 How Proteins Find Their Targets on DNA Anatoly B. KOLOMEISKY Rice University, Department of Chemistry Houston TX
More informationThe Joint Distribution of Server State and Queue Length of M/M/1/1 Retrial Queue with Abandonment and Feedback
The Joint Distribution of Server State and Queue Length of M/M/1/1 Retrial Queue with Abandonment and Feedback Hamada Alshaer Université Pierre et Marie Curie - Lip 6 7515 Paris, France Hamada.alshaer@lip6.fr
More informationGene Switches Teacher Information
STO-143 Gene Switches Teacher Information Summary Kit contains How do bacteria turn on and turn off genes? Students model the action of the lac operon that regulates the expression of genes essential for
More informationPerformance Analysis of a Telephone System with both Patient and Impatient Customers
Performance Analysis of a Telephone System with both Patient and Impatient Customers Yiqiang Quennel Zhao Department of Mathematics and Statistics University of Winnipeg Winnipeg, Manitoba Canada R3B 2E9
More informationPricing of an Exotic Forward Contract
Pricing of an Exotic Forward Contract Jirô Akahori, Yuji Hishida and Maho Nishida Dept. of Mathematical Sciences, Ritsumeikan University 1-1-1 Nojihigashi, Kusatsu, Shiga 525-8577, Japan E-mail: {akahori,
More informationModelling the performance of computer mirroring with difference queues
Modelling the performance of computer mirroring with difference queues Przemyslaw Pochec Faculty of Computer Science University of New Brunswick, Fredericton, Canada E3A 5A3 email pochec@unb.ca ABSTRACT
More informationRadioactivity III: Measurement of Half Life.
PHY 192 Half Life 1 Radioactivity III: Measurement of Half Life. Introduction This experiment will once again use the apparatus of the first experiment, this time to measure radiation intensity as a function
More information2. Illustration of the Nikkei 225 option data
1. Introduction 2. Illustration of the Nikkei 225 option data 2.1 A brief outline of the Nikkei 225 options market τ 2.2 Estimation of the theoretical price τ = + ε ε = = + ε + = + + + = + ε + ε + ε =
More informationNonparametric adaptive age replacement with a one-cycle criterion
Nonparametric adaptive age replacement with a one-cycle criterion P. Coolen-Schrijner, F.P.A. Coolen Department of Mathematical Sciences University of Durham, Durham, DH1 3LE, UK e-mail: Pauline.Schrijner@durham.ac.uk
More informationOptimal order placement in a limit order book. Adrien de Larrard and Xin Guo. Laboratoire de Probabilités, Univ Paris VI & UC Berkeley
Optimal order placement in a limit order book Laboratoire de Probabilités, Univ Paris VI & UC Berkeley Outline 1 Background: Algorithm trading in different time scales 2 Some note on optimal execution
More informationName Class Date. Figure 13 1. 2. Which nucleotide in Figure 13 1 indicates the nucleic acid above is RNA? a. uracil c. cytosine b. guanine d.
13 Multiple Choice RNA and Protein Synthesis Chapter Test A Write the letter that best answers the question or completes the statement on the line provided. 1. Which of the following are found in both
More informationNeural Networks and Learning Systems
Neural Networks and Learning Systems Exercise Collection, Class 9 March 2010 x 1 x 2 x N w 11 3 W 11 h 3 2 3 h N w NN h 1 W NN y Neural Networks and Learning Systems Exercise Collection c Medical Informatics,
More informationImplementing the combing method in the dynamic Monte Carlo. Fedde Kuilman PNR_131_2012_008
Implementing the combing method in the dynamic Monte Carlo Fedde Kuilman PNR_131_2012_008 Faculteit Technische Natuurwetenschappen Implementing the combing method in the dynamic Monte Carlo. Bachelor End
More informationMAINTAINED SYSTEMS. Harry G. Kwatny. Department of Mechanical Engineering & Mechanics Drexel University ENGINEERING RELIABILITY INTRODUCTION
MAINTAINED SYSTEMS Harry G. Kwatny Department of Mechanical Engineering & Mechanics Drexel University OUTLINE MAINTE MAINTE MAINTAINED UNITS Maintenance can be employed in two different manners: Preventive
More informationTutorial: Genetic circuits and noise
Tutorial: Genetic circuits and noise Matt Scott Quantitative Approaches to Gene Regulatory Systems Summer School, July 2006 University of California, San Diego The analysis of natural genetic networks
More informationUnderstanding the dynamics and function of cellular networks
Understanding the dynamics and function of cellular networks Cells are complex systems functionally diverse elements diverse interactions that form networks signal transduction-, gene regulatory-, metabolic-
More informationOnline Appendix to Stochastic Imitative Game Dynamics with Committed Agents
Online Appendix to Stochastic Imitative Game Dynamics with Committed Agents William H. Sandholm January 6, 22 O.. Imitative protocols, mean dynamics, and equilibrium selection In this section, we consider
More informationReaction Engineering of Polymer Electrolyte Membrane Fuel Cells
Reaction Engineering of Polymer Electrolyte Membrane Fuel Cells A new approach to elucidate the operation and control of Polymer Electrolyte Membrane (PEM) fuel cells is being developed. A global reactor
More informationarxiv:cond-mat/0005235 v1 15 May 2000
arxiv:cond-mat/0005235 v1 15 May 2000 Stability and noise in biochemical switches William Bialek NEC Research Institute 4 Independence Way Princeton, New Jersey 08540 bialek@research.nj.nec.com December
More informationUniversity of Maryland Fraternity & Sorority Life Spring 2015 Academic Report
University of Maryland Fraternity & Sorority Life Academic Report Academic and Population Statistics Population: # of Students: # of New Members: Avg. Size: Avg. GPA: % of the Undergraduate Population
More informationStructure and Function of DNA
Structure and Function of DNA DNA and RNA Structure DNA and RNA are nucleic acids. They consist of chemical units called nucleotides. The nucleotides are joined by a sugar-phosphate backbone. The four
More informationRNA Structure and folding
RNA Structure and folding Overview: The main functional biomolecules in cells are polymers DNA, RNA and proteins For RNA and Proteins, the specific sequence of the polymer dictates its final structure
More informationSTUDENT VERSION INSECT COLONY SURVIVAL OPTIMIZATION
STUDENT VERSION INSECT COLONY SURVIVAL OPTIMIZATION STATEMENT We model insect colony propagation or survival from nature using differential equations. We ask you to analyze and report on what is going
More informationMonte Carlo Methods in Finance
Author: Yiyang Yang Advisor: Pr. Xiaolin Li, Pr. Zari Rachev Department of Applied Mathematics and Statistics State University of New York at Stony Brook October 2, 2012 Outline Introduction 1 Introduction
More informationPHYSICAL REVIEW LETTERS
PHYSICAL REVIEW LETTERS VOLUME 86 28 MAY 21 NUMBER 22 Mathematical Analysis of Coupled Parallel Simulations Michael R. Shirts and Vijay S. Pande Department of Chemistry, Stanford University, Stanford,
More informationA Mathematical Study of Purchasing Airline Tickets
A Mathematical Study of Purchasing Airline Tickets THESIS Presented in Partial Fulfillment of the Requirements for the Degree Master of Mathematical Science in the Graduate School of The Ohio State University
More informationLimitations of Equilibrium Or: What if τ LS τ adj?
Limitations of Equilibrium Or: What if τ LS τ adj? Bob Plant, Laura Davies Department of Meteorology, University of Reading, UK With thanks to: Steve Derbyshire, Alan Grant, Steve Woolnough and Jeff Chagnon
More informationCHAPTER 6: Continuous Uniform Distribution: 6.1. Definition: The density function of the continuous random variable X on the interval [A, B] is.
Some Continuous Probability Distributions CHAPTER 6: Continuous Uniform Distribution: 6. Definition: The density function of the continuous random variable X on the interval [A, B] is B A A x B f(x; A,
More informationNuclear Physics. Nuclear Physics comprises the study of:
Nuclear Physics Nuclear Physics comprises the study of: The general properties of nuclei The particles contained in the nucleus The interaction between these particles Radioactivity and nuclear reactions
More informationMATH4427 Notebook 2 Spring 2016. 2 MATH4427 Notebook 2 3. 2.1 Definitions and Examples... 3. 2.2 Performance Measures for Estimators...
MATH4427 Notebook 2 Spring 2016 prepared by Professor Jenny Baglivo c Copyright 2009-2016 by Jenny A. Baglivo. All Rights Reserved. Contents 2 MATH4427 Notebook 2 3 2.1 Definitions and Examples...................................
More informationIntegrating DNA Motif Discovery and Genome-Wide Expression Analysis. Erin M. Conlon
Integrating DNA Motif Discovery and Genome-Wide Expression Analysis Department of Mathematics and Statistics University of Massachusetts Amherst Statistics in Functional Genomics Workshop Ascona, Switzerland
More informationFractional approaches to dielectric broadband spectroscopy
Fractional approaches to dielectric broadband spectroscopy Simon Candelaresi, Rudolf Hilfer ICP, Uni Stuttgart 2008-02-26 Overview Dielectric Broadband Spectroscopy Use composite fractional time evolution
More informationOnline Appendix. Supplemental Material for Insider Trading, Stochastic Liquidity and. Equilibrium Prices. by Pierre Collin-Dufresne and Vyacheslav Fos
Online Appendix Supplemental Material for Insider Trading, Stochastic Liquidity and Equilibrium Prices by Pierre Collin-Dufresne and Vyacheslav Fos 1. Deterministic growth rate of noise trader volatility
More informationStatistical mechanics for real biological networks
Statistical mechanics for real biological networks William Bialek Joseph Henry Laboratories of Physics, and Lewis-Sigler Institute for Integrative Genomics Princeton University Initiative for the Theoretical
More information4. DNA replication Pages: 979-984 Difficulty: 2 Ans: C Which one of the following statements about enzymes that interact with DNA is true?
Chapter 25 DNA Metabolism Multiple Choice Questions 1. DNA replication Page: 977 Difficulty: 2 Ans: C The Meselson-Stahl experiment established that: A) DNA polymerase has a crucial role in DNA synthesis.
More informationA stochastic individual-based model for immunotherapy of cancer
A stochastic individual-based model for immunotherapy of cancer Loren Coquille - Joint work with Martina Baar, Anton Bovier, Hannah Mayer (IAM Bonn) Michael Hölzel, Meri Rogava, Thomas Tüting (UniKlinik
More informationSecond Order Systems
Second Order Systems Second Order Equations Standard Form G () s = τ s K + ζτs + 1 K = Gain τ = Natural Period of Oscillation ζ = Damping Factor (zeta) Note: this has to be 1.0!!! Corresponding Differential
More informationTopic 2: Energy in Biological Systems
Topic 2: Energy in Biological Systems Outline: Types of energy inside cells Heat & Free Energy Energy and Equilibrium An Introduction to Entropy Types of energy in cells and the cost to build the parts
More informationDisease Transmission Networks
Dynamics of Disease Transmission Networks Winfried Just Ohio University Presented at the workshop Teaching Discrete and Algebraic Mathematical Biology to Undergraduates MBI, Columbus, OH, July 31, 2013
More informationBIOE 370 1. Lotka-Volterra Model L-V model with density-dependent prey population growth
BIOE 370 1 Populus Simulations of Predator-Prey Population Dynamics. Lotka-Volterra Model L-V model with density-dependent prey population growth Theta-Logistic Model Effects on dynamics of different functional
More informationEfficient Load Balancing by Adaptive Bypasses for the Migration on the Internet
Efficient Load Balancing by Adaptive Bypasses for the Migration on the Internet Yukio Hayashi yhayashi@jaist.ac.jp Japan Advanced Institute of Science and Technology ICCS 03 Workshop on Grid Computing,
More informationGenetic information (DNA) determines structure of proteins DNA RNA proteins cell structure 3.11 3.15 enzymes control cell chemistry ( metabolism )
Biology 1406 Exam 3 Notes Structure of DNA Ch. 10 Genetic information (DNA) determines structure of proteins DNA RNA proteins cell structure 3.11 3.15 enzymes control cell chemistry ( metabolism ) Proteins
More informationTranscription and Translation of DNA
Transcription and Translation of DNA Genotype our genetic constitution ( makeup) is determined (controlled) by the sequence of bases in its genes Phenotype determined by the proteins synthesised when genes
More informationNon-equilibrium Thermodynamics
Chapter 2 Non-equilibrium Thermodynamics 2.1 Response, Relaxation and Correlation At the beginning of the 21st century, the thermodynamics of systems far from equilibrium remains poorly understood. However,
More informationGenerating Random Numbers Variance Reduction Quasi-Monte Carlo. Simulation Methods. Leonid Kogan. MIT, Sloan. 15.450, Fall 2010
Simulation Methods Leonid Kogan MIT, Sloan 15.450, Fall 2010 c Leonid Kogan ( MIT, Sloan ) Simulation Methods 15.450, Fall 2010 1 / 35 Outline 1 Generating Random Numbers 2 Variance Reduction 3 Quasi-Monte
More informationReal-time PCR: Understanding C t
APPLICATION NOTE Real-Time PCR Real-time PCR: Understanding C t Real-time PCR, also called quantitative PCR or qpcr, can provide a simple and elegant method for determining the amount of a target sequence
More informationThe Dynamics of a Genetic Algorithm on a Model Hard Optimization Problem
The Dynamics of a Genetic Algorithm on a Model Hard Optimization Problem Alex Rogers Adam Prügel-Bennett Image, Speech, and Intelligent Systems Research Group, Department of Electronics and Computer Science,
More informationSection A. Index. Section A. Planning, Budgeting and Forecasting Section A.2 Forecasting techniques... 1. Page 1 of 11. EduPristine CMA - Part I
Index Section A. Planning, Budgeting and Forecasting Section A.2 Forecasting techniques... 1 EduPristine CMA - Part I Page 1 of 11 Section A. Planning, Budgeting and Forecasting Section A.2 Forecasting
More informationMDM. Metabolic Drift Mutations - Attenuation Technology
MDM Metabolic Drift Mutations - Attenuation Technology Seite 2 Origin of MDM attenuation technology Prof. Dr. Klaus Linde Pioneer in R&D of human and animal vaccines University of Leipzig Germany Origin
More informationProblem Solving 8: RC and LR Circuits
MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics Problem Solving 8: RC and LR Circuits Section Table and Group (e.g. L04 3C ) Names Hand in one copy per group at the end of the Friday Problem
More informationBiological Sciences Initiative. Human Genome
Biological Sciences Initiative HHMI Human Genome Introduction In 2000, researchers from around the world published a draft sequence of the entire genome. 20 labs from 6 countries worked on the sequence.
More informationSelf-organized exploration and automatic sensor integration from the homeokinetic principle
Self-organized exploration and automatic sensor integration from the homeokinetic principle Ralf Der, Frank Hesse and René Liebscher Universität Leipzig, Institut für Informatik POB 920 D-04009 Leipzig
More informationLecture 13 Linear quadratic Lyapunov theory
EE363 Winter 28-9 Lecture 13 Linear quadratic Lyapunov theory the Lyapunov equation Lyapunov stability conditions the Lyapunov operator and integral evaluating quadratic integrals analysis of ARE discrete-time
More informationGraph theoretic approach to analyze amino acid network
Int. J. Adv. Appl. Math. and Mech. 2(3) (2015) 31-37 (ISSN: 2347-2529) Journal homepage: www.ijaamm.com International Journal of Advances in Applied Mathematics and Mechanics Graph theoretic approach to
More information13.4 Gene Regulation and Expression
13.4 Gene Regulation and Expression Lesson Objectives Describe gene regulation in prokaryotes. Explain how most eukaryotic genes are regulated. Relate gene regulation to development in multicellular organisms.
More informationRANDOM INTERVAL HOMEOMORPHISMS. MICHA L MISIUREWICZ Indiana University Purdue University Indianapolis
RANDOM INTERVAL HOMEOMORPHISMS MICHA L MISIUREWICZ Indiana University Purdue University Indianapolis This is a joint work with Lluís Alsedà Motivation: A talk by Yulij Ilyashenko. Two interval maps, applied
More informationAn exact formula for default swaptions pricing in the SSRJD stochastic intensity model
An exact formula for default swaptions pricing in the SSRJD stochastic intensity model Naoufel El-Bachir (joint work with D. Brigo, Banca IMI) Radon Institute, Linz May 31, 2007 ICMA Centre, University
More informationChapter 13 Introduction to Nonlinear Regression( 非 線 性 迴 歸 )
Chapter 13 Introduction to Nonlinear Regression( 非 線 性 迴 歸 ) and Neural Networks( 類 神 經 網 路 ) 許 湘 伶 Applied Linear Regression Models (Kutner, Nachtsheim, Neter, Li) hsuhl (NUK) LR Chap 10 1 / 35 13 Examples
More information2.500 Threshold. 2.000 1000e - 001. Threshold. Exponential phase. Cycle Number
application note Real-Time PCR: Understanding C T Real-Time PCR: Understanding C T 4.500 3.500 1000e + 001 4.000 3.000 1000e + 000 3.500 2.500 Threshold 3.000 2.000 1000e - 001 Rn 2500 Rn 1500 Rn 2000
More informationHedging Options In The Incomplete Market With Stochastic Volatility. Rituparna Sen Sunday, Nov 15
Hedging Options In The Incomplete Market With Stochastic Volatility Rituparna Sen Sunday, Nov 15 1. Motivation This is a pure jump model and hence avoids the theoretical drawbacks of continuous path models.
More informationChemical Kinetics. Reaction Rate: The change in the concentration of a reactant or a product with time (M/s). Reactant Products A B
Reaction Rates: Chemical Kinetics Reaction Rate: The change in the concentration of a reactant or a product with time (M/s). Reactant Products A B change in number of moles of B Average rate = change in
More informationUniversitätsstrasse 1, D-40225 Düsseldorf, Germany 3 Current address: Institut für Festkörperforschung,
Lane formation in oppositely charged colloidal mixtures - supplementary information Teun Vissers 1, Adam Wysocki 2,3, Martin Rex 2, Hartmut Löwen 2, C. Patrick Royall 1,4, Arnout Imhof 1, and Alfons van
More informationTHE DYING FIBONACCI TREE. 1. Introduction. Consider a tree with two types of nodes, say A and B, and the following properties:
THE DYING FIBONACCI TREE BERNHARD GITTENBERGER 1. Introduction Consider a tree with two types of nodes, say A and B, and the following properties: 1. Let the root be of type A.. Each node of type A produces
More informationPart 2: Analysis of Relationship Between Two Variables
Part 2: Analysis of Relationship Between Two Variables Linear Regression Linear correlation Significance Tests Multiple regression Linear Regression Y = a X + b Dependent Variable Independent Variable
More informationDecay of Radioactivity. Radioactive decay. The Math of Radioactive decay. Robert Miyaoka, PhD. Radioactive decay:
Decay of Radioactivity Robert Miyaoka, PhD rmiyaoka@u.washington.edu Nuclear Medicine Basic Science Lectures https://www.rad.washington.edu/research/research/groups/irl/ed ucation/basic-science-resident-lectures/2011-12-basic-scienceresident-lectures
More informatione.g. arrival of a customer to a service station or breakdown of a component in some system.
Poisson process Events occur at random instants of time at an average rate of λ events per second. e.g. arrival of a customer to a service station or breakdown of a component in some system. Let N(t) be
More informationSTCE. Fast Delta-Estimates for American Options by Adjoint Algorithmic Differentiation
Fast Delta-Estimates for American Options by Adjoint Algorithmic Differentiation Jens Deussen Software and Tools for Computational Engineering RWTH Aachen University 18 th European Workshop on Automatic
More information