Event-Leaping in the Stochastic Simulation of Biochemistry State Space AnalysisThe Goddess Durga Marc Riedel, EE5393, Univ. of Minnesota.

Slides:



Advertisements
Similar presentations
Modeling and Simulation By Lecturer: Nada Ahmed. Introduction to simulation and Modeling.
Advertisements

Signals and Systems March 25, Summary thus far: software engineering Focused on abstraction and modularity in software engineering. Topics: procedures,
Cycle and Event Leaping State Space AnalysisThe Goddess Durga Marc Riedel, EE5393, Univ. of Minnesota.
1 Fault-Tolerant Computing Systems #6 Network Reliability Pattara Leelaprute Computer Engineering Department Kasetsart University
Simulation of Prokaryotic Genetic Circuits Jonny Wells and Jimmy Bai.
Probabilistic Verification of Discrete Event Systems using Acceptance Sampling Håkan L. S. YounesReid G. Simmons Carnegie Mellon University.
Applications of Stochastic Processes in Asset Price Modeling Preetam D’Souza.
Variants of Stochastic Simulation Algorithm Henry Ato Ogoe Department of Computer Science Åbo Akademi University.
Geog 409: Advanced Spatial Analysis & Modelling © J.M. Piwowar1Principles of Spatial Modelling.
Probabilistic Verification of Discrete Event Systems Håkan L. S. Younes Reid G. Simmons (initial work performed at HTC, Summer 2001)
Towards Systems Biology, October 2007, Grenoble Adam Halasz Ádám Halász joint work with Agung Julius, Vijay Kumar, George Pappas Mesoscopic and Stochastic.
Hidden Markov Models Fundamentals and applications to bioinformatics.
Weikang Qian Ph.D. Candidate Electrical & Computer Engineering
Marc Riedel Synthesizing Stochasticity in Biochemical Systems Electrical & Computer Engineering Jehoshua (Shuki) Bruck Caltech joint work with Brian Fett.
Digital Signal Processing with Biomolecular Reactions Hua Jiang, Aleksandra Kharam, Marc Riedel, and Keshab Parhi Electrical and Computer Engineering University.
Phillip Senum University of Minnesota. Motivation Much effort has been spent developing techniques for analyzing existing chemical systems. Comparatively.
Stochastic description of gene regulatory mechanisms Georg Fritz Statistical and Biological Physics Group LMU München Albert-Ludwigs Universität.
Stochasticity in molecular systems biology
Hidden Markov Models Pairwise Alignments. Hidden Markov Models Finite state automata with multiple states as a convenient description of complex dynamic.
Module Locking in Biochemical Synthesis Brian Fett and Marc D. Riedel Electrical and Computer Engineering University of Minnesota Brian’s Automated Modular.
Discrete Event Simulation How to generate RV according to a specified distribution? geometric Poisson etc. Example of a DEVS: repair problem.
ECE Synthesis & Verification1 ECE 667 Spring 2011 Synthesis and Verification of Digital Systems Verification Introduction.
Stochastic Simulation of Biological Systems. Chemical Reactions Reactants  Products m 1 R 1 + m 2 R 2 + ··· + m r R r – ! n 1 P 1 + n 2 P 2 + ··· + n.
Marc Riedel The Synthesis of Stochastic Logic for Nanoscale Computation IWLS 2007, San Diego May 31, 2007 Weikang Qian and John Backes Circuits & Biology.
Probabilistic Verification of Discrete Event Systems Håkan L. S. Younes.
Stochastic Transient Analysis of Biochemical Systems Marc D. Riedel Assistant Professor, Electrical and Computer Engineering Graduate Faculty, Biomedical.
Module C9 Simulation Concepts. NEED FOR SIMULATION Mathematical models we have studied thus far have “closed form” solutions –Obtained from formulas --
Marc Riedel A Discourse on Cycles Assistant Professor, ECE, Univ. Minnesota (in circuits and in computational biology) “In a good system, even evil men.
Circuit Engineers Doing Biology Marc D. Riedel Assistant Professor, Electrical and Computer Engineering University of Minnesota Café Scientifique A Discourse.
Simulation of Biochemical Reactions for Modeling of Cell DNA Repair Systems Dr. Moustafa Mohamed Salama Laboratory of Radiation Biology, JINR Supervisor.
Computer Simulation A Laboratory to Evaluate “What-if” Questions.
IE 594 : Research Methodology – Discrete Event Simulation David S. Kim Spring 2009.
Artificial Chemistries Autonomic Computer Systems University of Basel Yvonne Mathis.
Signals and Systems March 25, Summary thus far: software engineering Focused on abstraction and modularity in software engineering. Topics: procedures,
Stochastic models of chemical kinetics 5. Poisson process.
Artificial Intelligence Lecture No. 28 Dr. Asad Ali Safi ​ Assistant Professor, Department of Computer Science, COMSATS Institute of Information Technology.
1 Performance Evaluation of Computer Networks: Part II Objectives r Simulation Modeling r Classification of Simulation Modeling r Discrete-Event Simulation.
Stochastic Algorithms Some of the fastest known algorithms for certain tasks rely on chance Stochastic/Randomized Algorithms Two common variations – Monte.
Cristian Urs and Ben Riveira. Introduction The article we chose focuses on improving the performance of Genetic Algorithms by: Use of predictive models.
1 Local search and optimization Local search= use single current state and move to neighboring states. Advantages: –Use very little memory –Find often.
Some Probability Theory and Computational models A short overview.
1 6. Reliability computations Objectives Learn how to compute reliability of a component given the probability distributions on the stress,S, and the strength,
Tutor: Prof. Lucia Pomello Supervisors: Prof. Giancarlo Mauri Dr. Luciano Milanesi PhD Thesis Proposal Membrane systems: a framework for stochastic processes.
EE5393, Circuits, Computation, and Biology Computing with Probabilities 1,1,0,0,0,0,1,0 1,1,0,1,0,1,1,1 1,1,0,0,1,0,1,0 a = 6/8 c = 3/8 b = 4/8.
Marc D. Riedel Associate Professor, ECE University of Minnesota EE 5393: Circuits, Computation and Biology ORAND.
ECE 466/658: Performance Evaluation and Simulation Introduction Instructor: Christos Panayiotou.
Diffusion in Disordered Media Nicholas Senno PHYS /12/2013.
Conformant Probabilistic Planning via CSPs ICAPS-2003 Nathanael Hyafil & Fahiem Bacchus University of Toronto.
Marc Riedel – EE5393 The Synthesis of Robust Polynomial Arithmetic with Stochastic Logic Electrical & Computer Engineering University of Minnesota.
Synthesizing Stochasticity in Biochemical Systems In partial fulfillment of the requirements for a master of electrical engineering degree Brian Fett Marc.
Probabilistic Verification of Discrete Event Systems using Acceptance Sampling Håkan L. S. Younes Carnegie Mellon University.
The generalization of Bayes for continuous densities is that we have some density f(y|  ) where y and  are vectors of data and parameters with  being.
Writing and Compiling Code into Biochemistry Marc Riedel Assistant Professor, Electrical and Computer Engineering Graduate Faculty, Biomedical Informatics.
Biochemical Reactions: how types of molecules combine. Playing by the Rules + + 2a2a b c.
ECE 8443 – Pattern Recognition ECE 8527 – Introduction to Machine Learning and Pattern Recognition Objectives: Elements of a Discrete Model Evaluation.
Probabilistic Verification of Discrete Event Systems Håkan L. S. Younes.
Sayed Ahmad Salehi Marc D. Riedel Keshab K. Parhi University of Minnesota, USA Markov Chain Computations using Molecular Reactions 1.
Bio-Design Automation EE5393 – University of Minnesota Brian’s Automated Modular Biochemical Instantiator.
Biochemical Reactions computationinputsoutputs Molecular Triggers Molecular Products Synthesizing Biological Computation Protein-Protein Chemistry at the.
Final Project for Phys 642: An Introduction to Quantum Information and Quantum Computing Fall 2013 Implementing a Computer Simulation of Shor’s Quantum.
Business Modeling Lecturer: Ing. Martina Hanová, PhD.
Applications of Stochastic Processes in Asset Price Modeling Preetam D’Souza.
Analysis of Systems of Chemical Equations with Decision Diagrams A Decision DiagramThe Goddess Durga.
Overwiew of Various System Reliability Analysis Methods Kim Hyoung Ju 1.
Grammars, L-Systems Jim Whitehead UC Santa Cruz School of Engineering courses.soe.ucsc.edu/courses/cmps265/Spring14/01 23 Apr 2014.
Bacteria are engineered to produce an anti-cancer drug: Design Scenario drug triggering compound E. Coli.
Comparing Dynamic Programming / Decision Trees and Simulation Techniques BDAuU, Prof. Eckstein.
Example: Verification
Computational Biology
Dr. Arslan Ornek MATHEMATICAL MODELS
Presentation transcript:

Event-Leaping in the Stochastic Simulation of Biochemistry State Space AnalysisThe Goddess Durga Marc Riedel, EE5393, Univ. of Minnesota

Biochemical Reactions inputsoutputs Quantities of Different Types of Molecules computation View intra-cellular biochemistry as a form of computing. Chemical Reactions 

inputsoutputscomputation A = 1000 B = 333 C = 666 A = 0 B = 1334 C = 226  Chemical Reactions Biochemical Reactions View intra-cellular biochemistry as a form of computing. However, output is often stochastic.

inputsoutputscomputation A = 1000 B = 333 C = 666  Chemical Reactions Biochemical Reactions View intra-cellular biochemistry as a form of computing. C 1 : A 500 C 2 : B > 500 before A < 550 termination conditions Pr(C 1 ) = 0.61 Pr(C 2 ) = 0.39 A = 0 B = 1334 C = 226

Biochemical Reactions inputsoutputs Quantities of Different Types of Molecules Probability Distribution on terminal conditions computation View intra-cellular biochemistry as a form of computing. Chemical Reactions 

Model as a discrete Markov process. “States” ABC S1S1 S2S2 S3S3 A reaction transforms one state into another: e.g., Probabilistic Analysis Reactions R1R1 R2R2 R3R3

Why? Helpful for the purposes of analysis. Suggests the possibility of synthesis. Expertise from ECE can be brought to bear: algorithms, data structures, abstractions... Engineer a form of “logical” control of biochemical processes: outputs that depend on specific combinations of inputs. Biochemical Reactions View intra-cellular biochemistry as a form of computing.

See D. Gillespie, “Exact Stochastic Simulation of Coupled Chemical Reactions”, J. Phys. Chem R1R1 R2R2 R3R3 S 1 = [5, 5, 5] 0 Computing the Probability Distribution

S 1 = [5, 5, 5] 0 S 2 = [4, 7, 4] Choose R 3 and t = 3 seconds. R1R1 R2R2 R3R3 S 3 = [2, 6, 7] 4 Choose R 1 and t = 1 seconds. S 4 = [1, 8, 6] 6 Choose R 3 and t = 2 seconds. 3 Choose R 2 and t = 1 seconds. Computing the Probability Distribution

Randomness Pseudo-random numbers needed: R1R1 R2R2 R3R3 R4R4 probabilities generate a random number: choose R 2

choose R 2 Randomness Pseudo-random numbers needed: R1R1 R2R2 R3R3 R4R4 probabilities 01 generate a random number: choose R 4

Randomness Pseudo-random numbers needed: Generating random numbers is time consuming. If variance in probabilities is large, accuracy is wasted. R1R1 R2R2 R3R3 R4R4 probabilities 01 generate a random number: choose R 4

Event Leaping Explore high probability events further Along each path, probabilities are multiplicative.

Event Leaping Explore high probability events further When paths merge, probabilities are additive Along each path, probabilities are multiplicative.

Event Leaping Based on a single random number, leap directly to the boundary of explored region Explore high probability events further. When paths merge, probabilities are additive.

We need far fewer random numbers (e.g., factor of 10 reduction). We cache probability calculations. If we return to any portion of the region already visited, we immediately jump to the boundary of it. Event Leaping

State Space Analysis Characterize Evolution [0, 0, 12] [1, 1, 9][1, 5, 4][4, 4, 0][4, 0, 5] [2, 2, 6][2, 6, 1][5, 1, 2] p 1 p 2 p 3 p 4 p 5 p 6 p 7 p 8 p 9 p 10 p 11 p 12 p ppp )()(ppppppppppppp  [3, 3, 3] start [3, 3, 3] e.g., identify articulation points

State Space Analysis Characterize Evolution [2, 2, 6][2, 6, 1][5, 1, 2] [3, 3, 3] start e.g., identify “articulation” points Pr(C 1 ) > 0.99Pr(C 2 ) > 0.99

Synthesis Impose logical structure on computation. AND gate Conjunction of types X and Y : X Y Z N.B. operation is destructive Negation of X : T is a “source” (initialize to ≈ 1000) N is a neutral type X X If X ≈ 1000, T ≈ 0 If X ≈ 0, T ≈ 1000 NOT gate

Probabilistic Analysis Suppose:What is Analyze timing, “leakage currents”, etc. Reaction k1k1

Computing with Probabilistic Gates AND X Y Z p p   1)incorrectPr( )correctPr( q q   1)0X )1X q q   1)0Y )1Y 22 2)0 qpqpZ  22 21)1 qpqpZ 

Research Themes Conceptual Problems in Logic Design: models, physical attributes, complexity. Computational Approach: symbolic data structures, simulation, massively parallel computing. Application of Expertise to Computational Biology OR AND xxabcd