2nd q-bio Summer School Homework

These are representative open-ended homework problems that the students will be asked to work on. New problems will be added soon.

Before arriving to the school, please browse these projects/homework problems and select the ones you'd like to work on. We expect that some of the homeworks will continue well after the school is over, leading to collaborative publications between the school faculty and the students.

2nd q-bio Summer School Themes

After the summer school, students will participate in the q-bio Conference in Santa Fe, NM, Aug 6-9, 2008; this facilitated the choice of the themes for the summer school. They are

Signal Transduction Systems

Lecture 1

Scope
An introduction to the cell signaling problem
Lecturer
Byron Goldstein

Lecture 2

Scope
Rule-based modeling
Lecturer
William S. Hlavacek

Lecture 3

Scope
Spatiotemporal aspects of signal transduction: models and experiments
Lecturer
Bridget S. Wilson

Lecture 4

Scope
Reverse engineering calcium ion channel kinetics
Lecturer
John E. Pearson

Stochasticity in Biochemistry and Systems Biology

Lecture 1

Scope
Stochastic effects in systems biology: Theoretical Foundations and Experimental Results, Part I
Lecturer
Brian Munsky
Synopsis
  • The importance of stochasticity in gene regulatory networks. Discussion of a couple key examples.
  • The physics behind stochastic chemical kinetics.
  • Connection between deterministic reaction rates and propensity functions.
  • Derivation of the Master Equation for discrete stochastic processes.
  • Analysis of the master equation for a simple transcription process.
  • Discussion of the importance of stochasticity in small populations.
Homework

Lecture 2

Scope
Stochastic effects in systems biology: Theoretical Foundations and Experimental Results, Part II
Lecturer
Brian Munsky
Synopsis
  • Solution of the master equation for systems with affine linear propensity functions.
  • Discussion of the effect of feedback.
  • Discussion of Kinetic Monte Carlo algorithms. Tau Leaping. Chemical Langevin equation. Time separation schemes. Hybrid methods.
  • Finite State projections techniques. Switch rate analysis.
  • Moment Closure techniques.
Homework

Lecture 3

Scope
Probability generating functional in stochastic kinetics
Lecturer
Nikolai Sinitsyn
Synopsis
  • Definitions of mesoscopic scale, mesoscopic systems and mesoscopic fluctuations. E. coli as a mesoscopic system.
  • Complexity of Markov chain equations. Definition and simplifying role of the probability generating function. Demonstration on a simple reaction-diffusion model.
  • Michaelis-Menten kinetics: definition, full derivation of the chemical flux generating function, including the treatment of boundary terms.
  • Brief review of recent single molecule experiments. Fano factor.
  • (If time permits). Brief review of analogy of generating function with quantum mechanical wave function. Applications to stochastic biochemical networks.
References
 
A comprehensive introduction to the method of generating functional can be found in
  • C. W. Gardiner. Handbook of Stochastic methods (Springer-Verlag Berlin Heidelberg, 2004).
Basics of the Michaelis-Menten kinetics can be found in many introductory biochemistry textbooks. A good exposition is in
  • David L. Nelson and Michael M. Cox, Lehninger Principles of Biochemistr (4th edition, W. H. Freeman, 2004).
Stochastic analog of the Michaelis-Menten kinetics was discussed in several recent publications. For example,
  • N. A. Sinitsyn and I. Nemenman, "The Berry phase and the pump flux in stochastic chemical kinetics", Euro. Phys. Lett. 77, 58001 (2007).
  • I. V. Gopich and A. Szabo, "Theory of statistics of kinetic transitions with application to single molecule enzyme catalysis", J. Chem. Phys. 124, 154712 (2006).
For a good example of a single molecule experiment on stochastic enzyme kinetics see
  • B. P. English et al. “Ever-fluctuating single enzyme molecules: Michaelis-Menten equation revisited”, Nature Chemical Biology 2, 87-94 (2005).
Analogies between quantum mechanical and stochastic evolutions can be learned from
  • V. Elgart and A. Kamenev, “Rare event statistics in reaction-diffusion systems”, Phys. Rev. E 70, 041106 (2004).
Homework
 
Generating functional techniques

Lecture 4

Scope
Signal processing in biochemical networks: Fourier transforms, central limit heorem, and all that, Part I
Lecturer
Ilya Nemenman
Synopsis
  • Introduction of the phototransduction cascade
  • Derivation of the Langevin equation from the master equation
  • Linearization of the Langevin equation
  • Correlation functions and spectra
  • LInear noise approximation
  • Universal results and their significance:
    • Low-pass filtering
    • Fluctuation-dissipation theorem
  • Temporal integration as a way of reducing noise
  • Filtering at early stages of phototransduction
References

Lecture 5

Scope
Signal processing in biochemical networks: Fourier transforms, central limit theorem, and all that. Part II
Lectures
Ilya Nemenman
Synopsis
  • Noise suppression for early phototransduction
    • Are all of the ideas conceptually the same?
  • Constraints on the distinguishability of signals
  • Frequency-dependent gain of the push-pull amplifier (futile cycle)
    • Energy constraints, amplification, and bandwidth
    • Cascades vs. simple amplifiers
  • Filtering: intrinsic noise and extrinsic noise
  • Optimal filtering: Wiener's matched filter
  • Long-term feedback, adaptation, and band-pass filtering
  • Optimal adaptation: mean, and (maybe) variance.
References
 
Same as for lecture 4 above.

Lecture 6

Scope
Selective transport through biological channels: does theory work?
Lecturer
Anton Zilman
Brief Plan
  • Selective biological transport: active vs. passive transport
  • Several examples of passive but selective biological channels
  • Major issues: selectivity, efficiency, speed
  • Historical survey of methods and concepts
  • General formulation of the transport selectivity problem in terms of stochastic processes
  • Theoretical models of selectivity
  • Comparison of the theoretical predictions with experiments

Genetic Regulatory Networks

Lecture 1

Scope
Prokaryotic gene regulation
Lecturer
Michael E. Wall, Los Alamos National Laboratory
Homework
 

1. Test a common assumption of TF-dependent promoter activity models

2. Extract model parameters from an early paper on lac induction

Lecture 2

Scope (part 1)
Boolean network models of genetic regulatory systems
Lecturer
Cynthia J. Olson Reichhardt, Los Alamos National Laboratory
Scope (part 2)
Information theoretic reconstruction of transcriptional networks from mRNA data
Lecturer
Ilya Nemenman, Los Alamos National Laboratory

Lecture 3

Scope
Eukaryotic gene regulation
Lecturer
Andre Levchenko, Johns Hopkins University

Lecture 4

Scope
Stochastic effects in genetic regulatory networks and signal-transduction systems
Lecturer
Tomasz Lipniacki, Institute of Fundamental Technological Research

Lecture 5

Scope
Characterization of protein-DNA interactions
Lecturer
Martha L. Bulyk, Harvard Medical School

Other Topics in Biological Modeling

Lecture 1

Scope
Modeling Viral Dynamics, Part I: How to model HIV Infection
Lecturer
Alan Perelson
Abstract

Mathematical modeling of HIV infection has lead to asignificant dvances in our knowledge about HIV and its treatment. This lecture will provide a tutorial about how one goes from data to developing models that have practical utility. Modeling will involve ordinary differential equations. The basic biology of HIV will be reviewed as well as the action of drugs used in therapy. If you have questions about HIV/AIDS this would be good venue to ask them.

References

Perelson, A. S. and Nelson, P. (1999). Mathematical analysis of HIV-1 dynamics in vivo. SIAM Rev. 41, 3-44.

Callaway, D. S. and Perelson, A. S. (2002). HIV-1 infection and low steady-state viral loads. Bull. Math. Biol. 64, 29–64.

Perelson, A. S. (2002). Modelling viral and immune system dynamics. Nature Rev. Immunol. 2, 28-36.

Rong, L., Feng, Z. and Perelson, A. S. (2007). Mathematical analysis of age-structured HIV-1 dynamics with combination therapy. SIAM J. Appl. Math. 67, 731-756.

Lecture 2

Scope
Modeling Viral Dynamics, Part II: Dynamics of CD4+ T cells in HIV-1 Infection
Lecturer
Ruy Ribeiro
Abstract

Mathematical modeling is becoming established in the immunologist’s toolbox as a method to gain insight into the dynamics of the immune response and its components. No more so than in the case of the study of human immunodeficiency virus (HIV) infection, where earlier work on the viral dynamics brought significant advances in our understanding of HIV replication and evolution. Here, I review different areas of the study of the dynamics of CD4+ T-cells in the setting of HIV, where modeling played important and diverse roles in helping us understand CD4+ T-cell homeostasis and the effect of HIV infection. Modeling has been applied to understand experiments labeling dividing cells with the objective of quantifying the turnover of CD4+ T-cells in health and infection; as well, models of thymic production have been crucial to define rigorously the de novo production of T-cells in primates. As the experimental techniques become more accurate and quantitative, modeling should play a more important part in both experimental design and data analysis.

References

1. Ribeiro RM “Dynamics of CD4+ T-cells in HIV-1 infection”, Immunology and Cell Biology 85: 287 (2007)

2. Ribeiro RM & Perelson AS “Determining thymic output quantitatively: using models to interpret experimental T-cell receptor excision circle (TREC) data”, Immunological Reviews 216: 21 (2007)

3. Asquith B et al. “Lymphocyte kinetics: the interpretation of labelling data”, Trends in Immunology 23: 596 (2002)

Problem
In T-cell labeling experiments, performed to infer the turnover of these cells, the contribution of new production from the thymus is often not included. In this case, the dynamics of T-cells in the periphery is modeled by a simple set of differential equations (such as those presented in reference 1 above). Assume that the thymus behaves as a conveyor belt, corresponding to the maturation of T-cells, where some proliferation occurs. Thus, during maturation some cells will pick up label. Write a model or a simulation for the fraction of labeled cells in the periphery that takes into account both peripheral division and input from a conveyor-belt type thymus. Discuss any differences observed in the label profiles in relation to the simple periphery-only model.

Lecture 3

Scope
Modeling Cancer Development, Part I Experimental models
Lecturer
[ James Freyer]
Abstract
A solid tumor in a human is arguably one of the most unique, complex and chaotic biological systems in existence. Contributing greatly to this complexity is the highly heterogeneous tumor microenvironment, which has both spatial and temporal variations in an unaccountably large number of parameters (extracellular chemistry, cellular physiology, metabolism, gene expression and protein composition, to name a few). Unfortunately, this unique microenvironment has numerous adverse effects on the response of a tumor to essentially every therapy that has been devised to date. Thus, improving our understanding of this extremely complex biological system will have benefits for cancer therapy as well as for basic biology. An increasingly important tool in this field is the use of model systems, both experimental and theoretical. This lecture will start with a basic description of the tumor microenvironment, including mechanisms behind the heterogeneity, recent advances in assaying the microenvironment, and impacts on cancer therapy. This will be followed by a description of three-dimensional (3-D) experimental tumor models, focusing on the multicellular spheroid that we use in our laboratory. Two examples of our recent experimental work with spheroids will demonstrate how this system can be used to answer basic questions on the regulation of the cell cycle and protein expression. A new application for spheroids will be presented, along with a new experimental model system we have under development. The lecture will conclude with a description of theoretical models used to describe tumor growth and the tumor microenvironment, including an introduction to a multiscale model developed at Los Alamos that will be presented in much more detail in a subsequent lecture in this series.

Lecture 4

Scope
Modeling Cancer Development, Part II Multiscale cell-based models
Lecturer
Yi Jiang
Abstract
Cancer has become the leading cause of disease death for middle aged Americans. At the same time, after a quarter century of rapid advances, cancer research has generated a rich and complex body of knowledge. We have developed a cell-based, multiscale modeling framework to model cancer development based on this body of knowledge. Our model includes a cellular model for cell dynamics (cell growth, division, death, migration and adhesion), an intracellular protein regulatory network for cell cycle control and a signaling network for cell decision-making, and extracellular reaction-diffusion chemical dynamics. This model has produced avascular tumor growth dynamics that agree with tumor spheroid experiments; it has generated realistic sprout patterns in tumor-induced angiogenesis; it has also shown potential for investigating chemotherapeutic strategies for tumor. Given the biological flexibility of the model, we believe that it can facilitate a deeper understanding of the cellular and molecular interactions associated with cancer progression and treatment, and potentially guide experimental design and interpretation.
References

1.Yi Jiang, Jelena Pjesivac, Charles Cantrell and James Freyer, "A Multiscale Model for Avascular Tumor Growth ", Biophysical Journal , vol. 89, pp. 3873--3883, 2005

2.Amy Bauer, Trachette Jackson and Yi Jiang, "A Cell-Based Model Exhibiting Branching and Anastomosis During Tumor-Induced Angiogenesis", Biophysical Journal , vol. 92, pp. 3105--3121, 2007

Lecture 5

Scope
Protein dynamics
Lecturer
Hans Frauenfelder
Abstract
Proteins are involved in essentially every biological reaction. In texts they are usually shown just as X-ray diffraction reveals them, namely rigid, without hydration shell and bulk solvent. Proteins are, however, dynamic systems that continuously fluctuate and the fluctuations are essential for functions. The lecture will discuss two concepts that are the basis for understanding the dynamics, namely the existence of an energy landscape and the influence of the hydration shell and the bulk solvent.

Lecture 6

Scope
Random Walk Techniques in Quantitative Biology: Molecules to Mice
Lecturer
Nitant Kenkre
Abstract
Random Walk techniques, equivalently Master equation methods, will be introduced and applied to a quantitative description of biological systems on a wide variety of scales: transmembrane molecules diffusing in cells, bacteria moving in Petri dishes, and rodents traversing the landscape in the context of the Hantavirus epidemic. A brief exposition to effective medium theories and nonlinearities in diffusion equations will be included in the lecture.

Lecture 7

Scope
 ??
Lecturer
[Cliff Unkefer]

Lecture 8

Scope
 
Lecturer
[Pat Unkefer]

Lecture 9

Scope
Molecular Simulation Techniques: Kinetic Monte Carlo, Accelerated Molecular Dynamics
Lecturer
Art Voter

Lecture 10

Scope
Manipulation of biological systems in controlled environments
Lecturer
Robert H. Austin

2nd q-bio Summer School Travel Information

Flying in

You can fly either to Albuquerque airport (ABQ) or to Santa Fe airport (SAF). Service to Santa Fe is very limited and expensive, though the airport is closer. From our personal experience, you may want to avoid the last flight of the day to either of the airports, and especially to Santa Fe. Both airports are quite small by big-city standards, and rebooking may be a problem if your flight is cancelled or delayed due to weather or other problems.

Getting to Los Alamos from the airports

Shuttles to Los Alamos from both airports are about $80 or more, and they need to be reserved in advance. Currently, the shuttle companies are

  • Roadrunner Shuttle (1-505-424-3367)
  • LA Shuttle (1-505-695-9407)

A viable alternative is a one-way car rental from either airport to Los Alamos. You should be able to get LANL contracted rate if you rent from Hertz and supply the LANL Hertz corporate discount number 72120 at the time of reservation and, more importantly, rental. This might be cheaper than other rental options since you will be able to decline those insurance coverages that are built into the contract rates. The Hertz car rental dropoff at Los Alamos (at Los Alamos airport, which has no commercial air service) is within a walking distance from the school hotel. Hertz rents only to those 21 years old or older.

Driving time to Los Alamos from Santa Fe and Albuquerque airports is about one and two hours, respectively. Traveling on a shuttle will take longer.

Transportation in Los Alamos

Atomic City Transit (the Blue route and the Trinity Shuttle) provides free scheduled service between the school hotel (County Offices stop) and the LA Research Park (TA-3 Park and Ride Stop, and then 5 minutes walk), were the lectures will be held. You will need to identify yourself as affiliated with LANL once you board the bus to qualify for free rides.

Weekend Transportation

There is no bus service on weekends. If you want to explore the Los Alamos vicinity, go to Santa Fe, Bandelier National Monument, or elsewhere, you will need to rent a car. You won't be able to use LANL contract rates for these personal rentals.

Parking

If you are bringing your own car, The school hotel has ample parking. Parking near the LA Research Park, where the lectures will be held, is by permit only. The permits will be available for all needing them in the school booklet, which you will receiveon the first day of classes.

Transportation to the First q-bio Conference

We anticipate that many of you will able to share car rides to the Second q-bio Conference at St. John's College in Santa Fe in the morning of Aug 6, 2007. Those who cannot get a ride this way, will be able to get to Santa Fe using public transit and/or a van provided by the organizers.

Meals

Continental breakfasts will be served at the hotel. Lunches will be catered at the school classrom during weekdays. For the rest of the meals, you should plan for $7-15 for lunches, and $15-25 for dinners at Los Alamos town restaurants. Note that very few places in town remain open late (and late means past 7pm in Los Alamos).

Entertainment

For things to do during the weekends, see What to do in the vicinity of Los Alamos. Also, keep in mind that we will organize some weekend trips for interested students, like rafting, hiking, etc.

Summer School Hotel

The summer school students will be housed at the Best Western Hilltop House Hotel at Los Alamos. The hotel features high speed internet access, microwaves, and refrigerators in every room.

Most rooms will be double occupancy for the summer school participants who are receiving travel awards. If you have roommate preferences, please contact the organizers.

Check in is on Sunday, July 20. When checking in, you will need to provide your name and passport / driver's license to the hotel staff.

Atomic City Transit, Route 1, provides a bus service from the hotel to the summer school location and LANL. The service is free if you identify yourself as a LANL affiliate.

Lecture Hall Information

Unless posted otherwise, all summer school classes will be held at the Motorola Building in the Los Alamos Research Park, Room 203 A/B. This is across the road from the main Laboratory Technical Area. The building has a nice coffee shop for lunches and coffee breaks, and it is adjacent to one of Los Alamos canyons with a network of hiking trails. It's less than 10 minutes ride from the Pajarito Ski Area, which offers its own network of adjacent hiking trails over the summer, and the drive to trailhead in the Santa Fe National Forest, Bandelier National Monument, and the Valles Caldera National Preserve is less than 30 minutes, allowing for nice afternoon hikes.

  • Map - the Research Park is at the top of the map, a bit to the left from the center; building number is 4200.
  • Another map, the Research Park is the building with the bllue roof. Note that the Jemez/Diamond interchange is outdated on the map, and you should forward the directions below instead.
  • Directions from the School Hotel: from the Hilltop House Hotel take a right on Trinity Dr, follow to the intersection with Diamond Dr. (medical center is to your left), take left, pass the bridge, turn right immediately after the bridge. Park at the parking lot (behind the fire station). The research park is a building with UCSD/UCSB logos right in front of you. A walk from the hotel will take about half an hour.
  • Parking permits will be provided in your registration packages.
  • Wireless and wired internet access will be available at the classroom. To connect to the wireless network, simply start up your browser and accept the terms and conditions.

Safety and Security

  • Each of the students is responsible for his/her own safe and secure work practices.
  • You must have a valid LANL/DOE badge to enter LANL-owned buildings.
  • Always wear your LANL visitor badge (above your waist) on LANL property.
  • Never wear your LANL visitor badge off LANL property.
  • If a foreigner, even with a valid badge, your access is limited to pre-approved buildings.
  • You must always swipe your badge to enter a building. No holding doors open for anyone or piggybacking.
  • Don't take pictures of LANL property.
  • Know your host (William S. Hlavacek or Ilya Nemenman).
  • Fill out a form for each electronic device (laptop, phone etc) that you might be carrying with you on LANL property - these forms are available from Charlotte in CNLS.
  • Never operate a wireless device (LAN, Bluetooth, or similar) on LANL property or nearby.
  • Never operate peer-to-peer file sharing software or FTP servers on LANL computers.
  • Do not install personally owned software on LANL computers.
  • If you connect to the internet via the LANL visitor network, limit use to work purposes only. Internet use is monitored.
  • Mobile phones are prohibited in some buildings (Bldg 123 for example).
  • Safety and security questions should be directed to: William S. Hlavacek (505-665-1355) or Ilya Nemenman (505-665-8250).

2nd q-bio Summer School Students

  1. Pradeep Bandaru, Columbia University
  2. Roberto Bertolusso, Rice University
  3. Hui-Chun Cheng, University of Texas Southwestern Medical Center at Dallas
  4. Bryan Daniels, Cornell University
  5. Thomas Graham, University of Chicago
  6. Beata Hat-Plewinska, Institute of Fundamental Technological Research
  7. Elizabeth D. Jones, Baylor College of Medicine
  8. Michal Komorowski, University of Warwick
  9. Pilong Li, University of Texas Southwestern Medical Center at Dallas
  10. Jintao Liu, University of Pittsburgh
  11. Zhen Liu, Virginia Polytechnic Institute and State University
  12. Andrew Mugler, Columbia University
  13. Sarah A. Nowak, University of California, Los Angeles
  14. Krzysztof Puszynski, Silesian University of Technology
  15. Wiet H. de Ronde, FOM Institute for Atomic and Molecular Research
  16. Abhyudai Singh, University of California, Santa Barbara
  17. Soon Heng (Chris) Tan, University of Toronto
  18. Jose Teles, Lund University
  19. Margaritis Voliotis, University of Leeds
  20. Siyuan (Steven) Wang, Princeton University
  21. Qiong Yang, Massachusetts Institute of Technology

© 2017 New Mexico Consortium