The document discusses multi-scale models in immunobiology. It defines multi-scale models as dealing with problems that have important features at multiple organizational, spatial, and temporal scales. Examples of multi-scale processes discussed include the recruitment of macrophages and neutrophils in response to wounding in zebrafish. Simple multiscale models are presented to model leukocyte chemotaxis and cytokine gradients. Approaches for calibrating and performing inference on complicated multi-scale models, such as approximate Bayesian computation, are also discussed.
Gaining Confidence in Signalling and Regulatory NetworksMichael Stumpf
Mathematical models of signalling and gene regulatory systems are abstractions of much more complicated processes. Even as more and larger data sets are becoming available we are not be able to dispense entirely with mechanistic models of real-world processes; nor should we. However, trying to develop informative and realistic models of such systems typically involves suitable statistical inference methods, domain expertise and a modicum of luck. Except
for cases where physical principles provide sucient guidance it will also be generally possible to come up with a large number of potential models that are compatible with a given biological system and any finite amount of data generated from experiments on that system.
Here I will discuss how we can systematically evaluate
potentially vast sets of mechanistic candidate models in light
of experimental and prior knowledge about biological systems. This enables us to evaluate quantitatively
the dependence of model inferences and predictions on the assumed model structures. Failure to consider the impact of structural uncertainty introduces biases into the analysis and potentially gives rise to misleading conclusions.
Statistical analysis of network data and evolution on GPUs: High-performance ...Michael Stumpf
Talk given on the 25th of January 2012 at the GPU in Statistics workshop in Warwick.
The talk covers approximate Bayesian computation (ABC) on GPUs, how to use spectral graph theory in ABC, and how to generate good random numbers on GPUs.
Gaining Confidence in Signalling and Regulatory NetworksMichael Stumpf
Mathematical models of signalling and gene regulatory systems are abstractions of much more complicated processes. Even as more and larger data sets are becoming available we are not be able to dispense entirely with mechanistic models of real-world processes; nor should we. However, trying to develop informative and realistic models of such systems typically involves suitable statistical inference methods, domain expertise and a modicum of luck. Except
for cases where physical principles provide sucient guidance it will also be generally possible to come up with a large number of potential models that are compatible with a given biological system and any finite amount of data generated from experiments on that system.
Here I will discuss how we can systematically evaluate
potentially vast sets of mechanistic candidate models in light
of experimental and prior knowledge about biological systems. This enables us to evaluate quantitatively
the dependence of model inferences and predictions on the assumed model structures. Failure to consider the impact of structural uncertainty introduces biases into the analysis and potentially gives rise to misleading conclusions.
Statistical analysis of network data and evolution on GPUs: High-performance ...Michael Stumpf
Talk given on the 25th of January 2012 at the GPU in Statistics workshop in Warwick.
The talk covers approximate Bayesian computation (ABC) on GPUs, how to use spectral graph theory in ABC, and how to generate good random numbers on GPUs.
Embracing GenAI - A Strategic ImperativePeter Windle
Artificial Intelligence (AI) technologies such as Generative AI, Image Generators and Large Language Models have had a dramatic impact on teaching, learning and assessment over the past 18 months. The most immediate threat AI posed was to Academic Integrity with Higher Education Institutes (HEIs) focusing their efforts on combating the use of GenAI in assessment. Guidelines were developed for staff and students, policies put in place too. Innovative educators have forged paths in the use of Generative AI for teaching, learning and assessments leading to pockets of transformation springing up across HEIs, often with little or no top-down guidance, support or direction.
This Gasta posits a strategic approach to integrating AI into HEIs to prepare staff, students and the curriculum for an evolving world and workplace. We will highlight the advantages of working with these technologies beyond the realm of teaching, learning and assessment by considering prompt engineering skills, industry impact, curriculum changes, and the need for staff upskilling. In contrast, not engaging strategically with Generative AI poses risks, including falling behind peers, missed opportunities and failing to ensure our graduates remain employable. The rapid evolution of AI technologies necessitates a proactive and strategic approach if we are to remain relevant.
Unit 8 - Information and Communication Technology (Paper I).pdfThiyagu K
This slides describes the basic concepts of ICT, basics of Email, Emerging Technology and Digital Initiatives in Education. This presentations aligns with the UGC Paper I syllabus.
Welcome to TechSoup New Member Orientation and Q&A (May 2024).pdfTechSoup
In this webinar you will learn how your organization can access TechSoup's wide variety of product discount and donation programs. From hardware to software, we'll give you a tour of the tools available to help your nonprofit with productivity, collaboration, financial management, donor tracking, security, and more.
Biological screening of herbal drugs: Introduction and Need for
Phyto-Pharmacological Screening, New Strategies for evaluating
Natural Products, In vitro evaluation techniques for Antioxidants, Antimicrobial and Anticancer drugs. In vivo evaluation techniques
for Anti-inflammatory, Antiulcer, Anticancer, Wound healing, Antidiabetic, Hepatoprotective, Cardio protective, Diuretics and
Antifertility, Toxicity studies as per OECD guidelines
Macroeconomics- Movie Location
This will be used as part of your Personal Professional Portfolio once graded.
Objective:
Prepare a presentation or a paper using research, basic comparative analysis, data organization and application of economic information. You will make an informed assessment of an economic climate outside of the United States to accomplish an entertainment industry objective.
How to Make a Field invisible in Odoo 17Celine George
It is possible to hide or invisible some fields in odoo. Commonly using “invisible” attribute in the field definition to invisible the fields. This slide will show how to make a field invisible in odoo 17.
Read| The latest issue of The Challenger is here! We are thrilled to announce that our school paper has qualified for the NATIONAL SCHOOLS PRESS CONFERENCE (NSPC) 2024. Thank you for your unwavering support and trust. Dive into the stories that made us stand out!
2024 State of Marketing Report – by HubspotMarius Sescu
https://www.hubspot.com/state-of-marketing
· Scaling relationships and proving ROI
· Social media is the place for search, sales, and service
· Authentic influencer partnerships fuel brand growth
· The strongest connections happen via call, click, chat, and camera.
· Time saved with AI leads to more creative work
· Seeking: A single source of truth
· TLDR; Get on social, try AI, and align your systems.
· More human marketing, powered by robots
ChatGPT is a revolutionary addition to the world since its introduction in 2022. A big shift in the sector of information gathering and processing happened because of this chatbot. What is the story of ChatGPT? How is the bot responding to prompts and generating contents? Swipe through these slides prepared by Expeed Software, a web development company regarding the development and technical intricacies of ChatGPT!
Embracing GenAI - A Strategic ImperativePeter Windle
Artificial Intelligence (AI) technologies such as Generative AI, Image Generators and Large Language Models have had a dramatic impact on teaching, learning and assessment over the past 18 months. The most immediate threat AI posed was to Academic Integrity with Higher Education Institutes (HEIs) focusing their efforts on combating the use of GenAI in assessment. Guidelines were developed for staff and students, policies put in place too. Innovative educators have forged paths in the use of Generative AI for teaching, learning and assessments leading to pockets of transformation springing up across HEIs, often with little or no top-down guidance, support or direction.
This Gasta posits a strategic approach to integrating AI into HEIs to prepare staff, students and the curriculum for an evolving world and workplace. We will highlight the advantages of working with these technologies beyond the realm of teaching, learning and assessment by considering prompt engineering skills, industry impact, curriculum changes, and the need for staff upskilling. In contrast, not engaging strategically with Generative AI poses risks, including falling behind peers, missed opportunities and failing to ensure our graduates remain employable. The rapid evolution of AI technologies necessitates a proactive and strategic approach if we are to remain relevant.
Unit 8 - Information and Communication Technology (Paper I).pdfThiyagu K
This slides describes the basic concepts of ICT, basics of Email, Emerging Technology and Digital Initiatives in Education. This presentations aligns with the UGC Paper I syllabus.
Welcome to TechSoup New Member Orientation and Q&A (May 2024).pdfTechSoup
In this webinar you will learn how your organization can access TechSoup's wide variety of product discount and donation programs. From hardware to software, we'll give you a tour of the tools available to help your nonprofit with productivity, collaboration, financial management, donor tracking, security, and more.
Biological screening of herbal drugs: Introduction and Need for
Phyto-Pharmacological Screening, New Strategies for evaluating
Natural Products, In vitro evaluation techniques for Antioxidants, Antimicrobial and Anticancer drugs. In vivo evaluation techniques
for Anti-inflammatory, Antiulcer, Anticancer, Wound healing, Antidiabetic, Hepatoprotective, Cardio protective, Diuretics and
Antifertility, Toxicity studies as per OECD guidelines
Macroeconomics- Movie Location
This will be used as part of your Personal Professional Portfolio once graded.
Objective:
Prepare a presentation or a paper using research, basic comparative analysis, data organization and application of economic information. You will make an informed assessment of an economic climate outside of the United States to accomplish an entertainment industry objective.
How to Make a Field invisible in Odoo 17Celine George
It is possible to hide or invisible some fields in odoo. Commonly using “invisible” attribute in the field definition to invisible the fields. This slide will show how to make a field invisible in odoo 17.
Read| The latest issue of The Challenger is here! We are thrilled to announce that our school paper has qualified for the NATIONAL SCHOOLS PRESS CONFERENCE (NSPC) 2024. Thank you for your unwavering support and trust. Dive into the stories that made us stand out!
2024 State of Marketing Report – by HubspotMarius Sescu
https://www.hubspot.com/state-of-marketing
· Scaling relationships and proving ROI
· Social media is the place for search, sales, and service
· Authentic influencer partnerships fuel brand growth
· The strongest connections happen via call, click, chat, and camera.
· Time saved with AI leads to more creative work
· Seeking: A single source of truth
· TLDR; Get on social, try AI, and align your systems.
· More human marketing, powered by robots
ChatGPT is a revolutionary addition to the world since its introduction in 2022. A big shift in the sector of information gathering and processing happened because of this chatbot. What is the story of ChatGPT? How is the bot responding to prompts and generating contents? Swipe through these slides prepared by Expeed Software, a web development company regarding the development and technical intricacies of ChatGPT!
Product Design Trends in 2024 | Teenage EngineeringsPixeldarts
The realm of product design is a constantly changing environment where technology and style intersect. Every year introduces fresh challenges and exciting trends that mold the future of this captivating art form. In this piece, we delve into the significant trends set to influence the look and functionality of product design in the year 2024.
How Race, Age and Gender Shape Attitudes Towards Mental HealthThinkNow
Mental health has been in the news quite a bit lately. Dozens of U.S. states are currently suing Meta for contributing to the youth mental health crisis by inserting addictive features into their products, while the U.S. Surgeon General is touring the nation to bring awareness to the growing epidemic of loneliness and isolation. The country has endured periods of low national morale, such as in the 1970s when high inflation and the energy crisis worsened public sentiment following the Vietnam War. The current mood, however, feels different. Gallup recently reported that national mental health is at an all-time low, with few bright spots to lift spirits.
To better understand how Americans are feeling and their attitudes towards mental health in general, ThinkNow conducted a nationally representative quantitative survey of 1,500 respondents and found some interesting differences among ethnic, age and gender groups.
Technology
For example, 52% agree that technology and social media have a negative impact on mental health, but when broken out by race, 61% of Whites felt technology had a negative effect, and only 48% of Hispanics thought it did.
While technology has helped us keep in touch with friends and family in faraway places, it appears to have degraded our ability to connect in person. Staying connected online is a double-edged sword since the same news feed that brings us pictures of the grandkids and fluffy kittens also feeds us news about the wars in Israel and Ukraine, the dysfunction in Washington, the latest mass shooting and the climate crisis.
Hispanics may have a built-in defense against the isolation technology breeds, owing to their large, multigenerational households, strong social support systems, and tendency to use social media to stay connected with relatives abroad.
Age and Gender
When asked how individuals rate their mental health, men rate it higher than women by 11 percentage points, and Baby Boomers rank it highest at 83%, saying it’s good or excellent vs. 57% of Gen Z saying the same.
Gen Z spends the most amount of time on social media, so the notion that social media negatively affects mental health appears to be correlated. Unfortunately, Gen Z is also the generation that’s least comfortable discussing mental health concerns with healthcare professionals. Only 40% of them state they’re comfortable discussing their issues with a professional compared to 60% of Millennials and 65% of Boomers.
Race Affects Attitudes
As seen in previous research conducted by ThinkNow, Asian Americans lag other groups when it comes to awareness of mental health issues. Twenty-four percent of Asian Americans believe that having a mental health issue is a sign of weakness compared to the 16% average for all groups. Asians are also considerably less likely to be aware of mental health services in their communities (42% vs. 55%) and most likely to seek out information on social media (51% vs. 35%).
AI Trends in Creative Operations 2024 by Artwork Flow.pdfmarketingartwork
This article is all about what AI trends will emerge in the field of creative operations in 2024. All the marketers and brand builders should be aware of these trends for their further use and save themselves some time!
A report by thenetworkone and Kurio.
The contributing experts and agencies are (in an alphabetical order): Sylwia Rytel, Social Media Supervisor, 180heartbeats + JUNG v MATT (PL), Sharlene Jenner, Vice President - Director of Engagement Strategy, Abelson Taylor (USA), Alex Casanovas, Digital Director, Atrevia (ES), Dora Beilin, Senior Social Strategist, Barrett Hoffher (USA), Min Seo, Campaign Director, Brand New Agency (KR), Deshé M. Gully, Associate Strategist, Day One Agency (USA), Francesca Trevisan, Strategist, Different (IT), Trevor Crossman, CX and Digital Transformation Director; Olivia Hussey, Strategic Planner; Simi Srinarula, Social Media Manager, The Hallway (AUS), James Hebbert, Managing Director, Hylink (CN / UK), Mundy Álvarez, Planning Director; Pedro Rojas, Social Media Manager; Pancho González, CCO, Inbrax (CH), Oana Oprea, Head of Digital Planning, Jam Session Agency (RO), Amy Bottrill, Social Account Director, Launch (UK), Gaby Arriaga, Founder, Leonardo1452 (MX), Shantesh S Row, Creative Director, Liwa (UAE), Rajesh Mehta, Chief Strategy Officer; Dhruv Gaur, Digital Planning Lead; Leonie Mergulhao, Account Supervisor - Social Media & PR, Medulla (IN), Aurelija Plioplytė, Head of Digital & Social, Not Perfect (LI), Daiana Khaidargaliyeva, Account Manager, Osaka Labs (UK / USA), Stefanie Söhnchen, Vice President Digital, PIABO Communications (DE), Elisabeth Winiartati, Managing Consultant, Head of Global Integrated Communications; Lydia Aprina, Account Manager, Integrated Marketing and Communications; Nita Prabowo, Account Manager, Integrated Marketing and Communications; Okhi, Web Developer, PNTR Group (ID), Kei Obusan, Insights Director; Daffi Ranandi, Insights Manager, Radarr (SG), Gautam Reghunath, Co-founder & CEO, Talented (IN), Donagh Humphreys, Head of Social and Digital Innovation, THINKHOUSE (IRE), Sarah Yim, Strategy Director, Zulu Alpha Kilo (CA).
Trends In Paid Search: Navigating The Digital Landscape In 2024Search Engine Journal
The search marketing landscape is evolving rapidly with new technologies, and professionals, like you, rely on innovative paid search strategies to meet changing demands.
It’s important that you’re ready to implement new strategies in 2024.
Check this out and learn the top trends in paid search advertising that are expected to gain traction, so you can drive higher ROI more efficiently in 2024.
You’ll learn:
- The latest trends in AI and automation, and what this means for an evolving paid search ecosystem.
- New developments in privacy and data regulation.
- Emerging ad formats that are expected to make an impact next year.
Watch Sreekant Lanka from iQuanti and Irina Klein from OneMain Financial as they dive into the future of paid search and explore the trends, strategies, and technologies that will shape the search marketing landscape.
If you’re looking to assess your paid search strategy and design an industry-aligned plan for 2024, then this webinar is for you.
5 Public speaking tips from TED - Visualized summarySpeakerHub
From their humble beginnings in 1984, TED has grown into the world’s most powerful amplifier for speakers and thought-leaders to share their ideas. They have over 2,400 filmed talks (not including the 30,000+ TEDx videos) freely available online, and have hosted over 17,500 events around the world.
With over one billion views in a year, it’s no wonder that so many speakers are looking to TED for ideas on how to share their message more effectively.
The article “5 Public-Speaking Tips TED Gives Its Speakers”, by Carmine Gallo for Forbes, gives speakers five practical ways to connect with their audience, and effectively share their ideas on stage.
Whether you are gearing up to get on a TED stage yourself, or just want to master the skills that so many of their speakers possess, these tips and quotes from Chris Anderson, the TED Talks Curator, will encourage you to make the most impactful impression on your audience.
See the full article and more summaries like this on SpeakerHub here: https://speakerhub.com/blog/5-presentation-tips-ted-gives-its-speakers
See the original article on Forbes here:
http://www.forbes.com/forbes/welcome/?toURL=http://www.forbes.com/sites/carminegallo/2016/05/06/5-public-speaking-tips-ted-gives-its-speakers/&refURL=&referrer=#5c07a8221d9b
ChatGPT and the Future of Work - Clark Boyd Clark Boyd
Everyone is in agreement that ChatGPT (and other generative AI tools) will shape the future of work. Yet there is little consensus on exactly how, when, and to what extent this technology will change our world.
Businesses that extract maximum value from ChatGPT will use it as a collaborative tool for everything from brainstorming to technical maintenance.
For individuals, now is the time to pinpoint the skills the future professional will need to thrive in the AI age.
Check out this presentation to understand what ChatGPT is, how it will shape the future of work, and how you can prepare to take advantage.
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Multi-Scale Models in Immunobiology
1. Multi-Scale Models in Immunobiology
Learning to Guide the Behaviour of Cells
Michael P.H. Stumpf
Theoretical Systems Biology Group
04/09/2012
Multi-Scale Models in Immunobiology Michael P.H. Stumpf 1 of 26
2. Multi-Scale Modelling
Definitions
1. Multi-scale models deal with problems which have important (and
more or less separable) features at multiple organisational, spatial
and temporal scales.
2. For practical reasons we may choose to break down complex
computational problems into different scales and couple the
resulting sub-systems.
The different scales can emerge either naturally or as a consequence
of measurement, experimental or observational resolution.
Multi-Scale Models in Immunobiology Michael P.H. Stumpf Multi-Scale Systems 2 of 26
3. Multi-Scale Modelling
Definitions
1. Multi-scale models deal with problems which have important (and
more or less separable) features at multiple organisational, spatial
and temporal scales.
2. For practical reasons we may choose to break down complex
computational problems into different scales and couple the
resulting sub-systems.
The different scales can emerge either naturally or as a consequence
of measurement, experimental or observational resolution.
Our Definition
Here we consider problems where
molecular processes give rise to
behaviour that are accessible at the
organismic level.
Multi-Scale Models in Immunobiology Michael P.H. Stumpf Multi-Scale Systems 2 of 26
4. Examples of Multi-Scale Processes
Noever et al., NASA Tech Briefs 19(4):82 (1995).
Multi-Scale Models in Immunobiology Michael P.H. Stumpf Multi-Scale Systems 3 of 26
5. Examples of Multi-Scale Processes
48 In red are shown times by cyclists who
have been found guilty of doping.
46
44
Time/min
42
40
38
1950 1960 1970 1980 1990 2000 2010
Year
The 36 best times in the Tour de France for the Alpe
d’Huez.
Multi-Scale Models in Immunobiology Michael P.H. Stumpf Multi-Scale Systems 3 of 26
6. Statistical Challenges of Multi-Scale Systems
Z (t )
Yj ( t )
Xi ( t )
When trying to write down how Z (t ) depends on Y (t ) = {Y1 (t ), . . .} or
X (t ) = {X1 (t ), . . .} a range of potential problems become apparent.
• How can we write Z |Y and Y |X (or P (Z |Y ), P (Y |X ) and P (Z |X ))?
• How do we relate e.g. P (Yj |Xr ,...,s ) and P (Yk |Xu ,...,v ) with j = k and
{r , . . . , s } ∩ {u , . . . , v } = ∅ ?
• How does higher-level information flow back into dynamics at lower
levels?
Multi-Scale Models in Immunobiology Michael P.H. Stumpf Multi-Scale Systems 4 of 26
7. The Innate Immune Response in Zebrafish
Danio Rerio — Zebrafish
• Embryos are optically transparent (as are
some mutant strain adults).
• They are experimentally convenient.
We study the innate
• Zebrafish are an outbred model organism.
immune response to
• Life-expectancy up to two years. wounding.
• How are macrophages and neutrophils
recruited?
• Is the response different between
aseptic and septic wounding?
• How are cellular processes inside
leukocytes coupled to the tissue or
organism-wide signalling dynamics?
Multi-Scale Models in Immunobiology Michael P.H. Stumpf Spatio-Temporal Immune Response in Zebrafish 5 of 26
8. Leukocyte Chemotaxis in Zebrafish
We extract images,
identify and track
leukocytes and then
analyze their
trajectories for:
• random walk
behaviour
• random walk
behaviour in the x
direction
• random walk
behaviour in the y
direction
• bias in the
directionality
between steps.
Multi-Scale Models in Immunobiology Michael P.H. Stumpf Spatio-Temporal Immune Response in Zebrafish 6 of 26
9. Simple Multiscale Models
αt = mean(Nc (αt −1 , σ2 ), Nc (0, σ2 )||w )
p b
Wound varp = f1 (S (C ), pmax , pd ) and varb = f2 (S (C ), bmax , bd )
1 1
S (x ) = (R +x +Kd )− (R + x + Kd ) − Rx
2 4
C (y , t ) = unknown gradient function
y — Leukocytes
r
C — Cytokines R - number of receptors
Distance y
Multi-Scale Models in Immunobiology Michael P.H. Stumpf Spatio-Temporal Immune Response in Zebrafish 7 of 26
10. Calibration of Multiscale Models
Multi-Scale Models in Immunobiology Michael P.H. Stumpf Spatio-Temporal Immune Response in Zebrafish 8 of 26
11. Inference for Complicated Models
We have observed data, D, that was generated by some system of in
general unknown structure that we seek to describe by a
mathematical model. In principle we can have a model-set,
M = {M1 , . . . , Mν }, with model parameter θi .
We may know the different constituent parts of the system, Xi , and
have measurements for some or all of them under some experimental
designs, T .
Likelihood Prior
Posterior
f (D|θ, T)π(θ) For complicated models and/or
Pr(θ|T, D)= detailed data the likelihood
f (D|θ, T)π(θ)d θ evaluation can become
Θ
prohibitively expensive.
Evidence
Inference for Multi-Scale Models
The data is often collected at a level different from the one which
determines the dynamics. This places special demands on the
inferential framework.
Multi-Scale Models in Immunobiology Michael P.H. Stumpf Approximate Bayesian Computation 9 of 26
12. Approximate Bayesian Computation
Model Data, D
θ2 X (t )
t
θ1
Toni et al., J.Roy.Soc. Interface (2009).
Multi-Scale Models in Immunobiology Michael P.H. Stumpf Approximate Bayesian Computation 10 of 26
13. Approximate Bayesian Computation
Model Data, D
θ2 X (t )
t
θ1
Toni et al., J.Roy.Soc. Interface (2009).
Multi-Scale Models in Immunobiology Michael P.H. Stumpf Approximate Bayesian Computation 10 of 26
14. Approximate Bayesian Computation
Model Data, D
θ2 X (t ) Simulation, Xs (θ)
t
θ1
Toni et al., J.Roy.Soc. Interface (2009).
Multi-Scale Models in Immunobiology Michael P.H. Stumpf Approximate Bayesian Computation 10 of 26
15. Approximate Bayesian Computation
Model Data, D
θ2 X (t ) Simulation, Xs (θ)
t
d = ∆(Xs (θ), D)
θ1
Toni et al., J.Roy.Soc. Interface (2009).
Multi-Scale Models in Immunobiology Michael P.H. Stumpf Approximate Bayesian Computation 10 of 26
16. Approximate Bayesian Computation
Model Data, D
θ2 X (t ) Simulation, Xs (θ)
t
d = ∆(Xs (θ), D)
θ1 Reject θ if d >
Accept θ if d
Toni et al., J.Roy.Soc. Interface (2009).
Multi-Scale Models in Immunobiology Michael P.H. Stumpf Approximate Bayesian Computation 10 of 26
17. Approximate Bayesian Computation
Model Data, D
θ2 X (t ) Simulation, Xs (θ)
t
d = ∆(Xs (θ), D)
θ1 Reject θ if d >
Accept θ if d
Toni et al., J.Roy.Soc. Interface (2009).
Multi-Scale Models in Immunobiology Michael P.H. Stumpf Approximate Bayesian Computation 10 of 26
18. Approximate Bayesian Computation
Model Data, D
θ2 X (t ) Simulation, Xs (θ)
t
d = ∆(Xs (θ), D)
θ1 Reject θ if d >
Accept θ if d
Toni et al., J.Roy.Soc. Interface (2009).
Multi-Scale Models in Immunobiology Michael P.H. Stumpf Approximate Bayesian Computation 10 of 26
19. Approximate Bayesian Computation
Model Data, D
θ2 X (t ) Simulation, Xs (θ)
t
d = ∆(Xs (θ), D)
θ1 Reject θ if d >
Accept θ if d
Toni et al., J.Roy.Soc. Interface (2009).
Multi-Scale Models in Immunobiology Michael P.H. Stumpf Approximate Bayesian Computation 10 of 26
20. Approximate Bayesian Computation
Model Data, D
θ2 X (t ) Simulation, Xs (θ)
t
d = ∆(Xs (θ), D)
θ1 Reject θ if d >
Accept θ if d
Toni et al., J.Roy.Soc. Interface (2009).
Multi-Scale Models in Immunobiology Michael P.H. Stumpf Approximate Bayesian Computation 10 of 26
21. Approximate Bayesian Computation
Model Data, D
θ2 X (t ) Simulation, Xs (θ)
t
d = ∆(Xs (θ), D)
θ1 Reject θ if d >
Accept θ if d
Toni et al., J.Roy.Soc. Interface (2009).
Multi-Scale Models in Immunobiology Michael P.H. Stumpf Approximate Bayesian Computation 10 of 26
22. Approximate Bayesian Computation
Prior, π(θ) Define set of intermediate distributions, πt , t = 1, ...., T
1 > 2 > ...... > T
πt −1 (θ|∆(Xs , X ) < t −1 )
πt (θ|∆(Xs , X ) < t)
πT (θ|∆(Xs , X ) < T)
Sequential importance sampling:
Sample from proposal, ηt (θt ) and weight
wt (θt ) = πt (θt )/ηt (θt ) with
ηt (θt ) = πt −1 (θt −1 )Kt (θt −1 , θt )d θt −1 where
Kt (θt −1 , θt ) is Markov perturbation kernel
Toni et al., J.Roy.Soc. Interface (2009); Toni & Stumpf, Bioinformatics (2010).
Multi-Scale Models in Immunobiology Michael P.H. Stumpf Approximate Bayesian Computation 10 of 26
23. Model Selection on a Joint (M , θ) Space
M1 M2 M3 M4
Toni & Stumpf, Bioinformatics (2010); Barnes et al., PNAS (2011); Barnes et al., Stat.Comp. (2012).
Multi-Scale Models in Immunobiology Michael P.H. Stumpf Approximate Bayesian Computation 11 of 26
24. Model Selection on a Joint (M , θ) Space
M∗
M1 M2 M3 M4
Toni & Stumpf, Bioinformatics (2010); Barnes et al., PNAS (2011); Barnes et al., Stat.Comp. (2012).
Multi-Scale Models in Immunobiology Michael P.H. Stumpf Approximate Bayesian Computation 11 of 26
25. Model Selection on a Joint (M , θ) Space
M∗
M ∗∗ ∼ KM (M |M ∗ )
M1 M2 M3 M4
Toni & Stumpf, Bioinformatics (2010); Barnes et al., PNAS (2011); Barnes et al., Stat.Comp. (2012).
Multi-Scale Models in Immunobiology Michael P.H. Stumpf Approximate Bayesian Computation 11 of 26
26. Model Selection on a Joint (M , θ) Space
M∗
M ∗∗ ∼ KM (M |M ∗ )
M1 M2 M3 M4
Toni & Stumpf, Bioinformatics (2010); Barnes et al., PNAS (2011); Barnes et al., Stat.Comp. (2012).
Multi-Scale Models in Immunobiology Michael P.H. Stumpf Approximate Bayesian Computation 11 of 26
27. Model Selection on a Joint (M , θ) Space
(M3 , θ3 )
(M3 , θ7 )
M∗
(M3 , θ6 )
(M3 , θ2 )
M ∗∗ ∼ KM (M |M ∗ )
(M3 , θ8 ) (M3 , θ5 )
(M3 , θ1 )
(M3 , θ4 ) θ∗
(M3 , θ9 )
Toni & Stumpf, Bioinformatics (2010); Barnes et al., PNAS (2011); Barnes et al., Stat.Comp. (2012).
Multi-Scale Models in Immunobiology Michael P.H. Stumpf Approximate Bayesian Computation 11 of 26
28. Model Selection on a Joint (M , θ) Space
(M3 , θ3 )
(M3 , θ7 )
M∗
(M3 , θ6 )
(M3 , θ2 )
M ∗∗ ∼ KM (M |M ∗ )
(M3 , θ8 ) (M3, θ5)(M , θ ) 3 1
(M3 , θ4 ) θ∗
(M3 , θ9 )
Toni & Stumpf, Bioinformatics (2010); Barnes et al., PNAS (2011); Barnes et al., Stat.Comp. (2012).
Multi-Scale Models in Immunobiology Michael P.H. Stumpf Approximate Bayesian Computation 11 of 26
29. Model Selection on a Joint (M , θ) Space
(M3 , θ3 )
(M3 , θ7 )
M∗
(M3 , θ6 )
(M3 , θ2 )
M ∗∗ ∼ KM (M |M ∗ )
(M3 , θ8 ) (M3, θ5)(M , θ ) 3 1
(M3 , θ4 ) θ∗
(M3 , θ9 )
θ∗∗ ∼ KP (θ|θ∗ )
Toni & Stumpf, Bioinformatics (2010); Barnes et al., PNAS (2011); Barnes et al., Stat.Comp. (2012).
Multi-Scale Models in Immunobiology Michael P.H. Stumpf Approximate Bayesian Computation 11 of 26
30. Model Selection on a Joint (M , θ) Space
M∗
∗∗ ∗∗ M ∗∗ ∼ KM (M |M ∗ )
(M , θ )
θ∗
θ∗∗ ∼ KP (θ|θ∗ )
accept / reject
Toni & Stumpf, Bioinformatics (2010); Barnes et al., PNAS (2011); Barnes et al., Stat.Comp. (2012).
Multi-Scale Models in Immunobiology Michael P.H. Stumpf Approximate Bayesian Computation 11 of 26
31. Model Selection on a Joint (M , θ) Space
M∗
∗∗ ∗∗ M ∗∗ ∼ KM (M |M ∗ )
w (M , θ )
θ∗
θ∗∗ ∼ KP (θ|θ∗ )
accept / reject
calculate w
Toni & Stumpf, Bioinformatics (2010); Barnes et al., PNAS (2011); Barnes et al., Stat.Comp. (2012).
Multi-Scale Models in Immunobiology Michael P.H. Stumpf Approximate Bayesian Computation 11 of 26
32. Proof of Principle — In Vitro
Data describe the migration of
human neutrophils in a
microfluidic device with a
known linear IL 8 gradient.
Multi-Scale Models in Immunobiology Michael P.H. Stumpf Multi-Scale Models of Immunity 12 of 26
33. Proof of Principle — In Vitro
Models:
M1 : f (y ) = n0 − αy
M2 : f (y ) = h × en0 −αy / (1 + en0 −αy )
2
M3 : f ( y ) = √ A e−y /4πt
4πDt
Multi-Scale Models in Immunobiology Michael P.H. Stumpf Multi-Scale Models of Immunity 12 of 26
34. Leukocyte Chemotaxis Models — In Vivo
Wound M1 : f (y ) = n0 − αy
M2 : f (y ) = h × en0 −αy / (1 + en0 −αy )
2
M3 : f (y ) = √4A Dt e−y /4πt
π
y — Leukocyte
r
C - Cytokines R — number of receptors
Distance y
Model Calibration
We use ABC to infer the shape of the gradient and how it changes
with time since wounding from the observed leucocyte trajectories.
Multi-Scale Models in Immunobiology Michael P.H. Stumpf Multi-Scale Models of Immunity 13 of 26
35. Cytokine gradient
This changing gradient explains much of the cell-to-cell variability in
leukocyte chemotaxis.
Multi-Scale Models in Immunobiology Michael P.H. Stumpf Multi-Scale Models of Immunity 14 of 26
36. Robustness of Leukocyte Migration Behaviour
Liepe et al., Integrative Biology (2012).
Multi-Scale Models in Immunobiology Michael P.H. Stumpf Multi-Scale Models of Immunity 15 of 26
37. First Lessons from this Model
Sensing Mechanisms
In our analysis the biophysical
model appeared to matter very little.
This could be taken to mean that
Σ the sensing mechanism is robust to
the details of the receptor and
signalling architecture.
Probing Low Level Processes
We can next exploit the experimental strengths of the zebrafish model
to probe aspects of the cellular signalling machinery and its impact at
migratory patterns of leukocytes:
• inhibit p38 MAPK and JNK.
and study the impact of leukocyte motility (keeping in mind that
epithelial tissue may also be affected by such inhibitors).
Taylor, Liepe et al., Immun.Cell.Biol. (2012).
Multi-Scale Models in Immunobiology Michael P.H. Stumpf Multi-Scale Models of Immunity 16 of 26
38. Random walks in detail
Brownian motion (BM)
∂P (x , y , t ) 2
=A P
dt
biased random walk (BRW)
∂P (x , y , t ) 2
= −u P + A P
dt
persistent random walk (PRW)
∂2 P ∂P
+ 2λ = A2 2
P
dt 2 dt
biased persistent random walk (BPRW)
∂2 P ∂P ∂P
+(λ1 +λ2 ) −v (λ2 −λ1 ) = A2 2
P
dt 2 dt dy
Multi-Scale Models in Immunobiology Michael P.H. Stumpf Probing Cellular Processes — Observing Tissues 17 of 26
39. In Vivo Leukocyte Temporal Dynamics
Multi-Scale Models in Immunobiology Michael P.H. Stumpf Probing Cellular Processes — Observing Tissues 18 of 26
40. Multi-Scale Models in Immunobiology Michael P.H. Stumpf Probing Cellular Processes — Observing Tissues 18 of 26
41. In Vivo Leukocyte Spatial Dynamics
Multi-Scale Models in Immunobiology Michael P.H. Stumpf Probing Cellular Processes — Observing Tissues 19 of 26
42. The Case for a Spatio-Temporal Perspective
Data Treatment
• Finding the right level of
averaging and
homogenizing data is pivotal
for meaningful analysis and
If we average over modelling.
spatio-temporal scales • In the absence of physical
we miss much of the arguments we can employ
heterogeneity and can information theoretic
even fail to detect approaches to determine
significant functional relevant scales.
changes.
Multi-Scale Models in Immunobiology Michael P.H. Stumpf Probing Cellular Processes — Observing Tissues 20 of 26
43. Summarizing Multi-Scale Systems Statistics
Z (t )
Yj ( t )
Xi ( t )
We assume that dynamics are governed by processes at the lowest
level. That means the system is completely specified by the Xi .
Statistical Inference Based on Summary Statistics
We can often interpret Y /Z as summaries of X , e.g.
Yj = g (Xr , . . . , Xs ). Then we have to ensure that
P (θ|Z ) = P (θ|Y ) = P (θ|X )
which is not automatically the case.
For parameter estimation and especially for model selection we have
to account for relationships between data at different levels.
Multi-Scale Models in Immunobiology Michael P.H. Stumpf Probing Cellular Processes — Observing Tissues 21 of 26
44. Summarizing Multi-Scale Systems Statistics
Z (t )
Yj ( t )
Xi ( t )
We assume that dynamics are governed by processes at the lowest
level. That means the system is completely specified by the Xi .
Information Theoretical Perspective
In many circumstances we can interpret a higher levels as an
information compression device. Then we should ensure that the
mutual information
p(θ, x )
I (Θ; X ) = p(θ, x ) log d θdx = I (θ, Y )
Ω X p(θ)p(x )
In this case Y = g (X ) is a sufficient statistic of the lower-level data X .
Multi-Scale Models in Immunobiology Michael P.H. Stumpf Probing Cellular Processes — Observing Tissues 21 of 26
45. Haematopoietic Stem Cells
Similar problems of
biological processes not
Stem Cell Niche Dynamics
being observable at all
relevant scales abound. Stem cell niche
lineage differentiation migration
HSC A D D
determination
Bone marrow Blood stream
differentiation migration
Sub niche LSC T T
Here, too, we observe at the
tissue/organismic level but are really
trying to resolve processes at the
molecular level. Doing both
simultaneously is not yet possible.
Bone Marrow in Mouse, Cristina Lo Celso.
Multi-Scale Models in Immunobiology Michael P.H. Stumpf Haematopoiesis 22 of 26
46. Stem Cell Niche Dynamics with Leukaemia from a
Bayesian Perspective
Here we have mapped out the parameter regions that would allow
HSCs to win over leukaemic rivals.
Multi-Scale Models in Immunobiology Michael P.H. Stumpf Haematopoiesis 23 of 26
47. Bayesian Design or “Robustness of Behaviour”
I I I
A
1 A 2 A 3 A
1A Design objectives 1B Model definitions
B C B C B C
x ∼ fM1 (θ) x ∼ fM2 (θ) O O O
input output θ ∼ π(θ|M1 ) θ ∼ π(θ|M2 ) I I I
Model
4 A 5 A 6 A
B C B C B C
∆(x, O)
O O O
input I output O
I I I
7 A 8 A 9 A
x ∼ fM3 (θ) x ∼ fM4 (θ)
θ ∼ π(θ|M3 ) θ ∼ π(θ|M4 ) B C B C B C
O O O
t t
I I
1C System evolution 1D Posterior distribution 10 A 11 A
p(M |D)
1 2 3 4 5 B C B C
O O
population
0.4
B
0.3
posterior
1
0.2
2 M
0.1
p(θi |M1 ,D) p(θi |M2 ,D)
0.0
1 2 3 4 5 6 7 8 9 10 11
model
3
0.4
4 C
0.3
posterior
5
0.2
p(θj |M1 ,D) p(θj |M2 ,D) 0.1
0.0
Barnes et al., PNAS (2011); Silk et al.Nature Communication (2011). 1 2 3 4 5 6
model
7 8 9 10 11
Multi-Scale Models in Immunobiology Michael P.H. Stumpf Haematopoiesis 24 of 26
48. Conclusion and Outlook
Uses of Multi-Scale Models
They can be used as a computational device or a convenient
description of natural processes. Here we used them in the latter
sense.
Progress will require careful selection of experimental methodologies
and integration of different (though often collinear) data sources.
Some Caveats
• Often, especially in medical applications, data cannot be obtained
at lower levels. This can have far-reaching consequences for
statistical models.
• Generally, likelihoods are difficult to assess unless suitable
approximations are available.
• “Simple models can pretty much fit anything (up to a point).”
Multi-Scale Models in Immunobiology Michael P.H. Stumpf Conclusions 25 of 26
49. Acknowledgements
Multi-Scale Models in Immunobiology Michael P.H. Stumpf Conclusions 26 of 26