Physical Theory of the Immune System NIH Michael W. Deem DARPA - - PowerPoint PPT Presentation

Michael W. Deem Rice University NIH DARPA DOE

Physical Theory of the Immune System

Outline

• Grand challenges in global health
• The order parameter pepitope

(a new tool for vaccine design)

• Virus evolution
• Epidemiology
• Detection via clustering
• Dengue fever
• CRISPR

BRC, Rice University

Grand Challenges in Global Health

• H. Varmus et al., Science

302 (2003) 398-399.

• To improve

vaccines

• To create new

vaccines Bill Gates, World Economic Forum in Davos, Switzerland. Science and Technology: progress against disease.

Hilbert’s 23 open questions in mathematics 7 Millenium Problems, Clay Institute

Flu and Public Health

• Annual influenza epidemics kill

250,000-500,000 people worldwide

• Cause illness in 5 to 15% of total

population each year

• Typical annual cost in the US is

$10 billion

• Typical US mortality is 40,000

JAMA 289 (2003) 179

May be 90,000 if complications are included

• CDC estimates $71-167 billion in

US alone for pandemic

• Vaccination primary method to

prevent infection

La Grippe July 2009

• Arriving in Paris,

Gare du Nord

• Arriving in London, St. Pancras

Swine Flu CNN Headline

Background: History

Circulation of flu virus in history

Background: Virus structure

Structure of the virus

• Two antigenically critical proteins: hemagglutinin (HA) and

neuraminidase (NA)

• five epitopes on the surface of HA

Epitope A Epitope B Epitope C Epitope D Epitope E

~13 nm

~100 nm

Influenza Evolution

• Influenza is recognized by

the immune system antibodies binding the epitopes of hemagglutinin

• Hemagglutinin evolves as

cluster in sequence space

Time

Pressure on Hemagglutinin

• Antibody pressure on hemagglutinin from

antibodies

• Virus will evolve away from this pressure
• Simplest idea

– Viral fitness proportional to free energy of binding disruption

• E.g. virus may increase interaction with water

and decrease interaction with Ag

Background: Mortality data

• Upper left: Long‐time data. Source:

http://www.vaclib.org/legal/MTstat e/US‐Flu‐1900‐2002.gif

• Lower right: Annual data. Source:

http://media.mercola.com/imagese rver/public/2009/November/flu%20 mortality.gif

Influenza structure

Deem & Pan, Protein Engineering, Design and Application. 2009; 1‐4.

Nomenclature: A/Texas/05/2009(H1N1) type/locality of isolation/isolate number/year(H&N subtype)

Hierarchical Creation of Antibody Diversity

• Antibody genes are created by

recombination of gene segments in VDJ recombination

• Antibodies that recognize self die
• Antibodies that recognize disease

multiply

• The amino-acid space of disease-

recognizing antibodies is searched by point mutation in somatic hypermutation

Predicting Next Season’s Strain

• Each year the next likely epidemic strain is

identified by WHO by examining circulating strains in different locations

Vaccine Development and Efficacy

• Long development time
• Egg adaptation and individual

inoculation

• Varying efficacy from year to

year

• Lack of flexibility to make

arrangements for post inoculation changes

The Flu Shot Paradox

• “A flu shot this year and not next year, may

lead to a greater risk of contracting the flu next year”

(costco, 1998)

• Yet flu shot does not affect susceptibility to

most other diseases

• And vaccination normally provides protection

against disease for multiple years

• Surprising that vaccine can

make one more susceptible to the disease

Original Antigenic Sin and the Binding Constant

• Compare primary

and secondary immune response

• The localization is

visible in the binding constant

Deem and Lee, PRL 91 068101 (2003)

When Does Cross-Reactivity Cease?

• Examine affinity of memory

antibodies for mutated antigen

• Cross-Reactivity ceases

when Km

eq < 102 l/mol, the

non-specific value

• No cross-reactivity for

p > 0.36

• Experimentally, cross-

reactivity ceases for p = 0.33 - 0.42

• J. J. East et al., Mol. Immunol. 17 (1980) 1545

How Many Mutations Occur in the Dynamics?

• Mutations in primary and

secondary responses

• Measure smallest distance

between best evolved sequence and starting sequences

• Secondary response has fewer

mutations than primary for p < 0.20

• More mutations in secondary

than primary for 0.20 < p < 0.70

The Order Parameter pepitope

• The theory is a form of spin glass model,

first used to describe nuclear cross sections, e- spins in solid

• Mutation of the flu virus corresponds to

changing parameters in the model with probability p

• In the immune system, pepitope is the

fraction of amino acids that change in the dominant epitope

• We observe the efficacy of vaccination to

subsequent exposure to the flu

E = u − v u

Vaccine Efficacy

• H3N2 human efficacy from last 35 years (epidemiological)
• Efficacy correlates well with pepitope
• psequence and dferret correlate modestly with human efficacy
• Negative efficacy is mostly at large pepitope (OAS)
• Theory validates correlation

Gupta, Earl, and Deem, Vaccine 24 (2006) 3881-3888. Munoz and Deem, Vaccine 23 (2005) 1144-1148.

Pressure on Hemagglutinin

• Antibody pressure on hemagglutinin from

antibodies

• Virus will evolve away from this pressure
• Simplest idea

– Viral fitness proportional to free energy of binding disruption

• E.g. virus may increase interaction with water

and decrease interaction with Ag

Viral Evolution

• Expect pepitope > 0.19 to evade

immune system; For H3N2 – Vaccine(n) vs. virus(n, n+1) – average pepitope= 0.129, 0.157

The Hong Kong flu in Humans

• E.g. virus may increase charge in

epitope region

• Track fraction of Asp, Glu, Arg,

Lys, His

• Charge does increase in

dominant epitope, early on

• J. Mol. Evol. (2011) 72:90–103

Modeling the Selection Pressure

• One can fit amino acid selection

models to observed data

• The model is statistically

significantly different from standard protein evolution models, e.g. PAM22

• J. Mol. Evol. (2011) 72:90–103

Animal Models also show Selection Pressure

• Guinea pigs infected with

– CDC A/Wyoming/2003 virus mixture – homogeneous WyB4 virus isolate

• Naïve, primary, secondary

responses

• J. Mol. Evol. (2011) 72:90–103

More Sophisticated Theory

• Calculate free energy of

antibody/hemagglutinin interaction – Requires we have co-crystal – And that a single Ab is representative

• Assume viral fitness is monotonic in

disruption of recognition by antibody

• J. Chem. Theory Comput. 7 (2011) 1259

Calculate Free Energy Changes Due to aa Substitution

• Statistical Mechanics
• Details associated with thermodynamic integration
• Hess’s Law: ∆∆G=∆G42 - ∆G31 = ∆G43 - ∆G21

Thermodynamic Integration

• Free energy changes calculated from

simulations by exact formula:

• Some details associated with endpoints of

this integration (e.g. Einstein crystals)

∆∆G Values

• Tables of values

⁞

Average ∆∆G Values

• Charge is disruptive

Substitutions 1968-1975

Modeling Viral Dynamics

• Viral dynamics for some early substitutions

1970-1973

• Mutation rate from observation
• Fitness proportional to ∆∆G

Stochastic Model of Influenza Spread and Evolution

• Global Hierarchical Scale Free

Network

• Human distribution
• Worldwide air transportation
• Person to person contact

within city

• Virus Transmission & Evolution
• Contact based transmission
• Evolution derived by mutation
• H. Zhou, R. Pophale, and M. W. Deem, ``Computer-Assisted Vaccine Design,''

in Influenza: Molecular Virology, Horizon Scientific Press (2009)

Human Distribution

• N=10 Groups (≈10³

Persons/Group)

• Max=13,000 Groups/Cities

(12,778,721,Mumbai,India); Min=60 Groups/Cities (60,006, Evosmo,Greece)

• Distributed in around 4,000 cities
• P(k) k-2.2

(G., Zipf, “Human Behavior and the principle of last effort”, 1949) http://www.mongabay.com/cities_pop_01.htm

Human Distribution

Worldwide Air Transportation

• Max=4000 Flights/City/Day (R.

Guimera et al., PNAS, 2005)

Min=1 Flights/City/Day

• N=60,000 Flights/Day

(http://en.wikipedia.org/wiki/Airline_alliance)

Npred = 60,937 from model

• Assume Flights Contact Map:

P(k) k-2.01

(R. Guimera et al., PNAS, 2005)

Worldwide Air Transportation

Within City Network

• Group to Group Contact: Min=1
• P(k) k-2.8

(Stephen Eubank et al., Nature, 2005)

Model Prediction

• FluNet Database (Isolates)

Model Prediction

• Simulation & FluNet Data Comparison

Reproductive Ratio

• R0 should be a prediction of the model, not an

input

• R0 is time dependent
• R0 is spatially dependent

Viral Diversity

• Quantify viral diversity and

expected vaccine efficacy

• Expect more diversity late

in the season

• Because pressure to

evolve exists only as virus is being eradicated

Mitigation Strategies for Flu Pandemics

• Quantify expected vaccine efficacy, 2 initial strains
• Different percentages of population vaccinated
• Vaccination at different days
• Single-component or multi-component vaccine

Risk Analysis: Population at Risk (PaR)

• PaR: The fraction of the population that will

be infected in a X% of worst-case epidemic

• Depends on vaccination strategy

Clustering to Detect Strains

• Standard dimensional scaling (CMDSCALE)
• Project sequence to best 2 dimensions
• Kernel density estimation

#12: A/Texas/05/2009 #28: A/New York/19/2009

Protein distance map of swine flu

• Kernel density estimation estimates the probability density function

from protein distance map and it shows the density of influenza in sequence space

Protein distance map Kernel density estimation

A/Texas/05

A/New York/19

Criteria for New Strains

• Criteria

– New strain is in cluster found by kernel density estimation – pepitope between new cluster and current dominant strain cluster is larger than size of new cluster

• For novel A/H1N1(2009), there is no

new strain as of mid-2010

British Columbia H3N2

• A/British

Columbia/RV1222/2009 appeared 15 March 2009.

• CDC did not consider it a

new strain until 24 July 2009

• Our method can detect it

at end of March 2009

• 20-30% of some South

American epidemics were this strain this year

A/Fujian H3N2

• Became

dominant in 2003/2004

• We detect by

end of 2001/2002

A/California H3N2

• We detect at

end of 2003/2004 season

Systematic Summary

• Over past 15 years of H3N2

Dengue Fever

• The most important vector borne human virus Clin. Microbiol.
• Rev. 11 (1998) 480; PNAS 96 (1999) 7352; Rev. Med. Virol. 11 (2001) 301; BMJ 324 (2002)

1563; Emer Themes Epidemiol. 2 (2005) 1

• The most important mosquito-borne virus in 2005 (CDC,

WHO)

• Transmitted by Aedes aegypti and
• A. albopictus mosquitos
• 2.5 Billion people live in 100 countries affected
• 50-100 million people infected each year
• 500 000 cases of dengue hemorrhagic fever
• 24 000 yearly human mortality

Dengue fever: Immunodominance

• 4 serotypes of dengue fever, 1 conservative mutation

between each pair of strains

• Most important vector-borne human virus
• Immunodominance inhibits tetravalent vaccine

Rothman et al., Vaccine 19 (2001) 4694 Park and Deem, Physica A 341 (2004) 455 Zhou and Deem, Vaccine 24 (2006) 2451

Multisite Vaccination

• Humans have hundreds of lymph

nodes

• T cells take 4-5 days to leave

lymph nodes in large numbers

• Vaccination so that antigen is

presented in physiologically distinct lymph nodes

• 2-4x improvement in uniformity
• f response

Experimental Verification

• Two studies investigated the diversity of a CD8T cell response to a

mixture of HIV epitopes.

• In [1], mice were immunized with a mixture of AL11 and KV9 Db-

restricted HIV epitopes. Injection to the same site resulted in a specific response to the KV9 epitope. Anatomic separation between injection sites resulted in a response against both epitopes.

• In [2], whether a broad CD8 T cell response recognizing multiple HIV-1

clades could be induced by a multi-component vaccine was assessed in mice. Single-clade A, B, and C vaccines generated limited cross- clade reactivity. Combining the three clades into one vaccine resulted in a reduced breadth of response due to immunodominance. Simultaneous administration of individual clade-specific vaccines into anatomically distinct sites on the body alleviated immunodominance and increased the number of epitopes recognized by the T cell response.

• In [3], a broader immune response to the 4-component vaccine was

generated in moneys by multi-site than by single-site vaccination

• Sanofi-Pasteur dengue vaccine [4].
• 1) J. Virol., 80:11991–11997, 2006.
• 2) Eur. J. Immunol., 37:1–12, 2007.
• 3) AJTMH, 80:302-311, 2009.
• 4) US patent #7,718,358

CRISPR

• Discovered in 1987 in E. Coli, J Bacteriol 169 (12): 5429–33
• Found in other species, 2002, Mol Microbiol 43 (6): 1565–75
• 40% of bacteria
• 90% of archaea
• Spacers found to match

phage, noticed increased polymorphism toward leader

• crRNA from spacers silences

exogenous genes

• Immune system
• Gene knockdown

Science, 327 (2010) 167

(Clustered regularly interspaced short palindromic repeats)

The Spacers

• Typical repeat in S. thermophilus CRISPR1
• Hairpin repeats

Dynamics

• Five types of events

First Model

• 2 spacers
• Infinite population (mean field)
• Definitions

vk = population of viruses with spacer k xij = population of bacteria with spacers i,j

Prediction from Model

• Generalizes 2-spacer

model – Mutation, ε = 0.01 – 30 spacers – Random deletion – r = 0.05 – n = 10, 150 phage strains, logarithmic

• Diversity decreases with

leader distance

Experimental Result 1

• Diversity of spacers of 124 strains of S. Thermophilus
• Theoretical modeling consistent with experiment results
• J. Bacteriol., 190 (2008) 1401
• J. He, M.W. Deem, PRL, 105 (2010)128102

Conclusions

• H1N1 vaccine efficacy generally superior to H3N2
• pepitope measure of antigenic distance is a useful

tool for vaccine design

• Incipient novel dominant strains can be detected

early with multidimensional scaling and kernel density estimation

• Multi-site vaccination for dengue fever appears to

alleviate immunodominance