Physical Theory of the Immune System NIH Michael W. Deem DARPA Rice University DOE
Outline • Grand challenges in global health • The order parameter p epitope (a new tool for vaccine design) • Virus evolution • Epidemiology • Detection via clustering • Dengue fever • CRISPR BRC, Rice University
Grand Challenges in Global Health 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 H. Varmus et al. , Science 302 (2003) 398-399. • To improve vaccines • To create new vaccines
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 ~100 nm ~13 nm Epitope A Epitope B Epitope C Epitope D Epitope E
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 eq < 10 2 l/mol, the when K m 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 p epitope • 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, p epitope is the fraction of amino acids that change in the dominant epitope • We observe the efficacy of vaccination to subsequent exposure to the flu
Vaccine Efficacy • H3N2 human efficacy from last 35 years (epidemiological) • Efficacy correlates well with p epitope • p sequence and d ferret correlate modestly with human efficacy • Negative efficacy is mostly at large p epitope (OAS) • Theory validates correlation E = u − v u 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 p epitope > 0.19 to evade immune system; For H3N2 – Vaccine(n) vs. virus(n, n+1) – average p epitope = 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
H. Zhou, R. Pophale, and M. W. Deem, ``Computer-Assisted Vaccine Design,'' in Influenza: Molecular Virology , Horizon Scientific Press (2009) 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
Human Distribution • N=10 Groups ( ≈ 10³ Persons/Group) • Max=13,000 Groups/Cities (12,778,721,Mumbai,India); Min=60 Groups/Cities (60,006, http://www.mongabay.com/cities_pop_01.htm Evosmo,Greece) • Distributed in around 4,000 cities (G., Zipf, “Human Behavior and the principle of last effort”, 1949) • P(k) k -2.2
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 (Stephen Eubank et al., Nature, 2005) • P(k) k -2.8
Model Prediction • FluNet Database (Isolates)
Model Prediction • Simulation & FluNet Data Comparison
Reproductive Ratio • R 0 should be a prediction of the model, not an input • R 0 is time dependent • R 0 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
Recommend
More recommend
