Ishanu Chattopadhyay PRO
ML | Data Science Biomedical Informatics | Social Science | Assistant Professor
Large Science Models: Digital Twins for Viral Evolution
Ishanu Chattopadhyay, PhD
Assistant Professor of Biomedical Informatics & Computer Science
University of Kentucky
ishanu_ch@uky.edu
Stamping Out the Next Pandemic **Before** The First Human Infection
BioNorad
BioNorad
Chattopadhyay, Ishanu, Kevin Wu, Jin Li, and Aaron Esser-Kahn. "Emergenet: Fast Scalable Pandemic Risk Assessment of Influenza A Strains Circulating In Non-human Hosts." (2023). Under Review
PREEMPT
Predicting Future Mutations for Viral Genomes in the Wild
predict future emergence risk
Hemaglutinnin
Neuraminidase
Mediates Cellular Entry
Surface structures involved in host interaction
Mediates Cellular Exit
*Hothorn, Torsten, Kurt Hornik, and Achim Zeileis. "Unbiased recursive partitioning: A conditional inference framework." Journal of Computational and Graphical statistics 15, no. 3 (2006): 651-674.
emergent macro-structure
Component predictor (Conditional Inference Tree*)
Example: Influenza A HA protein
Recursive
LSM
forest
LSM Forest of Conditional Inference Trees*
Revealing Emergent Cross-talk from observed sequence variations
>200,000 HA sequences
LSM Forest
Recursive LSM forest: hyperlinked nodes capturing emergent macro-structures
- Set of conditional inference trees (CIT)
- Strict statistical guarantees: quantifies inference uncertainty
- Each tree models exactly one variable as a function of potentially all other variables
- Non-leaf nodes are "hyperlinked" to other trees
H3
Northern Hemisphere
2021
Influenza A: HA
LSM Forest
Recursive LSM forest: hyperlinked nodes capturing emergent macro-structures
- Set of conditional inference trees (CIT)
- Strict statistical guarantees: quantifies inference uncertainty
- Each tree models exactly one variable as a function of potentially all other variables
- Non-leaf nodes are "hyperlinked" to other trees
H5
2013
Influenza A: HA
Large Science Models: Mathematical Framework
\begin{aligned}
\text{Observables:} \quad & \color{yellow}X = \{x^1, \ldots, x^N\}, \overbrace{x^i \in \Sigma^i}^{\text{finite alphabet}} \\
{\color{gray}\text{Notation:} }\quad & \color{gray} x^{-i} = \{x^j : j \ne i\}\\
\text{Crosstalk:} \quad & \forall i \ P(x^i) = \color{red} f_i(x^{-i}) \\
\text{System state:} \quad & \color{Cyan} \psi = \bigotimes_{i=1}^N \psi^i, \quad \psi^i \in \mathscr{D}(\Sigma^i) \cup \varnothing \\
%\textbf{Degenerate case:} \quad & \psi^i \text{ is a delta distribution (fully observed)} \\
{\color{gray}\text{Notation:} }\quad & \color{gray}\psi^{-i} = \bigotimes_{j \ne i} \psi^j
\end{aligned}
| 222 | 223 | 224 | --- | 560 | |
|---|---|---|---|---|---|
| strain 1 | |||||
| strain 2 | |||||
| --- | |||||
| strain m |
observables
samples
Distributions over alphabet \(\Sigma^i\)
\phi = \bigotimes_{i=1}^N \phi^i, \quad \phi^i(\psi^{-i}) \in \mathscr{D}(\Sigma^i) \\
Individual Predictor (CIT)
cross-talk
\phi(\psi) \vert \vert \psi
Tension between predicted and observed distribution drives change
Example: HA Site 223 on Influenza A
\(\psi^i\)
| K | G | Y | S | T |
\Sigma^i
Digital Twin
\phi^i(\psi^{-i}) \sim \widetilde{\psi}^i
\(\phi\) estimates \(\psi\)
population
individual
estimate is always a non-empty non-degenerate distribution
missing observation
Large Science Models: Properties
LSM-Distance Metric*
\theta(\psi,\psi') \triangleq \frac{1}{N}\sum_{i=1}^{N} \sqrt{D_{JS}\Bigl(\phi^i(\psi^{-i}) \vert \vert \phi^i(\psi'^{-i})\Bigr)}
where \(D_{JS}(P\vert \vert Q)\) is the Jensen-Shannon divergence.
g_{ij}(\psi) \;=\; \frac{1}{2}\,\frac{\partial^2}{\partial \psi^i\,\partial \psi^j}\,\theta^2(\psi,\psi')\Biggr|_{\psi'=\psi}
\left \lvert \ln \frac{\Pr(\psi\to \psi')}{\Pr(\psi' \rightarrow \psi')}\right \rvert \le \beta\,\theta(\psi,\psi')
Large Deviation Bound*
Induced Riemannian metric tensor
This bound connects ``closeness'' of samples to the odds of perturbing from one to the other, bridging geometry to dynamics
Ergodic Projection
\psi_\star \triangleq \bigotimes_{i=1}^N\phi^i\left (\prod_{1}^{N-1}\varnothing\right )
(Sanov's Theorem, Pinkser's Inequality)
\(\psi\)
\(\psi'\)
\(\theta\)
"spatial average": average of all plausible worldviews or states
* Sizemore, Nicholas, Kaitlyn Oliphant, Ruolin Zheng, Camilia R. Martin, Erika C. Claud, and Ishanu Chattopadhyay. "A digital twin of the infant microbiome to predict neurodevelopmental deficits." Science Advances 10, no. 15 (2024): eadj0400. https://www.science.org/doi/full/10.1126/sciadv.adj0400
persistence probability
Ergodic dispersion
\Psi_\star = \theta(\psi,\psi_\star)
Central to Model Drift Quantification
Start with opinion vector with all entries missing
This is a standard Physics construct, quantifying curvature of the underlying latent geometry
Pr(\psi \rightarrow \psi')
Easily computable in LSM framework!
Apply \(\phi^i\)
Random variable quantifying dispersion around the spatial average of worlviews
const. scaling as \(N^2\)
\frac{\delta \theta(x,y)}{\delta y}
Influenza Risk Assessment Tool (IRAT) scoring for animal strains
slow (months), quasi-subjective, expensive
*https://www.cdc.gov/flu/pandemic-resources/monitoring/irat-virus-summaries.htm
24 scores in 14 years
~10,000 strains collected annually
CDC
Emergenet time: 1 second
Stamping Out the Next Pandemic **Before** The First Human Infection
BioNorad
BioNorad
Digital Twin & Fidelity of Simulation
\mathcal{N}_\epsilon(\psi) \triangleq \big\{ \psi': {\color{red}\forall i \ \psi'_i \sim \phi^i\left ( \psi^{-i}\right )}
\wedge {\color{yellow} \theta(\psi,\psi') \leqq \epsilon }\big \}
Sample predicted distributions
perturbed state within \(\epsilon\) of \(\psi\)
Digital Twin
-Neighborhood of state \(\psi\)
\epsilon
Definition
Sample neighborhood to impute missing data
\psi
\epsilon
}
LSM sampling: sampling the \(\epsilon\)-neighborhood of a strain reveals local "valid perturbations"
- Predict new "likely" strains before first observation, given current population
{\color{Tomato}\psi_\star }\rightarrow \psi \rightarrow \cdots \rightarrow \psi'
Null state (all missing observations)
Valid perturbations/ simulations
- Construct complete strains from scratch (from all "missing" site information)
- Track likely trajectories through strain space
Note: The LSM can evolve too (the rules can change over time)
Emergent Equations of Motion
L \triangleq \frac{1}{2} \sum_i g_{kl} P^k_p \dot{\psi}^p_i P^l_n \dot{\psi}^n_i - \theta(\psi, \phi)
Define Lagrangian*
\frac{d}{dt} \left( \frac{\partial L}{\partial \dot{\psi}^m_i} \right) - \frac{\partial L}{\partial \psi^m_i} = 0
Via the Euler-Lagrange Equations\(^\dag\):
\ddot{\psi}^m_i = -g^{km} P^k_m \frac{1}{2N} \sum_j \frac{1}{\sqrt{D_{JS}(\psi^m_j \| \phi^m_j)}} \left[ \ln\left( \frac{2e\psi^m_j}{\psi^m_j + \phi^m_j} \right) - \frac{1}{2(\psi^m_j + \phi^m_j)} \right]
Over-damped Gradient flow Equation*
where \(-g^{km}\) is the inverse metric tensor
kinetic energy
potential energy
* Einstein notation used
Goldstein, Herbert, et al. Classical Mechanics. 3rd ed., Pearson, 2002.
\(^\dag\)
Principle of stationary action
Local potential field eqn
Question:
Why has the Mississippi lineage of Influenza C vanished from human circulation recently, while other lineages continue to exist?
LSM Forest
Recursive LSM forest: hyperlinked nodes capturing emergent macro-structures
- Set of conditional inference trees (CIT)
- Strict statistical guarantees: quantifies inference uncertainty
- Each tree models exactly one variable as a function of potentially all other variables
- Non-leaf nodes are "hyperlinked" to other trees
H0
H1
M0
LSM-clustering on human HEV sequences
The three bovine sequences are not part of these clusters (these are all human ICV HE), but we can still compute the distance of the individual human sequences to each of the three bovine strains. And the cluster they come closest to.. Pretty clearly is the one labelled as M0. The other clusters are labeled H0 and H1.
Distance of bovine sequences to M0 cluster
'C/Miyagi/2/94', 'C/Saitama/2/2000', 'C/Yamagata/3/2000', 'C/Miyagi/7/93', 'C/Miyagi/4/96', 'C/Saitama/1/2004', 'C/Miyagi/7/96', 'C/Greece/1/79', 'C/Yamagata/5/92', 'C/Miyagi/3/93', 'C/Miyagi/4/93', 'C/Kyoto/41/82', 'C/Nara/82', 'C/Hyogo/1/83', 'C/Miyagi/1/94', 'C/Miyagi/6/93', 'C/Miyagi/3/94', 'C/Mississippi/80', 'C/Yamagata/26/2004', 'C/Mississippi/80'
Variation by Time of collection
Suggests movement from M0 to H0 to H1
Estimation of Cluster Fitness from LSM
\omega(\mathcal{C}) =\frac{1}{\vert \mathcal{C}\vert} \sum_{x \in \mathcal{C}}\log Pr(x \rightarrow x)
| M0 | -64.251 |
|---|---|
| H0 | -32.586 |
| H1 | -15.964 |
Fitness calculations are based on the Emergenet model, and correspond to the estimate loglikelihood of a strain NOT PERTURBING out of the cluster. Thus the H1 cluster is the most "fit", where the strains have moved over time, and is also the largest in the data. Overlap on the collection times between H0 and H1 implies this is not simply a collection bias effect (the sizes of the clusters). This has resulted in the strain disappearing from humans, as the virus found a more fit niche on the landscape.
Maximal Site Contribution to Fitness Delta
8 75 87 97 141 154 165 178 181 183 203 205 211 216 230 252 327 361 506 588
{i} =\argmax \delta \omega(x)
Local Potential Fields
Local potential fields can be computed given the LSM and dynamical considerations, which reveal future evolution
Stable
(captured by local extrema)
Free to move locally towards extrema
Observation: This lineage (Mississippi lineage) is now extinct since 2022/23
stable lineage
Equations of Motion
L \triangleq \frac{1}{2} \sum_i g_{kl} P^k_p \dot{\psi}^p_i P^l_n \dot{\psi}^n_i - \theta(\psi, \phi)
Define Lagrangian\(\dag\)
\ddot{\psi}^m_i = -g^{km} P^k_m \frac{1}{2N} \sum_j \frac{1}{\sqrt{D_{JS}(\psi^m_j \| \phi^m_j)}} \left[ \ln\left( \frac{2e\psi^m_j}{\psi^m_j + \phi^m_j} \right) - \frac{1}{2(\psi^m_j + \phi^m_j)} \right]
Over-damped Gradient flow Equation\(\dag\)
where \(-g^{km}\) is the inverse metric tensor
kinetic energy
potential energy
Goldstein, Herbert, et al. Classical Mechanics. 3rd ed., Pearson, 2002.
\(^\dag\)
Principle of stationary action
Local potential field eqn
Future
- Collaboration with Equine Expertise at UK to allow wet-lab validation
- Atlas of viral digital twins
- Bio-NORAD testbed
- Pathogenicity assays
- Future-proof Vaccine design
Feng Li
Professor, William Robert Mills Chair in Equine Infectious Diseases
Influenza
HIV
COVID
CCHF
ishanu_ch@uky.edu
LSM-emergenet
By Ishanu Chattopadhyay
LSM-emergenet
Emergenet Discussion
