Authors: Peter D Tonner, Abe Pressman (poster #92), David Ross (poster #96) preprint: biorxiv.org/content/10.1101/2021.06.11.448129v1

source code: https://github.com/usnistgov/lantern

Interpretable Modeling of Genotype-Phenotype Landscapes with State-of-the-Art Predictive Power

Approach: Interpretable genotype-phenotype modeling with LANTERN

Latent mutational effect space (z). LANTERN 

models the effect of individual mutations in a 

latent space where mutations combine additively. 

Individual mutations (i and j) are represented by 

their corresponding mutational effect vectors (z(i)

and z(j)). LANTERN computes the z position of a 

variant combining multiple mutations (g3 = {i, j}) 

through simple addition of both vectors (z(i) + z(j)).

Impact: Accurate predictions with automatic interpretability

Landscapes align with biophysics. Along z1 and z2, 

LANTERN discovers distinct modes of variation 

between EC50 and G∞ that match the impact of 

biophysical constants of an analytic model

LANTERN quantifies robustness and additivity

In a benchmark across large-scale GPL measurements, LANTERN equals or outperforms 

alternative predictive models - including deep neural networks - in ten-fold cross-validation.

Problem

LANTERN decomposes structural details of SARS-CoV-2 ACE2 binding

LANTERN models genotype-phenotype landscapes. 

Genotype-phenotype landscapes (GPLs) measure the 

joint relationship between genetic background 

(genotype) and downstream biological function 

(phenotype). LANTERN models this data through a 

predictive relationship from genotype to phenotype 

through two key components. 

Non-linear surface: f(z). 

LANTERN models a

smooth, non-linear surface

over the latent z space to

predict the phenotype for

each variant - given it’s 

learned position in the 

latent space.

• Large-scale 

genotype-phenotype 

measurements 

(GPLs) require 

predictive modeling 

to enable design 

new sequences

• Current approaches 

make a trade-off 

between model 

interpretability and 

predictive accuracy

Prediction: LANTERN achieves unprecedented predictive power.

Predictive 

accuracy

Interpretability

LacI

Mutations: 2,501

Phenotypes: EC50, Ginf

Observations: 47,462

Reference: Tack et al., 2021

SARS-CoV-2

Mutations: 4,002

Phenotypes: Kd, log MFI

Observations: 177,759

Reference: Starr et al., 2020

avGFP

Mutations: 1,879

Phenotypes: brightness

Observations: 54,025

Reference: 

Sarkisyan et al., 2015

10-fold

Cross

validation

Distribution of mutational effects. 

The distribution of single mutant

effects is enriched along a stability

axis, while a near orthogonal binding

axis is substantially less common

The joint landscape of SARS-CoV-2 binding (log Kd) and expression (Δlog MFI). Along 

the stability axis, changes in log Kd are combined with changes to Δlog MFI. Along the 

binding axis, however, the expression (Δlog MFI) stays near constant.

LANTERN discovers mechanisms of LacI allostery

Structural association of latent dimensions. 

The strongest mutational effects along z1 are 

clustered in structural regions of known 

function: the dimer interface, ligand-binding 

pocket, and DNA-binding domain

Joint surface of LacI allostery. LANTERN learns a multidimensional surface predicting EC50 and 

G∞ as a function of z. Individual variants are shown by their predicted location in z and colored 

by their observed phenotype. Contours show the predicted posterior mean of f(z). 

Distinct mechanisms 

of disrupted ACE2 

binding. The

predicted surface 

along the stability

and binding axes 

show that decreased 

ACE2 binding can 

arise with (stability) 

or without (binding) 

decreased 

expression

Structural associations of 

each axis. Structural regions 

of the SARS-CoV-2 receptor 

binding domain (RBD) are 

enriched for mutations 

aligned with the stability

axis throughout the core 

RBD while mutations most 

strongly aligned with the 

binding axis are closer to 

the primary ACE contact 

region.

Local properties of the surface f(z) quantify important behavior of 

phenotypes. For example, the gradient (left) describes that rate of change of 

the phenotype at each z. When the gradient is near-zero, we call this 

robustness (right) because the phenotype is robust to changes in z. We also 

quantify the additivity of the landscape similarly (not shown).

• Rather than making a trade-off

between prediction accuracy and 

interpretability, LANTERN can 

provide state-of-the-art predictions

that are inherently interpretable

• LANTERN enables discovery of 

underlying mechanisms driving 

complex GPL measurements

• LANTERN scales to millions of

observations

σk

2

p(σk

2

)

σK

2

...

σ2

2

σ1

2 w1

w2

wK

i j

z(i) z(j)

Inference

Dimensionality selection. 

A hierarchical prior on the variance 

of each latent dimension ensures 

LANTERN learns the dimensionality 

directly from the data

Gaussian process (GP) prior

LANTERN places a GP prior on f(z) to 

learn the non-linear surface directly 

from that data without requiring a 

predefined parametric form 

ACE2 contact

x : wild-type (origin)