Integrative Modeling Terminology
Jared Sagendorf
06/23/2023
General Modeling Workflow
Aims to be general enough to encompass all integrative structure modeling
Andrej Sali, 2023 (private communication)
Model Distribution
General Modeling Workflow
Bayesian inference/validation is a special case of this framework
Model Distribution
General Modeling Workflow
System
Measurements
Previous Models
Physical Theory
Statistical Information
Input Information
Model Distribution
General Modeling Workflow
System
Measurements
Previous Models
Physical Theory
Statistical Information
Input Information
Definitions
system*: a collection of biological entities and/or processes being modeled
input information: any combination of experimental measurements, previous modeling efforts, physical theories, and/or statistical preferences used to inform an output model via modeling
Model Distribution
General Modeling Workflow
System
Undergraduate: “It’s a bunch of balls and sticks!”
Quantum Chemist: “It’s a time dependent electron wave function!”
Particle Physicist: “It’s a soup of leptons and quark-gluon plasma!”
What is the true nature of the system?
Model Distribution
General Modeling Workflow
System
We don’t even attempt to learn the true nature of the system.
We just choose a representation of it such that we can rationalize, explain and predict what limited information we have
Model
Unknowable!
Model Distribution
General Modeling Workflow
atoms
beads
density components
rigid bodies
0.6
0.4
multiple conformational
states
time ordered
position, temperature factor,
occupancy
position, radius,
atom assignment
location, precision
center of mass, orientation
conformational states,
proportions
conformational states,
transition probabilities
Model Representations
surface mesh
vertices, edges
Model Distribution
General Modeling Workflow
atoms
beads
density components
rigid bodies
0.6
0.4
multiple conformational
states
time ordered
position, temperature factor,
occupancy
position, radius,
atom assignment
location, precision
center of mass, orientation
conformational states,
proportions
conformational states,
transition probabilities
Model Representations
surface mesh
vertices, edges
Definitions
model representation: the set of model variables whose values are determined by modeling based on the input information
model: a particular instantiation of all the model variables (e.g. spatial/temporal coordinates, geometric parameters) defined in the model representation
Model Distribution
General Modeling Workflow
Information Likelihoods
Information Priors
Bayes Rule
Posterior
“Bayesian scoring function”
Posterior Model Distribution
Input Information
prior modeling
likelihood modeling
(system model*)
Model Distribution
General Modeling Workflow
prior model distribution
prior modeling
likelihood modeling
modeled
uncertainty
forward model – data generating process* + epistemic uncertainty
noise model – aleatoric uncertainty
Model Distribution
General Modeling Workflow
modeling process
prior model distribution
prior modeling
likelihood modeling
modeled
uncertainty
forward model – data generating process* + epistemic uncertainty
noise model – aleatoric uncertainty
Definitions
prior model: a probability density or mass function of observing a model, given a subset of input information
likelihood model: a probability density or mass function of observing input information (typically experimental data), given a model
forward model: a model that describes the data generating process* for a given model representation and input information
noise model: a model for describing a kind of aleatoric uncertainty which arises from stochastic processes inherent in the system, its environment, or the measuring devices used to collect information
system model*: a model of the system – a less ambiguous synonym for “model”
General Modeling Workflow
modeling process
Bayesian Inference Search Process
MCMC Sampling
Variational Inference
Model Distribution
multi-state
representation
model represents a distribution
over three compositional states
posterior
representation of the distribution over models
(a distribution of distributions in this example)
ensembles of models
clusters of similar,
high-scoring models
Search Process
Input Information
filtering and/or clustering
General Modeling Workflow
modeling process
Bayesian Inference Search Process
MCMC Sampling
Variational Inference
Definitions
search process: any process which generates models or distributions of models that satisfy the scoring function defined in the modeling process
posterior: a representation of the unknown distribution over models, given input information. Representations can come in the form of samples, surrogate distributions, trajectories etc.
ensemble: a sample of sufficiently good-scoring models with respect to the scoring function defined during the modeling process. May also include a notion of similarity within the ensemble.
Model Distribution