1 of 15

Integrative Modeling Terminology

Jared Sagendorf

06/23/2023

2 of 15

General Modeling Workflow

Aims to be general enough to encompass all integrative structure modeling

  • multiple experimental data types
  • incorporate previous models
  • models can be multi-state, multi-scale and time-ordered

Andrej Sali, 2023 (private communication)

Model Distribution

3 of 15

General Modeling Workflow

Bayesian inference/validation is a special case of this framework

Model Distribution

4 of 15

General Modeling Workflow

System

Measurements

Previous Models

Physical Theory

Statistical Information

Input Information

Model Distribution

5 of 15

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

6 of 15

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

7 of 15

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

8 of 15

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

9 of 15

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

10 of 15

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

11 of 15

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

12 of 15

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”

13 of 15

General Modeling Workflow

modeling process

Bayesian Inference Search Process

MCMC Sampling

  • Gibbs sampling
  • NUTS

Variational Inference

  • gradient descent

Model Distribution

14 of 15

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

15 of 15

General Modeling Workflow

modeling process

Bayesian Inference Search Process

MCMC Sampling

  • Gibbs Sampling
  • NUTS

Variational Inference

  • Gradient Descent

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