Uncertainties in Markov State Models of Small Proteins
Nicolai Kozlowski1, Helmut Grubmüller1
1Department of Theoretical and Computational Biophysics, Max-Planck-Institute for Multidisciplinary Sciences, Göttingen 37077, Germany.
Journal of Chemical Theory and Computation
|August 4, 2023
Summary
Markov state models (MSMs) analyze protein dynamics but face sampling uncertainties. This study quantifies these, finding insufficient sampling is the largest issue, offering guidelines for trajectory length and structure.
Area of Science:
- Computational Biology
- Biophysics
- Protein Dynamics
Background:
- Markov state models (MSMs) are crucial for analyzing protein dynamics from molecular dynamics (MD) simulations.
- Extracting functionally relevant timescales and motions from MSMs is often hindered by significant uncertainties.
- Insufficient sampling is a primary concern, especially for larger biomolecules like proteins.
Purpose of the Study:
- To comprehensively quantify and rank all sources of uncertainty in Markov state models.
- To provide guidelines on required sampling for achieving desired accuracy in protein dynamics analysis.
- To compare the uncertainty contributions from insufficient sampling versus other factors like model parameters and limited observed transitions.
Main Methods:
- Analysis of molecular dynamics simulations for four small globular proteins.
- Quantification and ranking of uncertainties arising from sampling, Markov state number, lag time, and dimension reduction.
- Comparison of uncertainty from single long trajectories versus multiple short trajectories.
Main Results:
- Insufficient sampling was identified as the dominant source of uncertainty in MSMs.
- A critical trajectory length (T) was found, beyond which uncertainty decreases, offering sampling guidelines.
- Single long trajectories provide better sampling accuracy than multiple short ones.
- Bayesian uncertainty estimates capture only a fraction of the total uncertainty, often leading to underestimation.
Conclusions:
- Understanding and quantifying uncertainty is critical for reliable protein dynamics analysis using MSMs.
- Optimal sampling strategies, including trajectory length, can significantly improve the accuracy of MSMs.
- Current common uncertainty estimates, like Bayesian approaches, may drastically underestimate the true uncertainty.
Related Concept Videos
01:13Physiological Pharmacokinetic Models: Assumption with Protein Binding
70
Physiological models with protein binding in pharmacokinetics offer a sophisticated approach to understanding drug disposition. These models consider drug-protein interactions, enabling them to effectively predict drug concentrations in different organs and tissues. This precision aids in accurate drug dosing, providing a significant advantage over conventional models. A key process within these models is equilibration, which ensures that drug concentrations achieve a steady state within the...
70
01:58Cooperative Allosteric Transitions
7.9K
Cooperative allosteric transitions can occur in multimeric proteins, where each subunit of the protein has its own ligand-binding site. When a ligand binds to any of these subunits, it triggers a conformational change that affects the binding sites in the other subunits; this can change the affinity of the other sites for their respective ligands. The ability of the protein to change the shape of its binding site is attributed to the presence of a mix of flexible and stable segments in the...
7.9K
01:10Propagation of Uncertainty from Systematic Error
554
The atomic mass of an element varies due to the relative ratio of its isotopes. A sample's relative proportion of oxygen isotopes influences its average atomic mass. For instance, if we were to measure the atomic mass of oxygen from a sample, the mass would be a weighted average of the isotopic masses of oxygen in that sample. Since a single sample is not likely to perfectly reflect the true atomic mass of oxygen for all the molecules of oxygen on Earth, the mass we obtain from this...
554
02:04Covalently Linked Protein Regulators
6.9K
Proteins can undergo many types of post-translational modifications, often in response to changes in their environment. These modifications play an important role in the function and stability of these proteins. Covalently linked molecules include functional groups, such as methyl, acetyl, and phosphate groups, and also small proteins, such as ubiquitin. There are around 200 different types of covalent regulators that have been identified.
These groups modify specific amino acids in a protein....
These groups modify specific amino acids in a protein....
6.9K
00:59Propagation of Uncertainty from Random Error
726
An experiment often consists of more than a single step. In this case, measurements at each step give rise to uncertainty. Because the measurements occur in successive steps, the uncertainty in one step necessarily contributes to that in the subsequent step. As we perform statistical analysis on these types of experiments, we must learn to account for the propagation of uncertainty from one step to the next. The propagation of uncertainty depends on the type of arithmetic operation performed on...
726
04:08The Uncertainty Principle
23.5K
Werner Heisenberg considered the limits of how accurately one can measure properties of an electron or other microscopic particles. He determined that there is a fundamental limit to how accurately one can measure both a particle’s position and its momentum simultaneously. The more accurate the measurement of the momentum of a particle is known, the less accurate the position at that time is known and vice versa. This is what is now called the Heisenberg uncertainty principle. He...
23.5K