From molecular networks to qualitative cell behavior

Adaptation and behavior are characteristics of life which are fundamentally dynamic. If we want to model the living cell we have to describe it as a dynamic system. Typical dynamic models are based on quantitative differential equations requiring very detailed kinetic knowledge. Alternative modeling techniques for less fine-grained information are better suited to available functional genomics data. As such, constraint-based techniques and qualitative modeling have proven themselves to be valid approaches in cell biology. These approaches offer formal support to check the consistency of molecular networks against phenotypic observations in the light of dynamic systems.     

Applications of the molecular dynamics flexible fitting method

In recent years, cryo-electron microscopy (cryo-EM) has established itself as a key method in structural biology, permitting the structural characterization of large biomolecular complexes in various functional states. The data obtained through single-particle cryo-EM has recently seen a leap in resolution thanks to landmark advances in experimental and computational techniques, resulting in sub-nanometer resolution structures being obtained routinely. The remaining gap between these data and revealing the mechanisms of molecular function can be closed through hybrid modeling tools that incorporate known atomic structures into the cryo-EM data. One such tool, molecular dynamics flexible fitting (MDFF), uses molecular dynamics simulations to combine structures from X-ray crystallography with cryo-EM density maps to derive atomic models of large biomolecular complexes. The structures furnished by MDFF can be used subsequently in computational investigations aimed at revealing the dynamics of the complexes under study. In the present work, recent applications of MDFF are presented, including the interpretation of cryo-EM data of the ribosome at different stages of translation and the structure of a membrane-curvature-inducing photosynthetic complex.     

High performance computing in biology: multimillion atom simulations of nanoscale systems

Computational methods have been used in biology for sequence analysis (bioinformatics), all-atom simulation (molecular dynamics and quantum calculations), and more recently for modeling biological networks (systems biology). Of these three techniques, all-atom simulation is currently the most computationally demanding, in terms of compute load, communication speed, and memory load. Breakthroughs in electrostatic force calculation and dynamic load balancing have enabled molecular dynamics simulations of large biomolecular complexes. Here, we report simulation results for the ribosome, using approximately 2.64 million atoms, the largest all-atom biomolecular simulation published to date. Several other nano-scale systems with different numbers of atoms were studied to measure the performance of the NAMD molecular dynamics simulation program on the Los Alamos National Laboratory Q Machine. We demonstrate that multimillion atom systems represent a 'sweet spot' for the NAMD code on large supercomputers. NAMD displays an unprecedented 85% parallel scaling efficiency for the ribosome system on 1024 CPUs. We also review recent targeted molecular dynamics simulations of the ribosome that prove useful for studying conformational changes of this large biomolecular complex in atomic detail.     

Reverse engineering biomolecular systems using -omic data: challenges, progress and opportunities

Recent advances in high-throughput biotechnologies have led to the rapid growing research interest in reverse engineering of biomolecular systems (REBMS). 'Data-driven' approaches, i.e. data mining, can be used to extract patterns from large volumes of biochemical data at molecular-level resolution while 'design-driven' approaches, i.e. systems modeling, can be used to simulate emergent system properties. Consequently, both data- and design-driven approaches applied to -omic data may lead to novel insights in reverse engineering biological systems that could not be expected before using low-throughput platforms. However, there exist several challenges in this fast growing field of reverse engineering biomolecular systems: (i) to integrate heterogeneous biochemical data for data mining, (ii) to combine top-down and bottom-up approaches for systems modeling and (iii) to validate system models experimentally. In addition to reviewing progress made by the community and opportunities encountered in addressing these challenges, we explore the emerging field of synthetic biology, which is an exciting approach to validate and analyze theoretical system models directly through experimental synthesis, i.e. analysis-by-synthesis. The ultimate goal is to address the present and future challenges in reverse engineering biomolecular systems (REBMS) using integrated workflow of data mining, systems modeling and synthetic biology.     

Non-Ewald methods: theory and applications to molecular systems

Several non-Ewald methods for calculating electrostatic interactions have recently been developed, such as the Wolf method, the reaction field method, the pre-averaging method, and the zero-dipole summation method, for molecular dynamics simulations of various physical systems, including biomolecular systems. We review the theories of these approaches and their potential applications to molecular simulations, and discuss their relationships.     

Multiscale methods for macromolecular simulations

In this article we review the key modeling tools available for simulating biomolecular systems. We consider recent developments and representative applications of mixed quantum mechanics/molecular mechanics (QM/MM), elastic network models (ENMs), coarse-grained molecular dynamics, and grid-based tools for calculating interactions between essentially rigid protein assemblies. We consider how the different length scales can be coupled, both in a sequential fashion (e.g. a coarse-grained or grid model using parameterization from MD simulations), and via concurrent approaches, where the calculations are performed together and together control the progression of the simulation. We suggest how the concurrent coupling approach familiar in the context of QM/MM calculations can be generalized, and describe how this has been done in the CHARMM macromolecular simulation package.     

Information-Theoretic Analysis of the Dynamics of an Executable Biological Model

To facilitate analysis and understanding of biological systems, large-scale data are often integrated into models using a variety of mathematical and computational approaches. Such models describe the dynamics of the biological system and can be used to study the changes in the state of the system over time. For many model classes, such as discrete or continuous dynamical systems, there exist appropriate frameworks and tools for analyzing system dynamics. However, the heterogeneous information that encodes and bridges molecular and cellular dynamics, inherent to fine-grained molecular simulation models, presents significant challenges to the study of system dynamics. In this paper, we present an algorithmic information theory based approach for the analysis and interpretation of the dynamics of such executable models of biological systems. We apply a normalized compression distance (NCD) analysis to the state representations of a model that simulates the immune decision making and immune cell behavior. We show that this analysis successfully captures the essential information in the dynamics of the system, which results from a variety of events including proliferation, differentiation, or perturbations such as gene knock-outs. We demonstrate that this approach can be used for the analysis of executable models, regardless of the modeling framework, and for making experimentally quantifiable predictions.     

Mechanistic modeling confronts the complexity of molecular cell biology

Mechanistic modeling has the potential to transform how cell biologists contend with the inescapable complexity of modern biology. I am a physiologist–electrical engineer–systems biologist who has been working at the level of cell biology for the past 24 years. This perspective aims 1) to convey why we build models, 2) to enumerate the major approaches to modeling and their philosophical differences, 3) to address some recurrent concerns raised by experimentalists, and then 4) to imagine a future in which teams of experimentalists and modelers build—and subject to exhaustive experimental tests—models covering the entire spectrum from molecular cell biology to human pathophysiology. There is, in my view, no technical obstacle to this future, but it will require some plasticity in the biological research mind-set.     

Modeling cellular processes in 3D

Recent advances in photonic imaging and fluorescent protein technology offer unprecedented views of molecular space-time dynamics in living cells. At the same time, advances in computing hardware and software enable modeling of ever more complex systems, from global climate to cell division. As modeling and experiment become more closely integrated we must address the issue of modeling cellular processes in 3D. Here, we highlight recent advances related to 3D modeling in cell biology. While some processes require full 3D analysis, we suggest that others are more naturally described in 2D or 1D. Keeping the dimensionality as low as possible reduces computational time and makes models more intuitively comprehensible; however, the ability to test full 3D models will build greater confidence in models generally and remains an important emerging area of cell biological modeling.     

Bridging the gaps in systems biology

Systems biology aims at creating mathematical models, i.e., computational reconstructions of biological systems and processes that will result in a new level of understanding—the elucidation of the basic and presumably conserved “design” and “engineering” principles of biomolecular systems. Thus, systems biology will move biology from a phenomenological to a predictive science. Mathematical modeling of biological networks and processes has already greatly improved our understanding of many cellular processes. However, given the massive amount of qualitative and quantitative data currently produced and number of burning questions in health care and biotechnology needed to be solved is still in its early phases. The field requires novel approaches for abstraction, for modeling bioprocesses that follow different biochemical and biophysical rules, and for combining different modules into larger models that still allow realistic simulation with the computational power available today. We have identified and discussed currently most prominent problems in systems biology: (1) how to bridge different scales of modeling abstraction, (2) how to bridge the gap between topological and mechanistic modeling, and (3) how to bridge the wet and dry laboratory gap. The future success of systems biology largely depends on bridging the recognized gaps.     

Novel computational biology methods and their applications to drug discovery

Computational biology methods are now firmly entrenched in the drug discovery process. These methods focus on modeling and simulations of biological systems to complement and direct conventional experimental approaches. Two important branches of computational biology include protein homology modeling and the computational biophysics method of molecular dynamics. Protein modeling methods attempt to accurately predict three-dimensional (3D) structures of uncrystallized proteins for subsequent structure-based drug design applications. Molecular dynamics methods aim to elucidate the molecular motions of the static representations of crystallized protein structures. In this review we highlight recent novel methodologies in the field of homology modeling and molecular dynamics. Selected drug discovery applications using these methods conclude the review.     

Protocol for MM/PBSA molecular dynamics simulations of proteins

Continuum solvent models have been employed in past years for understanding processes such as protein folding or biomolecular association. In the last decade, several attempts have been made to merge atomic detail molecular dynamics simulations with solvent continuum models. Among continuum models, the Poisson-Boltzmann solvent accessible surface area model is one of the oldest and most fundamental. Notwithstanding its wide usage for simulation of biomolecular electrostatic potential, the Poisson-Boltzmann equation has been very seldom used to obtain solvation forces for molecular dynamics simulation. We propose here a fast and reliable methodology to implement continuum forces in standard molecular mechanics and dynamics algorithms. Results for a totally unrestrained 1 ns molecular dynamics simulation of a small protein are quantitatively similar to results obtained by explicit solvent molecular dynamics simulations.     

High-accuracy protein structures by combining machine-learning with physics-based refinement

Protein structure prediction has long been available as an alternative to experimental structure determination, especially via homology modeling based on templates from related sequences. Recently, models based on distance restraints from coevolutionary analysis via machine learning to have significantly expanded the ability to predict structures for sequences without templates. One such method, AlphaFold, also performs well on sequences where templates are available but without using such information directly. Here we show that combining machine-learning based models from AlphaFold with state-of-the-art physics-based refinement via molecular dynamics simulations further improves predictions to outperform any other prediction method tested during the latest round of CASP. The resulting models have highly accurate global and local structures, including high accuracy at functionally important interface residues, and they are highly suitable as initial models for crystal structure determination via molecular replacement.     

MoDEL (Molecular Dynamics Extended Library): a database of atomistic molecular dynamics trajectories

More than 1700 trajectories of proteins representative of monomeric soluble structures in the protein data bank (PDB) have been obtained by means of state-of-the-art atomistic molecular dynamics simulations in near-physiological conditions. The trajectories and analyses are stored in a large data warehouse, which can be queried for dynamic information on proteins, including interactions. Here, we describe the project and the structure and contents of our database, and provide examples of how it can be used to describe the global flexibility properties of proteins. Basic analyses and trajectories stripped of solvent molecules at a reduced resolution level are available from our web server.     

On the representability of complete genomes by multiple competing finite-context (Markov) models

A finite-context (Markov) model of order k yields the probability distribution of the next symbol in a sequence of symbols, given the recent past up to depth k. Markov modeling has long been applied to DNA sequences, for example to find gene-coding regions. With the first studies came the discovery that DNA sequences are non-stationary: distinct regions require distinct model orders. Since then, Markov and hidden Markov models have been extensively used to describe the gene structure of prokaryotes and eukaryotes. However, to our knowledge, a comprehensive study about the potential of Markov models to describe complete genomes is still lacking. We address this gap in this paper. Our approach relies on (i) multiple competing Markov models of different orders (ii) careful programming techniques that allow orders as large as sixteen (iii) adequate inverted repeat handling (iv) probability estimates suited to the wide range of context depths used. To measure how well a model fits the data at a particular position in the sequence we use the negative logarithm of the probability estimate at that position. The measure yields information profiles of the sequence, which are of independent interest. The average over the entire sequence, which amounts to the average number of bits per base needed to describe the sequence, is used as a global performance measure. Our main conclusion is that, from the probabilistic or information theoretic point of view and according to this performance measure, multiple competing Markov models explain entire genomes almost as well or even better than state-of-the-art DNA compression methods, such as XM, which rely on very different statistical models. This is surprising, because Markov models are local (short-range), contrasting with the statistical models underlying other methods, where the extensive data repetitions in DNA sequences is explored, and therefore have a non-local character.     

Transient dynamics of reduced-order models of genetic regulatory networks

In systems biology, a number of detailed genetic regulatory networks models have been proposed that are capable of modeling the fine-scale dynamics of gene expression. However, limitations on the type and sampling frequency of experimental data often prevent the parameter estimation of the detailed models. Furthermore, the high computational complexity involved in the simulation of a detailed model restricts its use. In such a scenario, reduced-order models capturing the coarse-scale behavior of the network are frequently applied. In this paper, we analyze the dynamics of a reduced-order Markov Chain model approximating a detailed Stochastic Master Equation model. Utilizing a reduction mapping that maintains the aggregated steady-state probability distribution of stochastic master equation models, we provide bounds on the deviation of the Markov Chain transient distribution from the transient aggregated distributions of the stochastic master equation model.     

Reconstruction of low-resolution molecular structures from simulated atomic force microscopy images

BackgroundAtomic Force Microscopy (AFM) is an experimental technique to study structure-function relationship of biomolecules. AFM provides images of biomolecules at nanometer resolution. High-speed AFM experiments produce a series of images following dynamics of biomolecules. To further understand biomolecular functions, information on three-dimensional (3D) structures is beneficial.MethodWe aim to recover 3D information from an AFM image by computational modeling. The AFM image includes only low-resolution representation of a molecule; therefore we represent the structures by a coarse grained model (Gaussian mixture model). Using Monte-Carlo sampling, candidate models are generated to increase similarity between AFM images simulated from the models and target AFM image.ResultsThe algorithm was tested on two proteins to model their conformational transitions. Using a simulated AFM image as reference, the algorithm can produce a low-resolution 3D model of the target molecule. Effect of molecular orientations captured in AFM images on the 3D modeling performance was also examined and it is shown that similar accuracy can be obtained for many orientations.ConclusionsThe proposed algorithm can generate 3D low-resolution protein models, from which conformational transitions observed in AFM images can be interpreted in more detail.General significanceHigh-speed AFM experiments allow us to directly observe biomolecules in action, which provides insights on biomolecular function through dynamics. However, as only partial structural information can be obtained from AFM data, this new AFM based hybrid modeling method would be useful to retrieve 3D information of the entire biomolecule.     

Crypt dynamics and colorectal cancer: advances in mathematical modelling

Mathematical modelling forms a key component of systems biology, offering insights that complement and stimulate experimental studies. In this review, we illustrate the role of theoretical models in elucidating the mechanisms involved in normal intestinal crypt dynamics and colorectal cancer. We discuss a range of modelling approaches, including models that describe cell proliferation, migration, differentiation, crypt fission, genetic instability, APC inactivation and tumour heterogeneity. We focus on the model assumptions, limitations and applications, rather than on the technical details. We also present a new stochastic model for stem-cell dynamics, which predicts that, on average, APC inactivation occurs more quickly in the stem-cell pool in the absence of symmetric cell division. This suggests that natural niche succession may protect stem cells against malignant transformation in the gut. Finally, we explain how we aim to gain further understanding of the crypt system and of colorectal carcinogenesis with the aid of multiscale models that cover all levels of organization from the molecular to the whole organ.     

Understanding biological functions through molecular networks

The completion of genome sequences and subsequent high-throughput mapping of molecular networks have allowed us to study biology from the network perspective. Experimental, statistical and mathematical modeling approaches have been employed to study the structure, function and dynamics of molecular networks, and begin to reveal important links of various network properties to the functions of the biological systems. In agreement with these functional links, evolutionary selection of a network is apparently based on the function, rather than directly on the structure of the network. Dynamic modularity is one of the prominent features of molecular networks. Taking advantage of such a feature may simplify network-based biological studies through construction of process-specific modular networks and provide functional and mechanistic insights linking genotypic variations to complex traits or diseases, which is likely to be a key approach in the next wave of understanding complex human diseases. With the development of ready-to-use network analysis and modeling tools the networks approaches will be infused into everyday biological research in the near future.     

Computational models of molecular self-organization in cellular environments

The cellular environment creates numerous obstacles to efficient chemistry, as molecular components must navigate through a complex, densely crowded, heterogeneous, and constantly changing landscape in order to function at the appropriate times and places. Such obstacles are especially challenging to self-organizing or self-assembling molecular systems, which often need to build large structures in confined environments and typically have high-order kinetics that should make them exquisitely sensitive to concentration gradients, stochastic noise, and other non-ideal reaction conditions. Yet cells nonetheless manage to maintain a finely tuned network of countless molecular assemblies constantly forming and dissolving with a robustness and efficiency generally beyond what human engineers currently can achieve under even carefully controlled conditions. Significant advances in high-throughput biochemistry and genetics have made it possible to identify many of the components and interactions of this network, but its scale and complexity will likely make it impossible to understand at a global, systems level without predictive computational models. It is thus necessary to develop a clear understanding of how the reality of cellular biochemistry differs from the ideal models classically assumed by simulation approaches and how simulation methods can be adapted to accurately reflect biochemistry in the cell, particularly for the self-organizing systems that are most sensitive to these factors. In this review, we present approaches that have been undertaken from the modeling perspective to address various ways in which self-organization in the cell differs from idealized models.