A physics-based approach of coarse-graining the cytoplasm of Escherichia coli (CGCYTO)

Docking-based long timescale simulation of cell-size protein systems at atomic resolution

Advances in computational modeling have led to an increasing focus on larger biomolecular systems, up to the level of a cell. Protein interactions are a central component of cellular processes. Techniques for modeling protein interactions have been divided between two fields: protein docking (predicting the static structures of protein complexes) and molecular simulation (modeling the dynamics of protein association, for relatively short simulation times at atomic resolution). Our study combined the two approaches to reach very long simulation times. The study makes the model more adequate to the real cells, to explore cellular processes at atomic resolution to better understand molecular mechanisms of life, and to use this knowledge to improve our ability to treat diseases.

Computational methodologies are increasingly addressing modeling of the whole cell at the molecular level. Proteins and their interactions are the key component of cellular processes. Techniques for modeling protein interactions, thus far, have included protein docking and molecular simulation. The latter approaches account for the dynamics of the interactions but are relatively slow, if carried out at all-atom resolution, or are significantly coarse grained. Protein docking algorithms are far more efficient in sampling spatial coordinates. However, they do not account for the kinetics of the association (i.e., they do not involve the time coordinate). Our proof-of-concept study bridges the two modeling approaches, developing an approach that can reach unprecedented simulation timescales at all-atom resolution. The global intermolecular energy landscape of a large system of proteins was mapped by the pairwise fast Fourier transform docking and sampled in space and time by Monte Carlo simulations. The simulation protocol was parametrized on existing data and validated on a number of observations from experiments and molecular dynamics simulations. The simulation protocol performed consistently across very different systems of proteins at different protein concentrations. It recapitulated data on the previously observed protein diffusion rates and aggregation. The speed of calculation allows reaching second-long trajectories of protein systems that approach the size of the cells, at atomic resolution.

Effect of Protein–Protein Interactions on Translational Diffusion of Spheroidal Proteins

One of the commonly accepted approaches to estimate protein–protein interactions (PPI) in aqueous solutions is the analysis of their translational diffusion. The present review article observes a phenomenological approach to analyze PPI effects via concentration dependencies of self- and collective translational diffusion coefficient for several spheroidal proteins derived from the pulsed field gradient NMR (PFG NMR) and dynamic light scattering (DLS), respectively. These proteins are rigid globular α-chymotrypsin (ChTr) and human serum albumin (HSA), and partly disordered α-casein (α-CN) and β-lactoglobulin (β-Lg). The PPI analysis enabled us to reveal the dominance of intermolecular repulsion at low ionic strength of solution (0.003–0.01 M) for all studied proteins. The increase in the ionic strength to 0.1–1.0 M leads to the screening of protein charges, resulting in the decrease of the protein electrostatic potential. The increase of the van der Waals potential for ChTr and α-CN characterizes their propensity towards unstable weak attractive interactions. The decrease of van der Waals interactions for β-Lg is probably associated with the formation of stable oligomers by this protein. The PPI, estimated with the help of interaction potential and idealized spherical molecular geometry, are in good agreement with experimental data.

Influence of Nonspecific Interactions on Protein Associations: Implications for Biochemistry In Vivo

The cellular interior is composed of a variety of microenvironments defined by distinct local compositions and composition-dependent intermolecular interactions. We review the various types of nonspecific interactions between proteins and between proteins and other macromolecules and supramolecular structures that influence the state of association and functional properties of a given protein existing within a particular microenvironment at a particular point in time. The present state of knowledge is summarized, and suggestions for fruitful directions of research are offered. Expected final online publication date for the Annual Review of Biochemistry, Volume 91 is June 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

Charge-driven condensation of RNA and proteins suggests broad role of phase separation in cytoplasmic environments

Phase separation processes are increasingly being recognized as important organizing mechanisms of biological macromolecules in cellular environments. Well-established drivers of phase separation are multi-valency and intrinsic disorder. Here, we show that globular macromolecules may condense simply based on electrostatic complementarity. More specifically, phase separation of mixtures between RNA and positively charged proteins is described from a combination of multiscale computer simulations with microscopy and spectroscopy experiments. Phase diagrams were mapped out as a function of molecular concentrations in experiment and as a function of molecular size and temperature via simulations. The resulting condensates were found to retain at least some degree of internal dynamics varying as a function of the molecular composition. The results suggest a more general principle for phase separation that is based primarily on electrostatic complementarity without invoking polymer properties as in most previous studies. Simulation results furthermore suggest that such phase separation may occur widely in heterogenous cellular environment between nucleic acid and protein components.

In-cell protein landscapes: making the match between theory, simulation and experiment

Theory, computation and experiment have matched up for the folding of small proteins in vitro, a difficult feat because folding energy landscapes are fairly smooth and free energy differences between states are small. Smoothness means that protein structure and folding are susceptible to the local environment inside living cells. Theory, computation and experiment are now exploring cellular modulation of energy landscapes. Interesting concepts have emerged, such as co-evolution of protein surfaces with their cellular environment to reduce detrimental interactions. Here we look at very recent work beginning to bring together theory, simulations and experiments in the area of protein landscape modulation, to see what problems might be solved in the near future by combining these approaches.

In-Cell Protein-Protein Contacts: Transient Interactions in the Crowd

Proteins in vivo are immersed in a crowded environment of water, ions, metabolites, and macromolecules. In-cell experiments highlight how transient weak protein-protein interactions promote (via functional "quinary structure") or hinder (via competitive binding or "sticking") complex formation. Computational models of the cytoplasm are expensive. We tackle this challenge with an all-atom model of a small volume of the E. coli cytoplasm to simulate protein-protein contacts up to the 5 μs time scale on the special-purpose supercomputer Anton 2. We use three CHARMM-derived force fields: C22*, C36m, and C36mCU (with CUFIX corrections). We find that both C36m and C36mCU form smaller contact surfaces than C22*. Although CUFIX was developed to reduce protein-protein sticking, larger contacts are observed with C36mCU than C36m. We show that the lifespan Δt of protein-protein contacts obeys a power law distribution between 0.03 and 3 μs, with ∼90% of all contacts lasting <1 μs (similar to the time scale for downhill folding).

Weak Chemical Interactions That Drive Protein Evolution: Crowding, Sticking, and Quinary Structure in Folding and Function

In recent years, better instrumentation and greater computing power have enabled the imaging of elusive biomolecule dynamics in cells, driving many advances in understanding the chemical organization of biological systems. The focus of this Review is on interactions in the cell that affect both biomolecular stability and function and modulate them. The same protein or nucleic acid can behave differently depending on the time in the cell cycle, the location in a specific compartment, or the stresses acting on the cell. We describe in detail the crowding, sticking, and quinary structure in the cell and the current methods to quantify them both in vitro and in vivo. Finally, we discuss protein evolution in the cell in light of current biophysical evidence. We describe the factors that drive protein evolution and shape protein interaction networks. These interactions can significantly affect the free energy, ΔG, of marginally stable and low-population proteins and, due to epistasis, direct the evolutionary pathways in an organism. We finally conclude by providing an outlook on experiments to come and the possibility of collaborative evolutionary biology and biophysical efforts.

Crowding-Induced Elongated Conformation of Urea-Unfolded Apoazurin: Investigating the Role of Crowder Shape in Silico

Here, we show by solution nuclear magnetic resonance measurements that the urea-unfolded protein apoazurin becomes elongated when the synthetic crowding agent dextran 20 is present, in contrast to the prediction from the macromolecular crowding effect based on the argument of volume exclusion. To explore the complex interactions beyond volume exclusion, we employed coarse-grained molecular dynamics simulations to explore the conformational ensemble of apoazurin in a box of monodisperse crowders under strong chemically denaturing conditions. The elongated conformation of unfolded apoazurin appears to result from the interplay of the effective attraction between the protein and crowders and the shape of the crowders. With a volume-conserving crowder model, we show that the crowder shape provides an anisotropic direction of the depletion force, in which a bundle of surrounding rodlike crowders stabilize an elongated conformation of unfolded apoazurin in the presence of effective attraction between the protein and crowders.

Self-adaptive multiscaling algorithm for efficient simulations of many-protein systems in crowded conditions

A method is described for the efficient simulation of multiprotein systems in crowded environments. It is based on an adaptive, reversible structural coarsening algorithm that preserves relevant physical features of the proteins across scales. Water is treated implicitly whereas all the other components of the aqueous solution, such as ions, cosolutes, or osmolytes, are treated in atomic detail. The focus is on the analytical adaptation of the solvent model to different levels of molecular resolutions, which allows continuous, on-the-fly transitions between scales. This permits the analytical calculation of forces during dynamics and preserves detailed balance in Monte Carlo simulations. A major computational speedup can be achieved in systems containing hundreds of proteins without cutting off the long-range interactions. The method can be combined with a self-adaptive configurational-bias sampling technique described previously, designed to detect strong, weak, or ultra-weak protein associations and shown to improve sampling efficiency and convergence. The implementation aims to simulate early stages of multimeric complexation, aggregation, or self-assembly. The method can be adopted as the basis for a more general algorithm to identify vertices, edges, and hubs in protein interaction networks or to predict critical steps in signal transduction pathways.

Towards developing principles of protein folding and dynamics in the cell

Proteins must fold and function in the immensely complex environment of a cell, i.e. the cytoplasm-this is far from the ideal test-tube setting of a dilute solution. Here we review the advances in protein folding and dynamics inside the cell. In developing principles of protein behavior in vivo, we also begin to understand the organization and dynamics of the cytoplasm, unifying the single protein scale with the many-protein architectures at the subcellular scale. Our group has significantly contributed to this frontier by characterizing the effect of macromolecular crowding on the distribution of protein conformations. Additionally, we provide a personal perspective on becoming a theoretical biological physicist in the era of interdisciplinary research that has been greatly influenced by Dr Kamal Shukla. We also share our view on the future direction of protein folding inside a cell.

Macromolecular crowding effects in flexible polymer solutions

Biological environments are often “crowded” due to high concentrations (300–400[Formula: see text]g/L) of macromolecules. Computational modeling approaches like Molecular Dynamics (MD), rigid-body Brownian Dynamics and Monte Carlo simulations have recently emerged, which allow to study the effects macromolecular crowding at a microscopic level and to provide complementary information to experiments. Here, we use a recently introduced multiple-conformation Monte Carlo (mcMC) approach in order to study the influence of intermolecular interactions on the structural equilibrium of flexible polyethylene glycol (PEG) polymers under self-crowding conditions. The large conformational space accessible to PEG polymers allows us to evaluate the general applicability of the mcMC approach, which describes the intramolecular degrees of freedom by a finite-size ensemble of discrete conformations. Despite the simplicity of the approach, we show that influences of intermolecular interactions on the intramolecular free energy surface can be described qualitatively using mcMC. By varying the magnitude of distinct terms in the intermolecular potential, we can further study the compensating effects of repulsive and nonspecific attractive intermolecular interactions, which favor compact and extended polymer states, respectively. We use our simulation results to derive an analytical model that describes the effects of intermolecular interactions on the stability of PEG polymer conformations as a function of the radius of gyration and the corresponding solvent accessible surface. We use this model to confirm the role of molecular surfaces for attractive interactions that can counteract excluded volume effects. Extrapolation of the model further allows for the analysis of scenarios that are not easily accessible to direct simulations as described here.

Molecular simulations of cellular processes

It is, nowadays, possible to simulate biological processes in conditions that mimic the different cellular compartments. Several groups have performed these calculations using molecular models that vary in performance and accuracy. In many cases, the atomistic degrees of freedom have been eliminated, sacrificing both structural complexity and chemical specificity to be able to explore slow processes. In this review, we will discuss the insights gained from computer simulations on macromolecule diffusion, nuclear body formation, and processes involving the genetic material inside cell-mimicking spaces. We will also discuss the challenges to generate new models suitable for the simulations of biological processes on a cell scale and for cell-cycle-long times, including non-equilibrium events such as the co-translational folding, misfolding, and aggregation of proteins. A prominent role will be played by the wise choice of the structural simplifications and, simultaneously, of a relatively complex energetic description. These challenging tasks will rely on the integration of experimental and computational methods, achieved through the application of efficient algorithms. Graphical abstract.

Crowding in Cellular Environments at an Atomistic Level from Computer Simulations

The effects of crowding in biological environments on biomolecular structure, dynamics, and function remain not well understood. Computer simulations of atomistic models of concentrated peptide and protein systems at different levels of complexity are beginning to provide new insights. Crowding, weak interactions with other macromolecules and metabolites, and altered solvent properties within cellular environments appear to remodel the energy landscape of peptides and proteins in significant ways including the possibility of native state destabilization. Crowding is also seen to affect dynamic properties, both conformational dynamics and diffusional properties of macromolecules. Recent simulations that address these questions are reviewed here and discussed in the context of relevant experiments.

Peptide folding in the presence of interacting protein crowders

Using Monte Carlo methods, we explore and compare the effects of two protein crowders, BPTI and GB1, on the folding thermodynamics of two peptides, the compact helical trp-cage and the β-hairpin-forming GB1m3. The thermally highly stable crowder proteins are modeled using a fixed backbone and rotatable side-chains, whereas the peptides are free to fold and unfold. In the simulations, the crowder proteins tend to distort the trp-cage fold, while having a stabilizing effect on GB1m3. The extent of the effects on a given peptide depends on the crowder type. Due to a sticky patch on its surface, BPTI causes larger changes than GB1 in the melting properties of the peptides. The observed effects on the peptides stem largely from attractive and specific interactions with the crowder surfaces, and differ from those seen in reference simulations with purely steric crowder particles.

A new coarse-grained model for E. coli cytoplasm: accurate calculation of the diffusion coefficient of proteins and observation of anomalous diffusion

A new coarse-grained model of the E. coli cytoplasm is developed by describing the proteins of the cytoplasm as flexible units consisting of one or more spheres that follow Brownian dynamics (BD), with hydrodynamic interactions (HI) accounted for by a mean-field approach. Extensive BD simulations were performed to calculate the diffusion coefficients of three different proteins in the cellular environment. The results are in close agreement with experimental or previously simulated values, where available. Control simulations without HI showed that use of HI is essential to obtain accurate diffusion coefficients. Anomalous diffusion inside the crowded cellular medium was investigated with Fractional Brownian motion analysis, and found to be present in this model. By running a series of control simulations in which various forces were removed systematically, it was found that repulsive interactions (volume exclusion) are the main cause for anomalous diffusion, with a secondary contribution from HI.

Macromolecular crowding meets tissue engineering by self-assembly: a paradigm shift in regenerative medicine

MMC, the addition of inert polydispersed macromolecules in the culture media, effectively emulates the dense in vivo extracellular space, resulting in amplified deposition of ECM in vitro and subsequent production of cohesive, ECM-rich living substitutes.

Perspective: Coarse-grained models for biomolecular systems

By focusing on essential features, while averaging over less important details, coarse-grained (CG) models provide significant computational and conceptual advantages with respect to more detailed models. Consequently, despite dramatic advances in computational methodologies and resources, CG models enjoy surging popularity and are becoming increasingly equal partners to atomically detailed models. This perspective surveys the rapidly developing landscape of CG models for biomolecular systems. In particular, this review seeks to provide a balanced, coherent, and unified presentation of several distinct approaches for developing CG models, including top-down, network-based, native-centric, knowledge-based, and bottom-up modeling strategies. The review summarizes their basic philosophies, theoretical foundations, typical applications, and recent developments. Additionally, the review identifies fundamental inter-relationships among the diverse approaches and discusses outstanding challenges in the field. When carefully applied and assessed, current CG models provide highly efficient means for investigating the biological consequences of basic physicochemical principles. Moreover, rigorous bottom-up approaches hold great promise for further improving the accuracy and scope of CG models for biomolecular systems.

Nested sampling for materials: the case of hard spheres

The recently introduced nested sampling algorithm allows the direct and efficient calculation of the partition function of atomistic systems. We demonstrate its applicability to condensed phase systems with periodic boundary conditions by studying the three-dimensional hard-sphere model. Having obtained the partition function, we show how easy it is to calculate the compressibility and the free energy as functions of the packing fraction and local order, verifying that the transition to crystallinity has a very small barrier, and that the entropic contribution of jammed states to the free energy is negligible for packing fractions above the phase transition. We quantify the previously proposed schematic phase diagram and estimate the extent of the region of jammed states. We find that within our samples, the maximally random jammed configuration is surprisingly disordered.

Balancing bond, nonbond, and gō-like terms in coarse grain simulations of conformational dynamics

Characterization of the protein conformational landscape remains a challenging problem, whether it concerns elucidating folding mechanisms, predicting native structures or modeling functional transitions. Coarse-grained molecular dynamics simulation methods enable exhaustive sampling of the energetic landscape at resolutions of biological interest. The general utility of structure-based models is reviewed along with their differing levels of approximation. Simple Gō models incorporate attractive native interactions and repulsive nonnative contacts, resulting in an ideal smooth landscape. Non-Gō coarse-grained models reduce the parameter set as needed but do not include bias to any desired native structure. While non-Gō models have achieved limited success in protein coarse-graining, they can be combined with native structured-based potentials to create a balanced and powerful force field. Recent applications of such Gō-like models have yielded insight into complex folding mechanisms and conformational transitions in large macromolecules. The accuracy and usefulness of reduced representations are also revealed to be a function of the mathematical treatment of the intrinsic bonded topology.

Reaching new levels of realism in modeling biological macromolecules in cellular environments

An increasing number of studies are aimed at modeling cellular environments in a comprehensive and realistic fashion. A major challenge in these efforts is how to bridge spatial and temporal scales over many orders of magnitude. Furthermore, there are additional challenges in integrating different aspects ranging from questions about biomolecular stability in crowded environments to the description of reactive processes on cellular scales. In this review, recent studies with models of biomolecules in cellular environments at different levels of detail are discussed in terms of their strengths and weaknesses. In particular, atomistic models, implicit representations of cellular environments, coarse-grained and spheroidal models of biomolecules, as well as the inclusion of reactive processes via reaction-diffusion models are described. Furthermore, strategies for integrating the different models into a comprehensive description of cellular environments are discussed.

Quinary protein structure and the consequences of crowding in living cells: leaving the test-tube behind

Although the importance of weak protein-protein interactions has been understood since the 1980s, scant attention has been paid to this "quinary structure". The transient nature of quinary structure facilitates dynamic sub-cellular organization through loose grouping of proteins with multiple binding partners. Despite our growing appreciation of the quinary structure paradigm in cell biology, we do not yet understand how the many forces inside the cell--the excluded volume effect, the "stickiness" of the cytoplasm, and hydrodynamic interactions--perturb the weakest functional protein interactions. We discuss the unresolved problem of how the forces in the cell modulate quinary structure, and to what extent the cell has evolved to exert control over the weakest biomolecular interactions. We conclude by highlighting the new experimental and computational tools coming on-line for in vivo studies, which are a critical next step if we are to understand quinary structure in its native environment.

Protein-protein interactions in a crowded environment

Protein-protein interactions are important in many essential biological functions, such as transcription, translation, and signal transduction. Much progress has been made in understanding protein-protein association in dilute solution via experimentation and simulation. Cells, however, contain various macromolecules, such as DNA, RNA, proteins, among many others, and a myriad of non-specific interactions (usually weak) are present between these cellular constituents. In this review article, we describe the important developments in recent years that have furthered our understanding and even allowed prediction of the consequences of macromolecular crowding on protein-protein interactions. We outline the development of our crowding theory that can predict the change in binding free energy due to crowding quantitatively for both repulsive and attractive protein-crowder interactions. One of the most important findings from our recent work is that weak attractive interactions between crowders and proteins can actually destabilize protein complex formation as opposed to the commonly assumed stabilizing effect predicted based on traditional crowding theories that only account for the entropic-excluded volume effects. We also discuss the implications of macromolecular crowding on the population of encounter versus specific native complex.

Computer Simulations of the Bacterial Cytoplasm

Ever since the pioneering work of Minton, it has been recognized that the highly crowded interior of biological cells has the potential to cause dramatic changes to both the kinetics and thermodynamics of protein folding and association events relative to behavior that might be observed in dilute solution conditions. One very productive way to explore the effects of crowding on protein behavior has been to use macromolecular crowding agents that exclude volume without otherwise strongly interacting with the protein under study. An alternative, complementary approach to understanding the potential differences between behavior in vivo and in vitro is to develop simulation models that explicitly attempt to model intracellular environments at the molecular scale, and that thereby can be used to directly monitor biophysical behavior in conditions that accurately mimic those encountered in vivo. It is with studies of this type that the present review will be concerned. We review in detail four published studies that have attempted to simulate the structure and dynamics of the bacterial cytoplasm and that have each explored different biophysical aspects of the cellular interior. While each of these studies has yielded important new insights, there are important questions that remain to be resolved in terms of determining the relative contributions made by energetic and hydrodynamic interactions to the diffusive behavior of macromolecules and to the thermodynamics of protein folding and associations in vivo. Some possible new directions for future generation simulation models of the cytoplasm are outlined.

Where soft matter meets living matter--protein structure, stability, and folding in the cell

A protein is a biopolymer that self-assembles through the process of protein folding. A cell is a crowded space where the surrounding macromolecules of a protein can limit the number of ways of folding. These crowding macromolecules can also affect the shape and the size of a physically malleable, or 'soft, squishy', protein with regulatory purposes. In this review, we focus on the in silico approaches of coarse-grained molecular simulations that enable the investigation of protein folding in a cell-like environment. When these simulation results were compared with experimentally measured properties of a protein, such joint effort has yielded new ideas on the specific function of a protein in cells. We also highlighted the recent developments of computer modeling and simulations that encompass the importance of the shape of a macromolecule, the interactions between macromolecules, and the hydrodynamic interactions on the kinetics and thermodynamics of a protein in a high concentration of protein solution and in cytoplasmic environments.

Influence of the shape of crowding particles on the structural transitions in a polymer

We investigate the structural transitions in a polymer induced by spherical and nonspherical crowding particles over a wide range of conditions. The polymer conformations are specified by the radius of gyration and the quality of the solvent in the absence of crowding particles. In the presence of crowding particles, the structures are altered by the volume fraction, size, shape, and polydispersity of the crowders. We show that crowding induces an array of structural changes, ranging from helix, helical hairpin (HH), and multiple helix bundles (HBs), depending on the interplay of multiple length and energy scales including the solvent quality, length of the polymer, temperature, and the characteristics of the crowding agents. In nearly good solvents, the polymer undergoes coil-helix transition in accord with the predictions based on the entropic stabilization mechanism. Higher-order (HH and HB) structures are obtained in poor or moderately poor solvents. In a binary mixture of spherical crowders, the effect of the two components is largely additive with the polymer undergoing greater compaction at higher volume fraction. In contrast to spherical crowders, spherocylinder-like crowders have a dramatically different effect on the diagram of states of the polymer. In the presence of spherocylinders, the polymer prefers to form a nearly ideal helix, especially at low temperatures and high aspect ratios of the crowders, at volume fractions that are not large enough for nematic order. Surprisingly, there is a complete absence of HH and HB in the range of conditions explored here. The dominant formation of spherocylinder-induced helix formation is due to the tendency of the spherocylinders and the polymer to align along the director formed by an increase in nematic order only in the vicinity of the polymer. Our study, which has produced several testable predictions, shows that only by probing the effects of crowding on a polymer (or a protein and RNA) over a wide range of conditions can the diagram of states be quantitatively described.