Investigation of protein self-assembly processes is important for the understanding of the growth processes of functional proteins as well as disease-causing amyloids. Inside cells, intrinsic molecular fluctuations are so high that they cast doubt on the validity of the deterministic rate equation approach. Furthermore, the protein environments inside cells are often crowded with other macromolecules, with volume fractions of the crowders as high as 40%. We study protein self-aggregation at the cellular level using Gillespie's stochastic algorithm and investigate the effects of macromolecular crowding using models built on scaled-particle and transition-state theories. The stochastic kinetic method can be formulated to provide information on the dominating aggregation mechanisms in a method called reaction frequency (or propensity) analysis. This method reveals that the change of scaling laws related to the lag time can be directly related to the change in the frequencies of reaction mechanisms. Further examination of the time evolution of the fibril mass and length quantities unveils that maximal fluctuations occur in the periods of rapid fibril growth and the fluctuations of both quantities can be sensitive functions of rate constants. The presence of crowders often amplifies the roles of primary and secondary nucleation and causes shifting in the relative importance of elongation, shrinking, fragmentation and coagulation of linear aggregates. Comparison of the results of stochastic simulations with those of rate equations gives us information on the convergence relation between them and how the roles of reaction mechanisms change as the system volume is varied.
We review the effects of macromolecular crowding on the folding of RNA by considering the simplest scenario when excluded volume interactions between crowding particles and RNA dominate. Using human telomerase enzyme as an example, we discuss how crowding can alter the equilibrium between pseudoknot and hairpin states of the same RNA molecule - a key aspect of crowder-RNA interactions. We summarize data showing that the crowding effect is significant only if the size of the spherical crowding particle is smaller than the radius of gyration of the RNA in the absence of crowding particles. The i…
Macromolecules occupy between 34 and 44% of the cell cytoplasm, about half the maximum pack- ing density of spheres in three dimension. Yet, there is no clear understanding of what is special about this value. To address this fundamental question we investigate the effect of macromolecular crowding on cell metabolism. We develop a cell scale flux balance model capturing the main features of cell metabolism at different nutrient uptakes and macromolecular densities. Using this model we show there are two metabolic regimes at low and high nutrient uptakes. The latter regime is charac- terized by…
Experiments show that macromolecular crowding modestly reduces the size of intrinsically disordered proteins (IDPs) even at volume fraction ($ϕ$) similar to that in the cytosol whereas DNA undergoes a coil-to-globule transition at very small $ϕ$. We show using a combination of scaling arguments and simulations that the polymer size $\overline{R}_g(ϕ)$ depends on $x = \overline{R}_g(0)/D$ where $D$ is the $ϕ$-dependent distance between the crowders. If $x\lesssim \mathcal{O}(1)$, there is only a small decrease in $\overline{R}_g(ϕ)$ as $ϕ$ increases. When $x\gg \mathcal{O}(1)$, a cooperative co…
We investigate, via Brownian dynamics simulations, the reaction dynamics of a simple, non-linear chemical network (the Willamowski-Rossler network) under spatial confinement and crowding conditions. Our results show that the presence of inert crowders has a non-nontrivial effect on the dynamics of the network and, consequently, that effective modeling efforts aiming at a general understanding of the behavior of biochemical networks in vivo should be stochastic in nature and based on an explicit representation of both spatial confinement and macromolecular crowding.
The looping of polymers such as DNA is a fundamental process in the molecular biology of living cells, whose interior is characterised by a high degree of molecular crowding. We here investigate in detail the looping dynamics of flexible polymer chains in the presence of different degrees of crowding. From the analysis of the looping-unlooping rates and the looping probabilities of the chain ends we show that the presence of small crowders typically slow down the chain dynamics but larger crowders may in fact facilitate the looping. We rationalise these non-trivial and often counterintuitive e…
Macromolecular crowding plays a principal role in a wide range of biological processes including gene expression, chromosomal compaction, and viral infection. However, the impact that crowding has on the dynamics of nucleic acids remains a topic of debate. To address this problem, we use single-molecule fluorescence microscopy and custom particle-tracking algorithms to investigate the impact of varying macromolecular crowding conditions on the transport and conformational dynamics of large DNA molecules. Specifically, we measure the mean-squared center-of-mass displacements, as well as the con…
The formation and regulation of macromolecular complexes provides the backbone of most cellular processes, including gene regulation and signal transduction. The inherent complexity of assembling macromolecular structures makes current computational methods strongly limited for understanding how the physical interactions between cellular components give rise to systemic properties of cells. Here we present a stochastic approach to study the dynamics of networks formed by macromolecular complexes in terms of the molecular interactions of their components. Exploiting key thermodynamic concepts, …
Collective behavior of proteins on biomembranes is usually studied within the spontaneous curvature model. Here we consider an alternative phenomenological approach, which accounts consistently for partial ordering of proteins as well as the anchoring forces exerted on a membrane by layer of proteins. We show analytically that such anisotropic interactions can drive membrane bending, resulting in non-trivial equilibrium morphologies. The predicted instabilities can advance our conceptual understanding of physical mechanisms behind collective phenomena in biological systems, in particular those…
A modeling framework for the internal conformational dynamics and external mechanical movement of single biological macromolecules in aqueous solution at constant temperature is developed. Both the internal dynamics and external movement are stochastic; the former is represented by a master equation for a set of discrete states, and the latter is described by a continuous Smoluchowski equation. Combining these two equations into one, a comprehensive theory for the Brownian dynamics and statistical thermodynamics of single macromolecules arises. This approach is shown to have wide applications.…
In the cell, proteins fold and perform complex functions through global structural rearrangements. Function requires a protein to be at the brink of stability to be susceptible to small environmental fluctuations, yet stable enough to maintain structural integrity. These apparently conflicting behaviors are exhibited by systems near a critical point, where distinct phases merge $-$ a concept beyond previous studies indicating proteins have a well-defined folded/unfolded phase boundary in the pressure-temperature plane. Here, by modeling the protein phosphoglycerate kinase (PGK) on the temperat…
Intrinsically disordered proteins (IDPs) abound in cellular regulation. Their interactions are often transitory and highly sensitive to salt concentration and posttranslational modifications. However, little is known about the effect of macromolecular crowding on the kinetics and stability of the interactions of IDPs with their cellular targets. Here, we investigate the influence of crowding on the coupled folding and binding between two IDPs, using polyethylene glycol as a crowding agent across a broad size range. Single-molecule Förster resonance energy transfer allows us to quantify several…
Two isoforms of beta amyloid peptides, Ab40 and Ab42, differ from each other only in the last two amino acids, IA, at the end of Ab42. They, however, differ significantly in their ability in inducing Alzheimer's disease (AD). The rate curves of fibril growth of Ab40 and Ab42 and the effects of molecular crowding have been measured in in vitro experiments. These experimental curves, on the other hand, have been fitted in terms of rate constants for elementary reaction steps using rate equation approaches. Several sets of such rate parameters have been reported in the literature. Employing a rec…
Unlike their model membrane counterparts, biological membranes are richly decorated with a heterogeneous assembly of membrane proteins. These proteins are so tightly packed that their excluded area interactions can alter the free energy landscape controlling the conformational transitions suffered by such proteins. For membrane channels, this effect can alter the critical membrane tension at which they undergo a transition from a closed to an open state, and therefore influence protein function \emph{in vivo}. Despite their obvious importance, crowding phenomena in membranes are much less well…
The formation of DNA loops by proteins and protein complexes that bind at distal DNA sites plays a central role in many cellular processes, such as transcription, recombination, and replication. Here we review the basic thermodynamic concepts underlying the assembly of macromolecular complexes on looped DNA and the effects that this process has in the properties of gene regulation. Beyond the traditional view of DNA looping as a mechanism to increase the affinity of regulatory molecules for their cognate sites, recent developments indicate that DNA looping can also lead to the suppression of c…
RNAs are negatively charged molecules residing in macromolecular crowding cellular environments. Macromolecular confinement can influence the ion effects in RNA folding. In this work, using the recently developed tightly bound ion model for ion fluctuation and correlation, we investigate the confinement effect on the ion-mediated RNA structural collapse for a simple model system. We found that, for both Na$^+$ and Mg$^{2+}$, ion efficiencies in mediating structural collapse/folding are significantly enhanced by the structural confinement. Such an enhancement in the ion efficiency is attributed…
During the life cycle of bacterial cells the non-mixing of the two ring-shaped daughter genomes is an important prerequisite for the cell division process. Mimicking the environments inside highly crowded biological cells, we study the dynamics and statistical behaviour of two flexible ring polymers in the presence of cylindrical confinement and crowding molecules. From extensive computer simulations we determine the degree of ring-ring overlap and the number of inter-monomer contacts for varying volume fractions $ϕ$ of crowders. We also examine the entropic de-mixing of polymer rings in the p…
In bacteria, regulatory proteins search for a specific DNA binding target via "facilitated diffusion": a series of rounds of 3D diffusion in the cytoplasm, and 1D linear diffusion along the DNA contour. Using large scale Brownian dynamics simulations we find that each of these steps is affected differently by crowding proteins, which can either be bound to the DNA acting as a road block to the 1D diffusion, or freely diffusing in the cytoplasm. Macromolecular crowding can strongly affect mechanistic features such as the balance between 3D and 1D diffusion, but leads to surprising robustness of…
We propose a model for the mechanical behavior of protein materials. Based on a limited number of experimental macromolecular parameters (persistence and contour lengths, rate of unfolding dissipation) we obtain the macroscopic behavior of keratin fibers (human, cow, and rabbit hair), taking into account the damage and residual stretches effects which are fundamental in many functions of life. We support our theoretical results by showing that our model is robust and able to reproduce with high quantitive accuracy the cyclic experimental behavior of different keratinous protein materials we te…
Ribosome is a molecular machine that polymerizes a protein where the sequence of the amino acid residues, the monomers of the protein, is dictated by the sequence of codons (triplets of nucleotides) on a messenger RNA (mRNA) that serves as the template. The ribosome is a molecular motor that utilizes the template mRNA strand also as the track. Thus, in each step the ribosome moves forward by one codon and, simultaneously, elongates the protein by one amino acid. We present a theoretical model that captures most of the main steps in the mechano-chemical cycle of a ribosome. The stochastic movem…
Thermodynamic bulk measurements of binding reactions critically rely on the validity of the law of mass action and the assumption of a dilute solution. Yet important biological systems such as allosteric ligand-receptor binding, macromolecular crowding, or misfolded molecules may not follow this fundamental law and require a particular reaction model. Here we introduce a fluctuation theorem for ligand binding and an experimental approach using single-molecule force-spectroscopy to determine binding energies, selectivity and allostery of nucleic acids, proteins and peptides in a model-independe…
Several important biological processes are initiated by the binding of a protein to a specific site on the DNA. The strategy adopted by a protein, called transcription factor (TF), for searching its specific binding site on the DNA has been investigated over several decades. In recent times the effects obstacles, like DNA-binding proteins, on the search by TF has begun to receive attention. RNA polymerase (RNAP) motors collectively move along a segment of the DNA during a genomic process called transcription. This RNAP traffic is bound to affect the diffusive scanning of the same segment of th…
Many {\it ribosomes} simultaneously move on the same messenger RNA (mRNA), each synthesizing separately a copy of the same protein. In contrast to the earlier models, here {\it we develop a ``unified'' theoretical model} that not only incorporates the {\it mutual exclusions} of the interacting ribosomes, but also describes explicitly the mechano-chemistry of each of these macromolecular machines during protein synthesis. Using analytical and numerical techniques of non-equilibrium statistical mechanics, we analyze the rates of protein synthesis and the spatio-temporal organization of the ribos…
Recent work has shown that the hydrophobic protein surfaces in aqueous solution sit near a drying transition. The tendency for these surfaces to expel water from their vicinity leads to self assembly of macromolecular complexes. In this article we show with a realistic model for a biologically pertinent system how this phenomenon appears at the molecular level. We focus on the association of the C-terminal domain (CA-C) of the human immunodeficiency virus (HIV) capsid protein. By combining all-atom simulations with specialized sampling techniques we measure the water density distribution durin…
Cell division site positioning is precisely regulated to generate correctly sized and shaped daughters. We uncover a novel strategy to position the FtsZ cytokinetic ring at midcell in the social bacterium Myxococcus xanthus. PomX, PomY and the nucleoid-binding ParA/MinD ATPase PomZ self-assemble forming a large nucleoid-associated complex that localizes at the division site before FtsZ to directly guide and stimulate division. PomXYZ localization is generated through self-organized biased random motion on the nucleoid towards midcell and constrained motion at midcell. Experiments and theory sh…
Motor enzymes are remarkable molecular machines that use the energy derived from the hydrolysis of a nucleoside triphosphate to generate mechanical movement, achieved through different steps that constitute their kinetic cycle. These macromolecules, nowadays investigated with advanced experimental techniques to unveil their molecular mechanisms and the properties of their kinetic cycles, are implicated in many biological processes, ranging from biopolymerisation (e.g. RNA polymerases and ribosomes) to intracellular transport (motor proteins such as kinesins or dyneins). Although the kinetics o…
Biopolymers serve as one-dimensional tracks on which motor proteins move to perform their biological roles. Motor protein phenomena have inspired theoretical models of one-dimensional transport, crowding, and jamming. Experiments studying the motion of Xklp1 motors on reconstituted antiparallel microtubule overlaps demonstrated that motors recruited to the overlap walk toward the plus end of individual microtubules and frequently switch between filaments. We study a model of this system that couples the totally asymmetric simple exclusion process (TASEP) for motor motion with switches between …
In cellular environment, confinement and macromulecular crowding play an important role on thermal stability and folding kinetics of a protein. We have resorted to a generalized version of the Wako-Saito-Munoz-Eaton model for protein folding to study the behavior of six different protein structures confined between two walls. Changing the distance 2R between the walls, we found, in accordance with previous studies, two confinement regimes: starting from large R and decreasing R, confinement first enhances the stability of the folded state as long as this is compact and until a given value of R…
Solutes added to solutions often dramatically impact molecular processes ranging from the suspension or precipitation of colloids to biomolecular associations and protein folding. Here we revisit the origins of the effective attractive interactions that emerge between and within macromolecules immersed in solutions containing cosolutes that are preferentially excluded from the macromolecular interfaces. Until recently, these depletion forces were considered to be entropic in nature, resulting primarily from the tendency to increase the space available to the cosolute. However, recent experimen…
Neurotransmitter receptor molecules, concentrated in synaptic membrane domains along with scaffolds and other kinds of proteins, are crucial for signal transmission across chemical synapses. In common with other membrane protein domains, synaptic domains are characterized by low protein copy numbers and protein crowding, with rapid stochastic turnover of individual molecules. We study here in detail a stochastic lattice model of the receptor-scaffold reaction-diffusion dynamics at synaptic domains that was found previously to capture, at the mean-field level, the self-assembly, stability, and …
Protein molecules in cells are synthesized by macromolecular machines called ribosomes. According to recent experimental data, we reduce the complexity of the ribosome and propose a model to express its activity in six main states. Using our model, we study the translation rate in different biological relevant situations in the presence of external force, and translation through the RNA double stranded region in the absence or presence of the external force. In the present study, we give a quantitative theory for translation rate and show that the ribosome behaves more like a Brownian Ratchet …
