Crowder Size Research Articles

Crowding induced switching of polymer translocation by the amalgamation of entropy and osmotic pressure

The translocation of polymers is omnipresent in inherently crowded biological systems. We investigate the dynamics of polymer translocation through a pore in free and crowded environments using Langevin dynamics simulation. We observed a location-dependent translocation rate of monomers showcasing counterintuitive behavior in stark contrast to the bead velocity along the polymer backbone. The free energy calculation of asymmetrically placed polymers indicates a critical number of segments to direct receiver-side translocation. For one-sided crowding, we have identified a critical crowding size revealing a nonzero probability of translocation toward the crowded-side. Moreover, we have observed that shifting the polymer toward the crowded-side compensates for one-sided crowding, yielding an equal probability akin to a crowder-free system. In two-sided crowding, a slight variation in crowder size and packing fraction induces a polymer to switch its translocation direction. These conspicuous yet counter-intuitive phenomena are rationalized by minimalistic theoretical arguments based on osmotic pressure and radial entropic forces.

Ethylene glycol energetically disfavours oligomerization of pseudoisocyanine dyestuffs at crowded concentrations.

The intriguing role of the intracellular crowded environment in regulating protein aggregation remains elusive. The convolution of several factors such as the protein sequence-dependence, crowder's shape and size and diverse intermolecular interactions makes it complex to identify systematic trends. One of the ways to simplify the problem is to study a synthetic model for self-assembling proteins. In this study, we examine the aggregation behaviour of the cationic pseudoisocyanine chloride (PIC) dyestuff which is known to self-assemble and form fibril-like J-aggregates in aqueous solutions, similar to those formed by amyloid-forming proteins. Prior experimental studies have shown that polyethylene glycol impedes and Ficoll-400 promotes the self-assembly of PIC dyes. To achieve molecular insights, we examine the effect of crowding by ethylene glycol on the solvation thermodynamics of oligomerization of dyes into H-type and J-type oligomers using extensive molecular dynamics simulations. The binding free energy calculations show that the formation of J-oligomers is more favourable than that of H-oligomers in water. The stability of H- and J- tetramers and pentamers decreases in crowded solutions. The formation of oligomers is supported by the favourable change in dye-solvent interaction energy in both pure water and aqueous ethylene glycol solution although it is opposed by the reduced dye-solvent entropy. Ethylene glycol, as a molecular crowder, disfavours the H- as well as J-oligomerization via preferential binding to the dye oligomers. An unfavourable change in dye-crowder and dye-dye interaction energy on dye association makes the H-oligomer formation less favourable in crowded solution than in pure water solution. In the case of J-oligomers, however, the unfavourable change in dye-crowder interaction energy primarily contributes to making total dye-solvent energy unfavourable. The results are supported by isothermal titration calorimetry measurements where the binding of ethylene glycol to PIC molecules is found to be endothermic. The results provide an emerging view that a crowded environment can disfavour self-assembly of PIC dyes by interactions with the oligomeric states. The findings have implications in understanding the role of a crowded environment in shaping the free energy landscapes of proteins.

Molecular Dynamics Simulations of Rhodamine B Zwitterion Diffusion in Polyelectrolyte Solutions.

Polyelectrolytes continue to find wide interest and application in science and engineering, including areas such as water purification, drug delivery, and multilayer thin films. We have been interested in the dynamics of small molecules in a variety of polyelectrolyte (PE) environments; in this paper, we report simulations and analysis of the small dye molecule rhodamine B (RB) in several very simple polyelectrolyte solutions. Translational diffusion of the RB zwitterion has been measured in fully atomistic, 2 μs long molecular dynamics simulations in four different polyelectrolyte solutions. Two solutions contain the common polyanion sodium poly(styrene sulfonate) (PSS), one with a 30-mer chain and the other with 10 trimers. The other two solutions contain the common polycation poly(allyldimethylammonium) chloride (PDDA), one with two 15-mers and the other with 10 trimers. RB diffusion was also simulated in several polymer-free solutions to verify its known experimental value for the translational diffusion coefficient, DRB, of 4.7 × 10-6 cm2/s at 300 K. RB diffusion was slowed in all four simulated PE solutions, but to varying degrees. DRB values of 3.07 × 10-6 and 3.22 × 10-6 cm2/s were found in PSS 30-mer and PSS trimer solutions, respectively, whereas PDDA 15-mer and trimer solutions yielded values of 2.19 × 10-6 and 3.34 × 10-6 cm2/s. Significant associations between RB and the PEs were analyzed and interpreted via a two-state diffusion model (bound and free diffusion) that describes the data well. Crowder size effects and anomalous diffusion were also analyzed. Finally, RB translation along the polyelectrolytes during association was characterized.

Size-Dependent Interplay of Volume Exclusion Versus Soft Interactions: Cytochrome c in Macromolecular Crowded Environment.

Even though there are a great number of possible conformational states, how a protein generated as a linear unfolded polypeptide efficiently folds into its physiologically active form remained a fascinating and unanswered enigma inside crowded conditions of cells. In this study, various spectroscopic techniques have been exploited to know and understand the effect and mechanism of action of two different sizes of polyethylene glycols, or PEGs (molecular mass ∼10 and ∼20kilo Daltons, kDa), on cytochrome c (cyt c). The outcomes showed that small size of the PEG leads to perturbation of the protein structure, and conversely, large size of the PEG has stabilizing effect on cyt c. Moreover, binding measurements showed that small size of PEG interacts strongly via soft interactions compared to the larger size of PEG, the latter being governed more by excluded volume effect or preferential exclusion from the protein. Overall, this finding suggests that conformations of protein may be influenced in cellular crowded conditions via interactions which depend upon the size of molecule in the environment. This study proposes that both volume exclusion and soft (chemical) interactions governs the protein's conformation and functional activities. The cellular environment's internal architecture as evident from crowder size and shape in this study has a significant role.

Quantification of Entropic Excluded Volume Effects Driving Crowding-Induced Collapse and Folding of a Disordered Protein.

We investigate the conformational properties of the intrinsically disordered DNA-binding domain of CytR in the presence of the polymeric crowder polyethylene glycol (PEG). Integrating circular dichroism, nuclear magnetic resonance, and single-molecule Förster resonance energy transfer measurements, we demonstrate that disordered CytR populates a well-folded minor conformation in its native ensemble, while the unfolded ensemble collapses and folds with an increase in crowder density independent of the crowder size. Employing a statistical-mechanical model, the effective reduction in the accessible conformational space of a residue in the unfolded state is estimated to be 10% at 300 mg/mL PEG8000, relative to dilute conditions. The experimentally consistent PEG-temperature phase diagram thus constructed reveals that entropic effects can stabilize disordered CytR by 10 kJ mol-1, driving the equilibrium toward folded conformations under physiological conditions. Our work highlights the malleable conformational landscape of CytR, the presence of a folded conformation in the disordered ensemble, and proposes a scaling relation for quantifying excluded volume effects on protein stability.

Kineto-Mechanistic Investigation of Effect of Macromolecular Crowding on the Breathing of DNA Bubble.

Macromolecular crowding along with hydrogen bonding or stacking interactions and hydration reportedly has enormous repercussions on elementary biochemical processes, such as the folding of proteins or nucleic acids involving the stability of DNA base pairing. By using the mismatch-induced DNA bubble as a mesoscopic model, the complex interplay of macromolecular crowding on the dynamical fluctuations at the bubble region within the thermodynamic limit has been monitored using single-molecule fluorescence resonance energy transfer (sm-FRET). These single-molecule experimental results have been further corroborated using physical models such as "scaled particle theory" (SPT) and "Gaussian cloud model" (GCM), to predict the biological activity of DNA. The two-state fluctuation of the DNA bubble has been visualized as a function of the nature, size, and concentration of the crowder. The influence of crowders on the DNA conformation has been investigated with the help of the m-factor, the eccentricity, and the kinetic and thermodynamic parameters without any prior assumption. The clear effect of crowding on the dynamics of such a simple biomolecular system emphasizes the power of single-molecule methods and the dependency of the radius of gyration of the co-solute as well as the preferential interaction with the crowder on the distinct conformational states adopted by the bubble. This study provides an idea and hypothesizes the preferential propensity of the DNA bubble to adopt a conformation with the single-stranded domains being far apart, independent of the crowder size, that may be beneficial for efficient recognition by proteins for an uninterrupted procession of the biological process of the central dogma.

Plasmid DNA Undergoes Two Compaction Regimes under Macromolecular Crowding.

The laser light scattering experiments were performed to explore the role of dextran (size (d): 2.6, 6.9, and 17.0 nm) in compacting the plasmids (pBS: 2.9 kbps; pCMV-Tag2B: 4.3 kbps; and pET28a: 5.3 kbps) in vitro in the volume fraction (ϕ) range 0.01 to 0.15 of the macromolecular crowder. Two compaction regimes were observed in terms of the radius of gyration (Rg) for plasmid-dextran combinations, wherein the plasmid diffusivity is governed by normal diffusion and subdiffusion, respectively. Generalized scaling, Rg ∼ ϕ-1/(1+x), where x represents the conformational geometry of plasmids, is reported. The plasmid conformation depends on the crowder's size, with larger conformational changes observed in the presence of smaller crowders. The second virial coefficient (A2) and translational diffusion coefficient (Dt) indicate that entropically driven depletion of crowders, excluded volume, and interplasmid repulsive interactions govern plasmids' conformational changes, validated herein from the scaling of Dt with molecular weight.

Theoretical study of the role of dynamic bulk crowders in the protein search for targets on DNA

The facilitated diffusion mechanism that involves the combination of one-dimensional and three-dimensional (3D) diffusion for recognition of a DNA target site by its protein is affected by the crowded cellular environment. Dynamic crowders can provide a better description of real processes in living cells. We develop a theoretical method based on a discrete state stochastic approach to understand the mechanism of the protein search on DNA in the presence of crowders that are moving around in the cellular medium. We obtain approximate analytical expressions for all dynamic properties. Our theoretical findings show that macromolecules present in the cellular volume and acting as dynamic crowders can influence 3D diffusion. The target search dynamics of proteins on DNA in the crowded cellular medium depend on the size and mobility of the macromolecular crowders. Highly mobile crowders do not affect the search dynamics, while slow moving crowders can significantly slow down the search process. Our theoretical results are discussed using physical explanations and they are also tested with extensive Monte Carlo computer simulations. Our theoretical predictions provide a physical understanding of the experimental observations and simulation results.

Macromolecular crowding effects on electrostatic binding affinity: Fundamental insights from theoretical, idealized models.

The crowded cellular environment can affect biomolecular binding energetics, with specific effects depending on the properties of the binding partners and the local environment. Often, crowding effects on binding are studied on particular complexes, which provide system-specific insights but may not provide comprehensive trends or a generalized framework to better understand how crowding affects energetics involved in molecular recognition. Here, we use theoretical, idealized molecules whose physical properties can be systematically varied along with samplings of crowder placements to understand how electrostatic binding energetics are altered through crowding and how these effects depend on the charge distribution, shape, and size of the binding partners or crowders. We focus on electrostatic binding energetics using a continuum electrostatic framework to understand effects due to depletion of a polar, aqueous solvent in a crowded environment. We find that crowding effects can depend predictably on a system's charge distribution, with coupling between the crowder size and the geometry of the partners' binding interface in determining crowder effects. We also explore the effect of crowder charge on binding interactions as a function of the monopoles of the system components. Finally, we find that modeling crowding via a lowered solvent dielectric constant cannot account for certain electrostatic crowding effects due to the finite size, shape, or placement of system components. This study, which comprehensively examines solvent depletion effects due to crowding, complements work focusing on other crowding aspects to help build a holistic understanding of environmental impacts on molecular recognition.

Smaller molecules crowd better: Crowder size dependence revealed by single-molecule FRET studies and depletion force modeling analysis.

The cell is an extremely crowded environment, which is known to have a profound impact on the thermodynamics, functionality, and conformational stability of biomolecules. Speculations from recent theoretical molecular dynamics studies suggest an intriguing size dependence to such purely entropic crowding effects, whereby small molecular weight crowders under constant enthalpy conditions are more effective than larger crowders on a per volume basis. If experimentally confirmed, this would be profoundly significant, as the cellular cytoplasm is also quite concentrated in smaller molecular weight solutes such as inorganic ions, amino acids, and various metabolites. The challenge is to perform such studies isolating entropic effects under isoenthalpic conditions. In this work, we first present results from single-molecule FRET spectroscopy (smFRET) on the molecular size-dependent crowding stabilization of a simple RNA tertiary motif (the GAAA tetraloop-tetraloop receptor), indeed providing evidence in support of the surprising notion in the crowding literature that "smaller is better." Specifically, systematic smFRET studies as a function of crowder solute size reveal that smaller molecules both significantly increase the RNA tertiary folding rate and, yet, simultaneously decrease the unfolding rate, predicting strongly size-dependent stabilization of RNA tertiary structures under crowded cellular conditions. The size dependence of these effects has been explored via systematic variation of crowder size over a broad range of molecular weights (90-3000 amu). Furthermore, corresponding temperature dependent studies indicate the systematic changes in the folding equilibrium to be predominantly entropic in origin, i.e., consistent with a fundamental picture of entropic molecular crowding without additional enthalpic interactions. Most importantly, all trends in the single-molecule crowding data can be quantitatively recapitulated by a simple analytic depletion force model, whereby excluded volume interactions represent the major thermodynamic driving force toward folding. Our study, thus, not only provides experimental evidence and theoretical support for small molecule crowding but also predicts further enhancement of crowding effects for even smaller molecules on a per volume basis.

Crowding Milleu stabilizes apo-myoglobin against chemical-induced denaturation: Dominance of hardcore repulsions in the heme devoid protein

Macromolecular crowding can have significant consequences on the structure and dynamics of a protein. The size and shape of a co-solute molecule and the nature of protein contribute significantly in macromolecular crowding, which results in different outcomes in similar conditions. The structure of apo-myoglobin (apo-Mb) both in the absence and presence of denaturants (GdmCl and urea) was investigated in crowded conditions at pH 7.0, with a comparable size of crowders (~70 kDa) but of different shapes (ficoll and dextran) at various concentrations using spectroscopic techniques like absorption and circular dichroism to monitor changes in secondary and tertiary structure, respectively. The crowders in the absence of denaturants showed structural stabilization of the tertiary structure while no significant change in the secondary structure was observed. The effect of crowders on the stability of the protein was also investigated using probes such as Δε291 and θ222 using chemical denaturants. The analysis of chemical-induced denaturation curves showed that both the crowders stabilize apo-Mb by increasing the values of the midpoint of transition (Cm) and change in free energy in the absence of denaturant (∆GD°), and it was observed that dextran 70 shows more stabilization than ficoll 70 under similar conditions. In this study apo-Mb showed stabilization under crowded conditions, which is a deviation from earlier work from our group where holo form of the same protein was destabilized. This study emphasizes that volume exclusion is a dominant force in a simple protein while soft interactions may play important role in the proteins that are possessing prosthetic group. Hence, the effect of crowders is protein-dependent, and excluded volume plays a great role in the stabilization of apo-Mb, which does not interact with the crowders.

Bead-based Padlock Rolling Circle Amplification under Molecular Crowding Conditions: The Effects of Crowder Charge and Size.

Bead-based padlock rolling circle amplification under molecular crowding conditions, which we have developed for ultrasensitive detection of DNA, is examined to improve the detection efficiency and sensitivity of the method as well as to gain insight into the mechanism of the method. Both non-magnetic and magnetic sepharose microbeads were employed. Biotinylated DNA had to be pre-immobilized onto the microbeads in order to obtain products on the magnetic beads. The optimal concentration of biotinylated DNA was found to be about 5 μM, above which the number of products decreased. The effect of the crowder charge was examined, and neutral polymers were found to be effective on ligation and the hybridization step, while charged polymers were only effective on the hybridization step and inhibited the ligation and primer extension. The effect of the molecular weight of neutral dextran on the number of products was investigated, and the number of products was found to be increased with an increase in the molecular weight of dextran.

Effects of active crowder size and activity-crowding coupling on polymer translocation.

Polymer translocation in complex environments is crucially important to many biological processes in life. In the present work, we adopted two-dimensional Langevin dynamics simulations to study the forced and unbiased polymer translocation dynamics in active and crowded media. The translocation time and probability are analyzed in terms of active force Fa, volume fraction φ and also the crowder size. The non-trivial active crowder size effect and activity-crowding coupling effect as well as the novel mechanism of unbiased translocation between two active environments with different active particle sizes are clarified. Firstly, for forced translocation, we reveal an intriguing non-monotonic dependence of the translocation time on the crowder size in the case of large activity. In particular, crowders of intermediate size similar to the polymer segment are proven to be the most favorable for translocation. Moreover, a facilitation-inhibition crossover of the translocation time with increasing volume fraction is observed, indicating a crucial activity-crowding coupling effect. Secondly, for unbiased translocation driven by different active crowder sizes, the translocation probability demonstrates a novel turnover phenomenon, implying the appearance of an opposite directional preference as the active force exceeds a critical value. The translocation time in both directions decreases monotonically with the active force. The asymmetric activity effect together with the entropic driving scenario provides a reasonable picture for the peculiar behavior observed in unbiased translocation.

Polymer looping kinetics in active heterogeneous environments.

A typical biological environment is usually featured by crowding and heterogeneity, leading to complex reaction kinetics of the immersed macromolecules. In the present work, we adopt Langevin dynamics simulations to systematically investigate polymer looping kinetics in active heterogeneous media crowded with a mixture of mobile active particles and immobile obstacles. For comparison, a parallel study is also performed in the passive heterogeneous media. We explicitly analyze the change of looping time and looping probability with the variation of obstacle ratio, volume fraction and crowder size. We reveal the novel phenomena of inhibition-facilitation transition of the looping rate induced by heterogeneity, crowdedness and activity. In addition, our results demonstrate a very non-trivial crowder size effect on the looping kinetics. The underlying mechanism is rationalized by the interplay of polymer diffusion, conformational change and looping free-energy barrier. The competing effect arising from active particles and obstacles on structural and dynamical properties of the polymer yields a consistent scenario for our observations. Lastly, the non-exponential kinetics of the looping process is also analyzed. We find that both activity and crowding can strengthen the heterogeneity degree of the looping kinetics.

Comparative study of polymer looping kinetics in passive and active environments.

Intra-chain looping in complex environments is significant in advancing our understanding of biological processes in life. We adopt Langevin dynamics simulations to perform a comparative study of polymer looping kinetics in passive and active environments. From the analysis of looping quantities, including looping-unlooping times and looping probabilities, we unraveled the intriguing effects of active crowder size, activity and crowding. Firstly, we figured out the phase diagram involving a novel facilitation-inhibition transition in the parameter space of active crowder size and active force, and the two-fold roles of activity are clarified. In particular, we find that active particles of a size comparable to the polymer monomer are most favorable for facilitated looping, while those with a similar size to the polymer gyration radius impede the looping most seriously. Secondly, the underlying looping mechanisms in different active crowder size regimes are rationalized by the interplay among diffusion, polymer conformational change and the free-energy barrier. For small active crowders, activity significantly promotes end-to-end distance diffusion, which dominantly facilitates both looping and unlooping processes. In the case of moderate active crowders, the polymer chain suffers from prominent swelling, and thus inevitable inhibited looping will occur. For large active crowders, activity induces a counterintuitive non-cage effect on the looping kinetics, through yielding a higher effective temperature and larger unlooping free-energy barrier. This is in sharp contrast to the caging phenomena observed in passive media. Lastly, the volume-fraction dependence of the looping quantities in an active bath demonstrates dramatic discrepancies from that in a passive bath, which highlights the contrasting effects of activity and crowding.

Effects of macromolecular crowding on the folding of a polymer chain: A Wang–Landau simulation study

A flexible polymer chain in the presence of inert macromolecular crowders will experience a loss of configurational entropy due to the crowder excluded volume. This entropy reduction will be most pronounced in good solvent conditions where the chain assumes an expanded coil conformation. For polymers that undergo a folding transition from a coil to a compact ordered state, as is the case for many globular proteins, macromolecular crowding is expected to stabilize the folded state and thereby shift the transition location. Here, we study such entropic stabilization effects for a tangent square-well sphere chain (monomer diameter σ) in the presence of hard-sphere (HS) crowders (diameter D ≥ σ). We use the Wang-Landau simulation algorithm to construct the density of states for this chain in a crowded environment and are thus able to directly compute the reduction in configurational entropy due to crowding. We study both a chain that undergoes all-or-none folding directly from the coil state and a chain that folds via a collapsed-globule intermediate state. In each case, we find an increase in entropic stabilization for the compact states with an increase in crowder density and, for fixed crowder density, with a decrease in crowder size (concentrated, small crowders have the largest effect). The crowder significantly reduces the average size for the unfolded states while having a minimal effect on the size of the folded states. In the athermal limit, our results directly provide the confinement free energy due to crowding for a HS chain in a HS solvent.

Understanding DNA interactions in crowded environments with a coarse-grained model.

Nucleic acid interactions under crowded environments are of great importance for biological processes and nanotechnology. However, the kinetics and thermodynamics of nucleic acid interactions in a crowded environment remain poorly understood. We use a coarse-grained model of DNA to study the kinetics and thermodynamics of DNA duplex and hairpin formation in crowded environments. We find that crowders can increase the melting temperature of both an 8-mer DNA duplex and a hairpin with a stem of 6-nt depending on the excluded volume fraction of crowders in solution and the crowder size. The crowding induced stability originates from the entropic effect caused by the crowding particles in the system. Additionally, we study the hybridization kinetics of DNA duplex formation and the formation of hairpin stems, finding that the reaction rate kon is increased by the crowding effect, while koff is changed only moderately. The increase in kon mostly comes from increasing the probability of reaching a transition state with one base pair formed. A DNA strand displacement reaction in a crowded environment is also studied with the model and we find that rate of toehold association is increased, with possible applications to speeding up strand displacement cascades in nucleic acid nanotechnology.

Non-monotonic dependence of polymer chain dynamics on active crowder size.

Configuration dynamics of flexible polymer chains is of ubiquitous importance in many biological processes. Here, we investigate a polymer chain immersed in a bath of size-changed active particles in two dimensional space using Langevin dynamics simulations. Particular attention is paid to how the radius of gyration Rg of the polymer chain depends on the size σc of active crowders. We find that Rg shows nontrivial non-monotonic dependence on σc: The chain first swells upon increasing σc, reaching a fully expanded state with maximum Rg, and then, Rg decreases until the chain collapses to a compact coil state if the crowder is large enough. Interestingly, the chain may oscillate between a collapse state and a stretched state at moderate crowder size. Analysis shows that it is the competition between two effects of active particles, one stretching the chain from inside due to persistence motion and the other compressing the chain from outside, that leads to the non-monotonic dependence. Besides, the diffusion of the polymer chain also shows nontrivial non-monotonic dependence on σc. Our results demonstrate the important interplay between particle activity and size associated with polymer configurations in active crowding environments.

Contrastive factors of activity and crowding on conformational properties of a flexible polymer

Activity and crowding effect is crucial in conformational change and relevant dynamics of biomolecules in complex environment, which remains a challenging problem. We perform a systematic Langevin simulation to investigate the conformational properties of a flexible polymer in an active bath. Firstly, we modulate both active force and bath particle size to probe the activity-induced polymer swelling. Results indicate a significant crowder size effect. Moreover, polymer conformational change shows a monotonic scaling on dynamical persistence length of active particles. Secondly, activity-crowding competition effect is rationalized. An intriguing shrinkage-expansion crossover of polymer dimension is observed with increasing activity.

Impact of crowders on the morphology of bacterial chromosomes

Inspired by recent experiments on the effects of cytosolic crowders on the organization of bacterial chromosomes, we consider a “feather-boa” type model chromosome in the presence of non-additive crowders, encapsulated within a cylindrical cell. We observe spontaneous emergence of complementary helicity of the confined polymer and crowders. This feature is reproduced within a simplified effective model of the chromosome. This latter model further establishes the occurrence of longitudinal and transverse spatial segregation transitions between the chromosome and crowders upon increasing the crowder size.