Protein Folding Dynamics in the Cell

Quantification of CH and NH/π-Stacking Interactions in Cells Using Nuclear Magnetic Resonance Spectroscopy

π-Stacking, a type of noncovalent interactions involving aromatic residues, plays an important role in protein folding and function. In this work, an attempt has been made to measure CH/π and NH/π stacking interactions in a protein in Escherichia coli cells using a combined double-mutant cycle and nuclear magnetic resonance spectroscopy method. The results show that the CH/π and NH/π stacking interactions are generally weaker in cells than those in the buffer. The transient intermolecular noncovalent interactions between the protein and the complex cellular environment may compete with and thus weaken the stacking interactions in the protein. The weakening of stacking interactions can enhance the local conformational opening of proteins in E. coli cells. This is evident from the faster rates of amide hydrogen/deuterium exchange observed in cells than in the buffer, for residues that undergo local conformational opening. This study highlights the influence of the cellular environment on π-stacking and the conformational dynamics of proteins.

Mechanism of Protein Aggregation Inhibition by Arginine: Blockage of Anionic Side Chains Favors Unproductive Encounter Complexes

Aggregation refers to the assembly of proteins into nonphysiological higher order structures. While amyloid has been studied extensively, much less is known about amorphous aggregation, a process that interferes with protein expression and storage. Free arginine (Arg+) is a widely used aggregation inhibitor, but its mechanism remains elusive. Focusing on myoglobin (Mb), we recently applied atomistic molecular dynamics (MD) simulations for gaining detailed insights into amorphous aggregation (Ng J. Phys. Chem. B 2021, 125, 13099). Building on that approach, the current work for the first time demonstrates that MD simulations can directly elucidate aggregation inhibition mechanisms. Comparative simulations with and without Arg+ reproduced the experimental finding that Arg+ significantly decreased the Mb aggregation propensity. Our data reveal that, without Arg+, protein-protein encounter complexes readily form salt bridges and hydrophobic contacts, culminating in firmly linked dimeric aggregation nuclei. Arg+ promotes the dissociation of encounter complexes. These "unproductive" encounter complexes are favored because Arg+ binding to D- and E- lowers the tendency of these anionic residues to form interprotein salt bridges. Side chain blockage is mediated largely by the guanidinium group of Arg+, which binds carboxylates through H-bond-reinforced ionic contacts. Our MD data revealed Arg+ self-association into a dynamic quasi-infinite network, but we found no evidence that this self-association is important for protein aggregation inhibition. Instead, aggregation inhibition by Arg+ is similar to that mediated by free guanidinium ions. The computational strategy used here should be suitable for the rational design of aggregation inhibitors with enhanced potency.

Effects of External Perturbations on Protein Systems: A Microscopic View

Protein folding can be viewed as the origami engineering of biology resulting from the long process of evolution. Even decades after its recognition, research efforts worldwide focus on demystifying molecular factors that underlie protein structure-function relationships; this is particularly relevant in the era of proteopathic disease. A complex co-occurrence of different physicochemical factors such as temperature, pressure, solvent, cosolvent, macromolecular crowding, confinement, and mutations that represent realistic biological environments are known to modulate the folding process and protein stability in unique ways. In the current review, we have contextually summarized the substantial efforts in unveiling individual effects of these perturbative factors, with major attention toward bottom-up approaches. Moreover, we briefly present some of the biotechnological applications of the insights derived from these studies over various applications including pharmaceuticals, biofuels, cryopreservation, and novel materials. Finally, we conclude by summarizing the challenges in studying the combined effects of multifactorial perturbations in protein folding and refer to complementary advances in experiment and computational techniques that lend insights to the emergent challenges.

Quantifying Protein Electrostatic Interactions in Cells by Nuclear Magnetic Resonance Spectroscopy

Most proteins perform their functions in cells. How the cellular environment modulates protein interactions is an important question. In this work, electrostatic interactions between protein charges were studied using in-cell nuclear magnetic resonance (NMR) spectroscopy. A total of eight charge pairs were introduced in protein GB3. Compared to the charge pair electrostatic interactions in a buffer, five charge pairs in cells displayed no apparent changes whereas three pairs had the interactions weakened by more than 70%. Further investigation suggests that the transfer free energy is responsible for the electrostatic interaction modulation. Both the transfer free energy of the folded state and that of the unfolded state can contribute to the cellular environmental effect on protein electrostatics, although the latter is generally larger (more negative) than the former. Our work highlights the importance of direct in-cell studies of protein interactions and thus protein function.

Super-resolution fluorescence imaging of extracellular environments

The extracellular matrix (ECM) is an important biophysical environment that plays a role in a number of physiological processes. The ECM is highly dynamic, with changes occurring as local, nanoscale, physicochemical variations in physical confinement and chemistry from the perspective of biological molecules. The length and time scale of ECM dynamics are challenging to measure with current spectroscopic techniques. Super-resolution fluorescence microscopy has the potential to probe local, nanoscale, physicochemical variations in the ECM. Here, we review super-resolution imaging and analysis methods and their application to study model nanoparticles and biomolecules within synthetic ECM hydrogels and the brain extracellular space (ECS). We provide a perspective of future directions for the field that can move super-resolution imaging of the ECM towards more biomedically-relevant samples. Overall, super-resolution imaging is a powerful tool that can increase our understanding of extracellular environments at new spatiotemporal scales to reveal ECM processes at the molecular-level.

Macromolecular crowding in solution alters huntingtin interaction and aggregation at interfaces

Huntington's disease (HD) is a fatal neurodegenerative disease caused by an extended polyglutamine (polyQ) domain within the first exon of the huntingtin protein (htt). PolyQ expansion directly invokes the formation of a heterogenous mixture of toxic htt aggregates, including fibrils and oligomers. While htt is a cytosolic protein, it also associates with numerous membranous surfaces within the cell, leading to altered organelle morphology and dysfunction. Here, the impact of macromolecular crowding on htt aggregation in bulk solution and at solid/liquid or membrane/liquid interfaces was investigated. Dextran, Ficoll, and polyethylene glycol (PEG) were used as crowding agents. In bulk solution, crowding enhanced the heterogeneity of non-fibrillar aggregate species formed in a crowder dependent manner. However, crowding agents interfered with the deposition of htt fibrils on mica, suggesting that a crowded aqueous phase influences the interaction of htt with interfaces. By use of in situ atomic force microcopy (AFM), the aggregation of htt directly at mica and bilayer interfaces was tracked. The predominate aggregates type observed to form at the mica interface was fibrillar, but oligomeric aggregates of various stabilities were also observed. Crowding in the aqueous phase suppressed deposition and formation of htt aggregates on mica. In contrast, the addition of crowders enhanced deposition of htt aggregates onto supported total brain lipid extract (TBLE) bilayers. Different crowding agents led to distinct htt aggregates on supported bilayers with unique morphological impact on bilayer integrity. Collectively, these observations point to the complexity of htt aggregation at interfaces and that crowding in the aqueous phase profoundly influences this process.

Osmolytes Can Destabilize Proteins in Cells by Modulating Electrostatics and Quinary Interactions

Although numerous in vitro studies have shown that osmolytes are capable of stabilizing proteins, their effect on protein folding in vivo has been less understood. In this work, we investigated the effect of osmolytes, including glycerol, sorbitol, betaine, and taurine, on the folding of a protein GB3 variant in E. coli cells using NMR spectroscopy. 400 mM osmolytes were added to E. coli cells; only glycerol stabilizes the folded protein, whereas betaine and taurine considerably destabilize the protein through modulating folding and unfolding rates. Further investigation indicates that betaine and taurine can enhance the quinary interaction between the protein and cellular environment and manifestly weaken the electrostatic attraction in protein salt bridges. The combination of the two factors causes destabilization of the protein in E. coli cells. These factors counteract the preferential exclusion mechanism that is adopted by osmolytes to stabilize proteins.

Dimerization Drives Proper Folding of Human Alanine:Glyoxylate Aminotransferase But Is Dispensable for Peroxisomal Targeting

Peroxisomal matrix proteins are transported into peroxisomes in a fully-folded state, but whether multimeric proteins are imported as monomers or oligomers is still disputed. Here, we used alanine:glyoxylate aminotransferase (AGT), a homodimeric pyridoxal 5′-phosphate (PLP)-dependent enzyme, whose deficit causes primary hyperoxaluria type I (PH1), as a model protein and compared the intracellular behavior and peroxisomal import of native dimeric and artificial monomeric forms. Monomerization strongly reduces AGT intracellular stability and increases its aggregation/degradation propensity. In addition, monomers are partly retained in the cytosol. To assess possible differences in import kinetics, we engineered AGT to allow binding of a membrane-permeable dye and followed its intracellular trafficking without interfering with its biochemical properties. By fluorescence recovery after photobleaching, we measured the import rate in live cells. Dimeric and monomeric AGT displayed a similar import rate, suggesting that the oligomeric state per se does not influence import kinetics. However, when dimerization is compromised, monomers are prone to misfolding events that can prevent peroxisomal import, a finding crucial to predicting the consequences of PH1-causing mutations that destabilize the dimer. Treatment with pyridoxine of cells expressing monomeric AGT promotes dimerization and folding, thus, demonstrating the chaperone role of PLP. Our data support a model in which dimerization represents a potential key checkpoint in the cytosol at the crossroad between misfolding and correct targeting, a possible general mechanism for other oligomeric peroxisomal proteins.

Conformational Dynamics from Ambiguous Zinc Coordination in the RanBP2-Type Zinc Finger of RBM5

The multi-domain RNA binding protein RBM5 is a molecular signature of metastasis. RBM5 regulates alternative splicing of apoptotic genes including the cell death receptor Fas and the initiator Caspase-2. The RBM5 RanBP2-type zinc finger (Zf1) is known to specifically recognize single-stranded RNAs with high affinity. Here, we study the structure and conformational dynamics of the Zf1 zinc finger of human RBM5 using NMR. We show that the presence of a non-canonical cysteine in Zf1 kinetically destabilizes the protein. Metal-exchange kinetics show that mutation of the cysteine establishes high-affinity coordination of the zinc. Our data indicate that selection of such a structurally destabilizing mutation during the course of evolution could present an opportunity for functional adaptation of the protein.

Adaptive threshold-stochastic resonance (AT-SR) in MHC clusters on the cell surface

Highly conserved 2D receptor clusters (membrane rafts) of immunological signaling molecules with MHCI and MHCII antigens as their cores have been observed in the past on the surface of T- and B-cell lines of lymphoid origin, as well as on cells from patients with colon tumor and Crohn's disease. Conservativity is related to the ever presence of MHCI molecules. Although they are suspected to play a role in maintaining these clusters and facilitating transmembrane signaling, their exact role has been left largely enigmatic. Here we are suggesting stochastic resonance (SR), or "noise-assisted signal detection", as a general organizing principle for transmembrane signaling events evoked by processes like immune recognition and cytokine binding taking place in these clusters. In the conceptual framework of SR, in immune recognition as a prototype of transmembrane signaling, the sea of self-peptide-MHC complexes around a nonself-peptide presenting MHC is conceived as a source of quickly fluctuating unspecific signal ("athermal noise") serving the extra energy for amplifying the weak sub-threshold specific signal of the nonself-peptide presenting MHC. This same noise is also utilized for a readjustment of the threshold - and also the sensitivity and specificity - of detection by a closed loop feedback control of the TcR-CD8 (CD4) proximity on the detecting T-cell. The weak sub threshold specific signal of nonself-peptide presenting MHC is amplified by the superposing unspecific signals of the neighboring self peptide-MHC complexes towards the T-cell receptor as the detector. Because in a successful detection event both self- and nonself-peptides are detected simultaneously, the principle of coincidence (or lock-in) detection is also realized. The ever presence of MHC islands gets a natural explanation as a source of extra power - in a form of "athermal noise" - needed for coincidence detection and frequency encoding the evoked downstream signals. The effect is quite general, because the actual type of molecules surrounding a chief signaling molecule - like nonself-peptide holding MHC, interleukin-2 and -15 cytokine receptors (IL-2R/15R) - as the fluctuating interaction energy sources is immaterial. The model applies also for other types of signaling, such as those evoked by cytokine binding. The phenomenon of SR can also be interpreted as sampling of a low frequency, specific signal with a high frequency unspecific signal, the "noise". Recipes for identifying other forms of SR in membrane clusters with biophysical tools are recommended.

Proteins: "Boil 'Em, Mash 'Em, Stick 'Em in a Stew"

Cells of the vast majority of organisms are subject to temperature, pressure, pH, ionic strength, and other stresses. We discuss these effects in the light of protein folding and protein interactions in vitro, in complex environments, in cells, and in vivo. Protein phase diagrams provide a way of organizing different structural ensembles that occur under stress and how one can move among ensembles. Experiments that perturb biomolecules in vitro or in cells by stressing them have revealed much about the underlying forces that are competing to control protein stability, folding, and function. Two phenomena that emerge and serve to broadly classify effects of the cellular environment are crowding (mainly due to repulsive forces) and sticking (mainly due to attractive forces). The interior of cells is closely balanced between these emergent effects, and stress can tip the balance one way or the other. The free energy scale involved is small but significant on the scale of the "on/off switches" that control signaling in cells or of protein-protein association with a favorable function such as increased enzyme processivity. Quantitative tools from biophysical chemistry will play an important role in elucidating the world of crowding and sticking under stress.

Characterizing proteins in their cellular environment: Examples of recent advances in quantitative fluorescence microscopy

Quantitative characterization of protein interactions, both intramolecular and intermolecular, is crucial in understanding the mechanisms and regulation of their function. In recent years, it has become possible to obtain such information on protein systems in live cells, from bacteria to mammalian cell lines. This review discusses recent advances in measuring protein folding, absolute concentration, oligomerization, diffusion, transport, and organization at super-resolution.

Intrinsically disordered proteins in crowded milieu: when chaos prevails within the cellular gumbo

Effects of macromolecular crowding on structural and functional properties of ordered proteins, their folding, interactability, and aggregation are well documented. Much less is known about how macromolecular crowding might affect structural and functional behaviour of intrinsically disordered proteins (IDPs) or intrinsically disordered protein regions (IDPRs). To fill this gap, this review represents a systematic analysis of the available literature data on the behaviour of IDPs/IDPRs in crowded environment. Although it was hypothesized that, due to the excluded-volume effects present in crowded environments, IDPs/IDPRs would invariantly fold in the presence of high concentrations of crowding agents or in the crowded cellular environment, accumulated data indicate that, based on their response to the presence of crowders, IDPs/IDPRs can be grouped into three major categories, foldable, non-foldable, and unfoldable. This is because natural cellular environment is not simply characterized by the presence of high concentration of "inert" macromolecules, but represents an active milieu, components of which are engaged in direct physical interactions and soft interactions with target proteins. Some of these interactions with cellular components can cause (local) unfolding of query proteins. In other words, since crowding can cause both folding and unfolding of an IDP or its regions, the outputs of the placing of a query protein to the crowded environment would depend on the balance between these two processes. As a result, and because of the spatio-temporal heterogeneity in structural organization of IDPs, macromolecular crowding can differently affect structures of different IDPs. Recent studies indicate that some IDPs are able to undergo liquid-liquid-phase transitions leading to the formation of various proteinaceous membrane-less organelles (PMLOs). Although interiors of such PMLOs are self-crowded, being characterized by locally increased concentrations of phase-separating IDPs, these IDPs are minimally foldable or even non-foldable at all (at least within the physiologically safe time-frame of normal PMLO existence).

Toward an understanding of biochemical equilibria within living cells

Four types of environmental effects that can affect macromolecular reactions in a living cell are defined: nonspecific intermolecular interactions, side reactions, partitioning between microenvironments, and surface interactions. Methods for investigating these interactions and their influence on target reactions in vitro are reviewed. Methods employed to characterize conformational and association equilibria in vivo are reviewed and difficulties in their interpretation cataloged. It is concluded that, in order to be amenable to unambiguous interpretation, in vivo studies must be complemented by in vitro studies carried out in well-characterized and controllable media designed to contain key elements of selected intracellular microenvironments.

Estimating the mean first passage time of protein misfolding

Most theoretical and experimental studies confirm that proteins fold in the time scale of microseconds to milliseconds, but the kinetics of the protein misfolding remains largely unexplored. The kinetics of unfolding-folding-misfolding equilibrium in proteins is formulated in the analytical framework of the Master equation. The folded, unfolded and the misfolded state are characterized in terms of their respective contacts. The Mean First Passage Time (MFPT) to acquire the misfolded conformation from the native or folded state is derived from this equation with different boundary conditions. The MFPT is found to be practically independent of the length of the protein, the number of native contacts and the rate constant for the misfolded to the folded state. The results obtained from the survival probability are directly correlated to the age of onset and appearance of misfolding diseases in humans.

Evidence of homo-FRET in quantum dot–dye heterostructured assembly

Evidence of homo-FRET in inorganic–organic hybrid hetero-structured assembly is demonstrated

Direct Imaging of Protein Stability and Folding Kinetics in Hydrogels

We apply fast relaxation imaging (FReI) as a novel technique for investigating the folding stability and dynamics of proteins within polyacrylamide hydrogels, which have diverse and widespread uses in biotechnology. FReI detects protein unfolding in situ by imaging changes in fluorescence resonance energy transfer (FRET) after temperature jump perturbations. Unlike bulk measurements, diffraction-limited epifluorescence imaging combined with fast temperature perturbations reveals the impact of local environment effects on protein-biomaterial compatibility. Our experiments investigated a crowding sensor protein (CrH2) and phosphoglycerate kinase (PGK), which undergoes cooperative unfolding. The crowding sensor quantifies the confinement effect of the cross-linked hydrogel: the 4% polyacrylamide hydrogel is similar to aqueous solution (no confinement), while the 10% hydrogel is strongly confining. FRAP measurements and protein concentration gradients in the 4% and 10% hydrogels further support this observation. PGK reveals that noncovalent interactions of the protein with the polymer surface are more important than confinement for determining protein properties in the gel: the mere presence of hydrogel increases protein stability, speeds up folding relaxation, and promotes irreversible binding to the polymer even at the solution-gel interface, whereas the difference between the 4% and the 10% hydrogels is negligible despite their large difference in confinement. The imaging capabilities of FReI, demonstrated to be diffraction limited, further revealed spatially homogeneous protein unfolding across the hydrogels at 500 nm length scales and revealed differences in protein properties at the gel-solution boundary.

Meandering Down the Energy Landscape of Protein Folding: Are We There Yet?

As judged by a single publication metric, the activity in the protein folding field has been declining over the past 5 years, after enjoying a decade-long growth. Does this development indicate that the field is sunsetting or is this decline only temporary? Upon surveying a small territory of its landscape, we find that the protein folding field is still quite active and many important findings have emerged from recent experimental studies. However, it is also clear that only continued development of new techniques and methods, especially those enabling dissection of the fine details and features of the protein folding energy landscape, will fuel this old field to move forward.

Ligand-promoted protein folding by biased kinetic partitioning

Protein folding in cells occurs in the presence of high concentrations of endogenous binding partners, and exogenous binding partners have been exploited as pharmacological chaperones. A combined mathematical modeling and experimental approach shows that a ligand improves the folding of a destabilized protein by biasing the kinetic partitioning between folding and alternative fates (aggregation or degradation). Computationally predicted inhibition of test protein aggregation and degradation as a function of ligand concentration are validated by experiments in two disparate cellular systems.

Thermodynamics of Macromolecular Association in Heterogeneous Crowding Environments: Theoretical and Simulation Studies with a Simplified Model

The cytoplasm of a cell is crowded with many different kinds of macromolecules. The macromolecular crowding affects the thermodynamics and kinetics of biological reactions in a living cell, such as protein folding, association, and diffusion. Theoretical and simulation studies using simplified models focus on the essential features of the crowding effects and provide a basis for analyzing experimental data. In most of the previous studies on the crowding effects, a uniform crowder size is assumed, which is in contrast to the inhomogeneous size distribution of macromolecules in a living cell. Here, we evaluate the free energy changes upon macromolecular association in a cell-like inhomogeneous crowding system via a theory of hard-sphere fluids and free energy calculations using Brownian dynamics trajectories. The inhomogeneous crowding model based on 41 different types of macromolecules represented by spheres with different radii mimics the physiological concentrations of macromolecules in the cytoplasm of Mycoplasma genitalium. The free energy changes of macromolecular association evaluated by the theory and simulations were in good agreement with each other. The crowder size distribution affects both specific and nonspecific molecular associations, suggesting that not only the volume fraction but also the size distribution of macromolecules are important factors for evaluating in vivo crowding effects. This study relates in vitro experiments on macromolecular crowding to in vivo crowding effects by using the theory of hard-sphere fluids with crowder-size heterogeneity.

Macromolecular Crowding In Vitro, In Vivo, and In Between

Biochemical processes take place in heterogeneous and highly volume-occupied or crowded environments that can considerably influence the reactivity and distribution of participating macromolecules. We summarize here the thermodynamic consequences of excluded-volume and long-range nonspecific intermolecular interactions for macromolecular reactions in volume-occupied media. In addition, we summarize and compare the information content of studies of crowding in vitro and in vivo. We emphasize the importance of characterizing the behavior not only of labeled tracer macromolecules but also the composition and behavior of unlabeled macromolecules in the immediate vicinity of the tracer. Finally, we propose strategies for extending quantitative analyses of crowding in simple model systems to increasingly complex media up to and including intact cells.

Protein Domain-Swapping Can Be a Consequence of Functional Residues

Monomer topology has been implicated in domain-swapping, a potential first step on the route to disease-causing protein aggregation. Despite having the same topology (β1-α1-β2-β3-β4-β5), the cysteine protease inhibitor stefin-B domain swaps more readily than a single-chain variant of the heterodimeric sweet protein monellin (scMn). Here, we computationally study the folding of stefin-B and scMn in order to understand the molecular basis for the difference in their domain-swapping propensities. In agreement with experiments, our structure-based simulations show that scMn folds cooperatively without the population of an intermediate while stefin-B populates an equilibrium intermediate state. Since the simulation intermediate has only one domain structured (β3-β4-β5), it can directly lead to domain-swapping. Using computational variants of stefin-B, we show that the population of this intermediate is caused by regions of stefin-B that have been implicated in protease inhibition. We also find that the protease-binding regions are located on two structural elements and localized in space. In contrast, the residues that contribute to the sweetness of monellin are not localized to a few structural elements but are distributed over the protein fold. We conclude that the distributed functional residues of monellin do not induce large local perturbations in the protein structure, eliminating the formation of folding intermediates and in turn domain-swapping. On the other hand, the localized protease-binding regions of stefin-B promote the formation of a folding intermediate which can lead to domain-swapping. Thus, domain-swapping can be a direct consequence of the constraints that function imposes on the protein structure.

Stochastic Resonance in Protein Folding Dynamics

Although protein folding reactions are usually studied under static external conditions, it is likely that proteins fold in a locally fluctuating cellular environment in vivo. To mimic such behavior in in vitro experiments, the local temperature of the solvent can be modulated either harmonically or using correlated noise. In this study, coarse-grained molecular simulations are used to investigate these possibilities, and it is found that both periodic and correlated random fluctuations of the environment can indeed accelerate folding kinetics if the characteristic frequencies of the applied fluctuations are commensurate with the internal timescale of the folding reaction; this is consistent with the phenomenon of stochastic resonance observed in many other condensed-matter processes. To test this theoretical prediction, the folding dynamics of phosphoglycerate kinase under harmonic temperature fluctuations are experimentally probed using Förster resonance energy transfer fluorescence measurements. To analyze these experiments, a combination of theoretical approaches is developed, including stochastic simulations of folding kinetics and an analytical mean-field kinetic theory. The experimental observations are consistent with the theoretical predictions of stochastic resonance in phosphoglycerate kinase folding. When combined with an alternative experiment on the protein VlsE using a power spectrum analysis, elaborated in Dave et al., ChemPhysChem 2016, 10.1002/cphc.201501041, the overall data overwhelmingly point to the experimental confirmation of stochastic resonance in protein folding dynamics.

Unexpected Swelling of Stiff DNA in a Polydisperse Crowded Environment

We investigate the conformations of DNA-like stiff chains, characterized by contour length (L) and persistence length (lp), in a variety of crowded environments containing monodisperse soft spherical (SS) and spherocylindrical (SC) particles, a mixture of SS and SC, and a milieu mimicking the composition of proteins in the Escherichia coli cytoplasm. The stiff chain, whose size modestly increases in SS crowders up to ϕ ≈ 0.1, is considerably more compact at low volume fractions (ϕ ≤ 0.2) in monodisperse SC particles than in a medium containing SS particles. A 1:1 mixture of SS and SC crowders induces greater chain compaction than the pure SS or SC crowders at the same ϕ, with the effect being highly nonadditive. We also discover a counterintuitive result that the polydisperse crowding environment, mimicking the composition of a cell lysate, swells the DNA-like polymer, which is in stark contrast to the size reduction of flexible polymers in the same milieu. Trapping of the stiff chain in a fluctuating tube-like environment created by large-sized crowders explains the dramatic increase in size and persistence length of the stiff chain. In the polydisperse medium, mimicking the cellular environment, the size of the DNA (or related RNA) is determined by L/lp. At low L/lp, the size of the polymer is unaffected, whereas there is a dramatic swelling at an intermediate value of L/lp. We use these results to provide insights into recent experiments on crowding effects on RNA and also make testable predictions.

Identification of two-step chemical mechanisms using small temperature oscillations and a single tagged species

In order to identify two-step chemical mechanisms, we propose a method based on a small temperature modulation and on the analysis of the concentration oscillations of a single tagged species involved in the first step. The thermokinetic parameters of the first reaction step are first determined. Then, we build test functions that are constant only if the chemical system actually possesses some assumed two-step mechanism. Next, if the test functions plotted using experimental data are actually even, the mechanism is attributed and the obtained constant values provide the rate constants and enthalpy of reaction of the second step. The advantage of the protocol is to use the first step as a probe reaction to reveal the dynamics of the second step, which can hence be relieved of any tagging. The protocol is anticipated to apply to many mechanisms of biological relevance. As far as ligand binding is considered, our approach can address receptor conformational changes or dimerization as well as competition with or modulation by a second partner. The method can also be used to screen libraries of untagged compounds, relying on a tracer whose concentration can be spectroscopically monitored.