Quantifying the Influence of the Crowded Cytoplasm on Small Molecule Diffusion

Bacterial cell volume regulation and the importance of cyclic di-AMP

SUMMARYNucleotide-derived second messengers are present in all domains of life. In prokaryotes, most of their functionality is associated with general lifestyle and metabolic adaptations, often in response to environmental fluctuations of physical parameters. In the last two decades, cyclic di-AMP has emerged as an important signaling nucleotide in many prokaryotic lineages, including Firmicutes, Actinobacteria, and Cyanobacteria. Its importance is highlighted by the fact that both the lack and overproduction of cyclic di-AMP affect viability of prokaryotes that utilize cyclic di-AMP, and that it generates a strong innate immune response in eukaryotes. In bacteria that produce the second messenger, most molecular targets of cyclic di-AMP are associated with cell volume control. Besides, other evidence links the second messenger to cell wall remodeling, DNA damage repair, sporulation, central metabolism, and the regulation of glycogen turnover. In this review, we take a biochemical, quantitative approach to address the main cellular processes that are directly regulated by cyclic di-AMP and show that these processes are very connected and require regulation of a similar set of proteins to which cyclic di-AMP binds. Altogether, we argue that cyclic di-AMP is a master regulator of cell volume and that other cellular processes can be connected with cyclic di-AMP through this core function. We further highlight important directions in which the cyclic di-AMP field has to develop to gain a full understanding of the cyclic di-AMP signaling network and why some processes are regulated, while others are not.

Physiology of intracellular calcium buffering

Calcium signaling underlies much of physiology. Almost all the Ca2+ in the cytoplasm is bound to buffers, with typically only ∼1% being freely ionized at resting levels in most cells. Physiological Ca2+ buffers include small molecules and proteins, and experimentally Ca2+ indicators will also buffer calcium. The chemistry of interactions between Ca2+ and buffers determines the extent and speed of Ca2+ binding. The physiological effects of Ca2+ buffers are determined by the kinetics with which they bind Ca2+ and their mobility within the cell. The degree of buffering depends on factors such as the affinity for Ca2+, the Ca2+ concentration, and whether Ca2+ ions bind cooperatively. Buffering affects both the amplitude and time course of cytoplasmic Ca2+ signals as well as changes of Ca2+ concentration in organelles. It can also facilitate Ca2+ diffusion inside the cell. Ca2+ buffering affects synaptic transmission, muscle contraction, Ca2+ transport across epithelia, and the killing of bacteria. Saturation of buffers leads to synaptic facilitation and tetanic contraction in skeletal muscle and may play a role in inotropy in the heart. This review focuses on the link between buffer chemistry and function and how Ca2+ buffering affects normal physiology and the consequences of changes in disease. As well as summarizing what is known, we point out the many areas where further work is required.

Self-Organization of Enzyme-Catalyzed Reactions Studied by the Maximum Entropy Production Principle

The self-organization of open reaction systems is closely related to specific mechanisms that allow the export of internally generated entropy from systems to their environment. According to the second law of thermodynamics, systems with effective entropy export to the environment are better internally organized. Therefore, they are in thermodynamic states with low entropy. In this context, we study how self-organization in enzymatic reactions depends on their kinetic reaction mechanisms. Enzymatic reactions in an open system are considered to operate in a non-equilibrium steady state, which is achieved by satisfying the principle of maximum entropy production (MEPP). The latter is a general theoretical framework for our theoretical analysis. Detailed theoretical studies and comparisons of the linear irreversible kinetic schemes of an enzyme reaction in two and three states are performed. In both cases, in the optimal and statistically most probable thermodynamic steady state, a diffusion-limited flux is predicted by MEPP. Several thermodynamic quantities and enzymatic kinetic parameters, such as the entropy production rate, the Shannon information entropy, reaction stability, sensitivity, and specificity constants, are predicted. Our results show that the optimal enzyme performance may strongly depend on the number of reaction steps when linear reaction mechanisms are considered. Simple reaction mechanisms with a smaller number of intermediate reaction steps could be better organized internally and could allow fast and stable catalysis. These could be features of the evolutionary mechanisms of highly specialized enzymes.

Myofilament-associated proteins with intrinsic disorder (MAPIDs) and their resolution by computational modeling

The cardiac sarcomere is a cellular structure in the heart that enables muscle cells to contract. Dozens of proteins belong to the cardiac sarcomere, which work in tandem to generate force and adapt to demands on cardiac output. Intriguingly, the majority of these proteins have significant intrinsic disorder that contributes to their functions, yet the biophysics of these intrinsically disordered regions (IDRs) have been characterized in limited detail. In this review, we first enumerate these myofilament-associated proteins with intrinsic disorder (MAPIDs) and recent biophysical studies to characterize their IDRs. We secondly summarize the biophysics governing IDR properties and the state-of-the-art in computational tools toward MAPID identification and characterization of their conformation ensembles. We conclude with an overview of future computational approaches toward broadening the understanding of intrinsic disorder in the cardiac sarcomere.

Postmortem changes in brain cell structure: a review

Brain cell structure is a key determinant of neural function that is frequently altered in neurobiological disorders. Following the global loss of blood flow to the brain that initiates the postmortem interval (PMI), cells rapidly become depleted of energy and begin to decompose. To ensure that our methods for studying the brain using autopsy tissue are robust and reproducible, there is a critical need to delineate the expected changes in brain cell morphometry during the PMI. We searched multiple databases to identify studies measuring the effects of PMI on the morphometry (i.e. external dimensions) of brain cells. We screened 2119 abstracts, 361 full texts, and included 172 studies. Mechanistically, fluid shifts causing cell volume alterations and vacuolization are an early event in the PMI, while the loss of the ability to visualize cell membranes altogether is a later event. Decomposition rates are highly heterogenous and depend on the methods for visualization, the structural feature of interest, and modifying variables such as the storage temperature or the species. Geometrically, deformations of cell membranes are common early events that initiate within minutes. On the other hand, topological relationships between cellular features appear to remain intact for more extended periods. Taken together, there is an uncertain period of time, usually ranging from several hours to several days, over which cell membrane structure is progressively lost. This review may be helpful for investigators studying human postmortem brain tissue, wherein the PMI is an unavoidable aspect of the research.

Crowding within synaptic junctions influences the degradation of nucleotides by CD39 and CD73 ectonucleotidases

Synapsed cells can communicate using exocytosed nucleotides like adenosine triphosphate (ATP). Ectonucleotidases localized to synaptic junctions degrade nucleotides into metabolites like adenosine monophosphate (AMP) or adenosine. Oftentimes nucleotide degradation occurs in a sequential manner, of which ATP degradation by CD39 and CD73 is a representative example. Here, CD39 first converts ATP and adenosine diphosphate (ADP) into AMP, after which AMP is dephosphorylated into adenosine by CD73. Hence, the concerted activity of CD39 and CD73 can help shape cellular responses to extracellular ATP. In a previous study, we demonstrated that coupled CD39 and CD73 activity within synapse-like junctions is strongly controlled by the enzymes' co-localization, their surface charge densities, and the electrostatic potential of the surrounding cell membranes. In this study, we demonstrate that crowders within synaptic junctions, which can include globular proteins like cytokines and membrane-bound proteins, impact coupled CD39 and CD73 ectonucleotidase activity and, in turn, the availability of intrasynapse ATP. Specifically, we developed a spatially explicit, reaction-diffusion model for the coupled conversion of ATP → AMP and AMP → adenosine in a model synaptic junction with crowders that is solved via the finite element method. Our modeling results suggest that the association rate for ATP to CD39 is strongly influenced by the density of intrasynaptic protein crowders, as increasing crowder density generally suppressed ATP association kinetics. Much of this suppression can be rationalized based on a loss of configurational entropy. The surface charges of crowders can further influence the association rate, with the surprising result that favorable crowder-nucleotide electrostatic interactions can yield CD39 association rates that are faster than crowder-free configurations. However, attractive crowder-nucleotide interactions decrease the rate and efficiency of adenosine production, which in turn increases the availability of ATP and AMP within the synapse relative to crowder-free configurations. These findings highlight how CD39 and CD73 ectonucleotidase activity, electrostatics, and crowding within synapses influence the availability of nucleotides for intercellular communication.

Assessment of transient changes in oxygen diffusion of single red blood cells using a microfluidic analytical platform

Red blood cells (RBCs) capability to deliver oxygen (O₂) has been routinely measured by P50. Although this defines the ability of RBCs to carry O₂ under equilibrium states, it cannot determine the efficacy of O₂ delivery in dynamic blood flow. Here, we developed a microfluidic analytical platform (MAP) that isolates single RBCs for assessing transient changes in their O₂ release rate. We found that in vivo (biological) and in vitro (blood storage) aging of RBC could lead to an increase in the O₂ release rate, despite a decrease in P50. Rejuvenation of stored RBCs (Day 42), though increased the P50, failed to restore the O₂ release rate to basal level (Day 0). The temporal dimension provided at the single-cell level by MAP could shed new insights into the dynamics of O₂ delivery in both physiological and pathological conditions.

Flexibility of enzymatic transitions as a hallmark of optimized enzyme steady-state kinetics and thermodynamics

We investigate the relations between the enzyme kinetic flexibility, the rate of entropy production, and the Shannon information entropy in a steady-state enzyme reaction. All these quantities are maximized with respect to enzyme rate constants. We show that the steady-state, which is characterized by the most flexible enzymatic transitions between the enzyme conformational states, coincides with the global maxima of the Shannon information entropy and the rate of entropy production. This steady-state of an enzyme is referred to as globally optimal. This theoretical approach is then used for the analysis of the kinetic and the thermodynamic performance of the enzyme triose-phosphate isomerase. The analysis reveals that there exist well-defined maxima of the kinetic flexibility, the rate of entropy production, and the Shannon information entropy with respect to any arbitrarily chosen rate constant of the enzyme and that these maxima, calculated from the measured kinetic rate constants for the triose-phosphate isomerase are lower, however of the same order of magnitude, as the maxima of the globally optimal state of the enzyme. This suggests that the triose-phosphate isomerase could be a well, but not fully evolved enzyme, as it was previously claimed. Herein presented theoretical investigations also provide clear evidence that the flexibility of enzymatic transitions between the enzyme conformational states is a requirement for the maximal Shannon information entropy and the maximal rate of entropy production.

Moonlighting Proteins Shine New Light on Molecular Signaling Niches

Plants as sessile organisms face daily environmental challenges and have developed highly nuanced signaling systems to enable suitable growth, development, defense, or stalling responses. Moonlighting proteins have multiple tasks and contribute to cellular signaling cascades where they produce additional variables adding to the complexity or fuzziness of biological systems. Here we examine roles of moonlighting kinases that also generate 3',5'-cyclic guanosine monophosphate (cGMP) in plants. These proteins include receptor like kinases and lipid kinases. Their guanylate cyclase activity potentiates the development of localized cGMP-enriched nanodomains or niches surrounding the kinase and its interactome. These nanodomains contribute to allosteric regulation of kinase and other molecules in the immediate complex directly or indirectly modulating signal cascades. Effects include downregulation of kinase activity, modulation of other members of the protein complexes such as cyclic nucleotide gated channels and potential triggering of cGMP-dependent degradation cascades terminating signaling. The additional layers of information provided by the moonlighting kinases are discussed in terms of how they may be used to provide a layer of fuzziness to effectively modulate cellular signaling cascades.

Viruses as 'Truffle Hounds': Molecular Tools for Untangling Brain Cellular Pathology

The ability of viruses to evolve several orders of magnitude faster than their host cells has enabled them to exploit host cellular machinery by selectively recruiting multiprotein complexes (MPCs) for their catalyzed assembly and replication. This hijacking may depend on alternative, 'moonlighting' functions of host proteins that deviate from their canonical functions thereby inducing cellular pathology. Here, we posit that if virus-induced cellular pathology is similar to that of other, unknown (non-viral) causes, the identification and molecular characterization of the host proteins involved in virus-mediated cellular pathology can be leveraged to decipher the non-viral disease-relevant mechanisms. We focus on how virus-induced aberrant proteostasis and protein aggregation resemble the cellular pathology of sporadic neurodegenerative diseases (NDs) and how this can be exploited for drug discovery.

Metabolic Compartmentalization at the Leading Edge of Metastatic Cancer Cells

Despite advances in targeted therapeutics and understanding in molecular mechanisms, metastasis remains a substantial obstacle for cancer treatment. Acquired genetic mutations and transcriptional changes can promote the spread of primary tumor cells to distant tissues. Additionally, recent studies have uncovered that metabolic reprogramming of cancer cells is tightly associated with cancer metastasis. However, whether intracellular metabolism is spatially and temporally regulated for cancer cell migration and invasion is understudied. In this review, we highlight the emergence of a concept, termed “membraneless metabolic compartmentalization,” as one of the critical mechanisms that determines the metastatic capacity of cancer cells. In particular, we focus on the compartmentalization of purine nucleotide metabolism (e.g., ATP and GTP) at the leading edge of migrating cancer cells through the uniquely phase-separated microdomains where dynamic exchange of nucleotide metabolic enzymes takes place. We will discuss how future insights may usher in a novel class of therapeutics specifically targeting the metabolic compartmentalization that drives tumor metastasis.

Co-localization and confinement of ecto-nucleotidases modulate extracellular adenosine nucleotide distributions

Nucleotides comprise small molecules that perform critical signaling roles in biological systems. Adenosine-based nucleotides, including adenosine tri-, di-, and mono-phosphate, are controlled through their rapid degradation by diphosphohydrolases and ecto-nucleotidases (NDAs). The interplay between nucleotide signaling and degradation is especially important in synapses formed between cells, which create signaling 'nanodomains'. Within these 'nanodomains', charged nucleotides interact with densely-packed membranes and biomolecules. While the contributions of electrostatic and steric interactions within such nanodomains are known to shape diffusion-limited reaction rates, less is understood about how these factors control the kinetics of nucleotidase activity. To quantify these factors, we utilized reaction-diffusion numerical simulations of 1) adenosine triphosphate (ATP) hydrolysis into adenosine monophosphate (AMP) and 2) AMP into adenosine (Ado) via two representative nucleotidases, CD39 and CD73. We evaluate these sequentially-coupled reactions in nanodomain geometries representative of extracellular synapses, within which we localize the nucleotidases. With this model, we find that 1) nucleotidase confinement reduces reaction rates relative to an open (bulk) system, 2) the rates of AMP and ADO formation are accelerated by restricting the diffusion of substrates away from the enzymes, and 3) nucleotidase co-localization and the presence of complementary (positive) charges to ATP enhance reaction rates, though the impact of these contributions on nucleotide pools depends on the degree to which the membrane competes for substrates. As a result, these contributions integratively control the relative concentrations and distributions of ATP and its metabolites within the junctional space. Altogether, our studies suggest that CD39 and CD73 nucleotidase activity within junctional spaces can exploit their confinement and favorable electrostatic interactions to finely control nucleotide signaling.

Chromatin as a key consumer in the metabolite economy

In eukaryotes, chromatin remodeling and post-translational modifications (PTMs) shape the local chromatin landscape to establish permissive and repressive regions within the genome, orchestrating transcription, replication, and DNA repair in concert with other epigenetic mechanisms. Though cellular nutrient signaling encompasses a huge number of pathways, recent attention has turned to the hypothesis that the metabolic state of the cell is communicated to the genome through the type and concentration of metabolites in the nucleus that are cofactors for chromatin-modifying enzymes. Importantly, both epigenetic and metabolic dysregulation are hallmarks of a range of diseases, and this metabolism-chromatin axis may yield a well of new therapeutic targets. In this Perspective, we highlight emerging themes in the inter-regulation of the genome and metabolism via chromatin, including nonenzymatic histone modifications arising from chemically reactive metabolites, the expansion of PTM diversity from cofactor-promiscuous chromatin-modifying enzymes, and evidence for the existence and importance of subnucleocytoplasmic metabolite pools.

Cascade Kinetics in an Enzyme-Loaded Aqueous Two-Phase System

Macromolecular crowding plays a critical role in the kinetics of enzymatic reactions. Dynamic compartmentalization of biological components in living cells due to liquid-liquid phase separation represents an important cell regulatory mechanism that can increase enzyme concentration locally and influence the diffusion of substrates. In the present study, we probed partitioning of two enzymes (horseradish-peroxidase and urate-oxidase) in a poly(ethylene glycol)-dextran aqueous two-phase system (ATPS) as a function of salt concentration and ion position in the Hofmeister series. Moreover, we investigated enzymatic cascade reactions and their kinetics within the ATPS, which revealed a strong influence of the ion hydration stemming from the background electrolyte on the partitioning coefficients of proteins following the Hofmeister series. As a result, we were able to realize cross-partitioning of two enzymes because of different protein net charges at a chosen pH. Our study reveals a strong dependency of the enzyme activity on the substrate type and crowding agent interaction on the final kinetics of enzymatic reactions in the ATPS and therefore provides substantial implications en route toward dynamic regulation of reactivity in synthetic protocells.

Tuning the Permeability of Dense Membranes by Shaping Nanoscale Potentials

Permeability is one of the most fundamental transport properties in soft matter physics, material engineering, and nanofluidics. Here, we report by means of Langevin simulations of ideal penetrants in a nanoscale membrane made of a fixed lattice of attractive interaction sites, how the permeability can be massively tuned, even minimized or maximized, by tailoring the potential energy landscape for the diffusing penetrants, depending on the membrane attraction, topology, and density. Supported by limiting scaling theories we demonstrate that the observed nonmonotonic behavior and the occurrence of extreme values of the permeability is far from trivial and triggered by a strong anticorrelation and substantial (orders of magnitude) cancellation between penetrant partitioning and diffusivity, especially within dense and highly attractive membranes.

Increasing Salt Rejection of Polybenzimidazole Nanofiltration Membranes via the Addition of Immobilized and Aligned Aquaporins

Aquaporins are water channel proteins in cell membrane, highly specific for water molecules while restricting the passage of contaminants and small molecules, such as urea and boric acid. Cysteine functional groups were installed on aquaporin Z for covalent attachment to the polymer membrane matrix so that the proteins could be immobilized to the membranes and aligned in the direction of the flow. Depth profiling using x-ray photoelectron spectrometer (XPS) analysis showed the presence of functional groups corresponding to aquaporin Z modified with cysteine (Aqp-SH). Aqp-SH modified membranes showed a higher salt rejection as compared to unmodified membranes. For 2 M NaCl and CaCl₂ solutions, the rejection obtained from Aqp-SH membranes was 49.3 ± 7.5% and 59.1 ± 5.1%. On the other hand, the rejections obtained for 2 M NaCl and CaCl₂ solutions from unmodified membranes were 0.8 ± 0.4% and 1.3 ± 0.2% respectively. Furthermore, Aqp-SH membranes did not show a significant decrease in salt rejection with increasing feed concentrations, as was observed with other membranes. Through simulation studies, it was determined that there was approximately 24% capping of membrane pores by dispersed aquaporins.

Reaction and diffusion thermodynamics explain optimal temperatures of biochemical reactions

Ubiquitous declines in biochemical reaction rates above optimal temperatures (Topt) are normally attributed to enzyme state changes, but such mechanisms appear inadequate to explain pervasive Topt well below enzyme deactivation temperatures (Tden). Here, a meta-analysis of 92 experimental studies shows that product formation responds twice as strongly to increased temperature than diffusion or transport. This response difference has multiple consequences for biochemical reactions, such as potential shifts in the factors limiting reactions as temperature increases and reaction-diffusion dynamics that predict potential product inhibition and limitation of the reaction by entropy production at temperatures below Tden. Maximizing entropy production by the reaction predicts Topt that depend on enzyme concentration and efficiency as well as reaction favorability, which are patterns not predicted by mechanisms of enzyme state change. However, these predictions are strongly supported by patterns in a meta-analysis of 121 enzyme kinetic studies. Consequently, reaction-diffusion thermodynamics and entropy production may constrain organism performance at higher temperatures, yielding temperature optima of life that may depend on reaction characteristics and environmental features rather than just enzyme state changes.

Metabolic regulation of transcription through compartmentalized NAD+ biosynthesis

NAD⁺ (nicotinamide adenine dinucleotide in its oxidized state) is an essential molecule for a variety of physiological processes. It is synthesized in distinct subcellular compartments by three different synthases (NMNAT-1, -2, and -3). We found that compartmentalized NAD⁺ synthesis by NMNATs integrates glucose metabolism and adipogenic transcription during adipocyte differentiation. Adipogenic signaling rapidly induces cytoplasmic NMNAT-2, which competes with nuclear NMNAT-1 for the common substrate, nicotinamide mononucleotide, leading to a precipitous reduction in nuclear NAD⁺ levels. This inhibits the catalytic activity of poly[adenosine diphosphate (ADP)-ribose] polymerase-1 (PARP-1), a NAD⁺-dependent enzyme that represses adipogenic transcription by ADP-ribosylating the adipogenic transcription factor C/EBPβ. Reversal of PARP-1-mediated repression by NMNAT-2-mediated nuclear NAD⁺ depletion in response to adipogenic signals drives adipogenesis. Thus, compartmentalized NAD⁺ synthesis functions as an integrator of cellular metabolism and signal-dependent transcriptional programs.

Product interactions and feedback in diffusion-controlled reactions

Steric or attractive interactions among reactants or between reactants and inert crowders can substantially influence the total rate of a diffusion-influenced reaction in the liquid phase. However, the role of the product species, which has typically different physical properties than the reactant species, has been disregarded so far. Here we study the effects of reactant-product and product-product interactions as well as asymmetric diffusion properties on the rate of diffusion-controlled reactions in the classical Smoluchowski-setup for chemical transformations at a perfect catalytic sphere. For this, we solve the diffusion equation with appropriate boundary conditions coupled by a mean-field approach on the second virial level to account for the particle interactions. We find that all particle spatial distributions and the total rate can change significantly, depending on the diffusion and interaction properties of the accumulated products. Complex competing and self-regulating (homeostatic) or self-amplifying effects are observed for the system, leading to both decrease and increase in the rates, as the presence of interacting products feeds back to the reactant flux and thus the rate with which the products are generated.

Bridging intracellular scales by mechanistic computational models

The impact of intracellular spatial organization beyond classical compartments on processes such as cell signaling is increasingly recognized. A quantitative, mechanistic understanding of cellular systems therefore needs to account for different scales in at least three coordinates: time, molecular abundances, and space. Mechanistic mathematical models may span all these scales, but corresponding multi-scale models need to resolve mechanistic details on small scales while maintaining computational tractability for larger ones. This typically results in models that combine different levels of description: from a microscopic representation of chemical reactions up to continuum dynamics in space and time. We highlight recent progress in bridging these model classes and outline current challenges in multi-scale models such as active transport and dynamic geometries.

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.

Electrodiffusion phenomena in neuroscience: a neglected companion

The emerging technological revolution in genetically encoded molecular sensors and super-resolution imaging provides neuroscientists with a pass to the real-time nano-world. On this small scale, however, classical principles of electrophysiology do not always apply. This is in large part because the nanoscopic heterogeneities in ionic concentrations and the local electric fields associated with individual ions and their movement can no longer be ignored. Here, we review basic principles of molecular electrodiffusion in the cellular environment of organized brain tissue. We argue that accurate interpretation of physiological observations on the nanoscale requires a better understanding of the underlying electrodiffusion phenomena.