Quantifying Protein Diffusion and Capture on Filaments

The functional relevance of regulating proteins is often limited to specific binding sites such as the ends of microtubules or actin-filaments. A localization of proteins on these functional sites is of great importance. We present a quantitative theory for a diffusion and capture process, where proteins diffuse on a filament and stop diffusing when reaching the filament’s end. It is found that end-association after one-dimensional diffusion is the main source for tip-localization of such proteins. As a consequence, diffusion and capture is highly efficient in enhancing the reaction velocity of enzymatic reactions, where proteins and filament ends are to each other as enzyme and substrate. We show that the reaction velocity can effectively be described within a Michaelis-Menten framework. Together, one-dimensional diffusion and capture beats the (three-dimensional) Smoluchowski diffusion limit for the rate of protein association to filament ends.     

Protein Diffusion on Charged Biopolymers: DNA versus Microtubule

Protein diffusion in lower-dimensional spaces is used for various cellular functions. For example, sliding on DNA is essential for proteins searching for their target sites, and protein diffusion on microtubules is important for proper cell division and neuronal development. On the one hand, these linear diffusion processes are mediated by long-range electrostatic interactions between positively charged proteins and negatively charged biopolymers and have similar characteristic diffusion coefficients. On the other hand, DNA and microtubules have different structural properties. Here, using computational approaches, we studied the mechanism of protein diffusion along DNA and microtubules by exploring the diffusion of both protein types on both biopolymers. We found that DNA-binding and microtubule-binding proteins can diffuse on each other’s substrates; however, the adopted diffusion mechanism depends on the molecular properties of the diffusing proteins and the biopolymers. On the protein side, only DNA-binding proteins can perform rotation-coupled diffusion along DNA, with this being due to their higher net charge and its spatial organization at the DNA recognition helix. By contrast, the lower net charge on microtubule-binding proteins enables them to diffuse more quickly than DNA-binding proteins on both biopolymers. On the biopolymer side, microtubules possess intrinsically disordered, negatively charged C-terminal tails that interact with microtubule-binding proteins, thus supporting their diffusion. Thus, although both DNA-binding and microtubule-binding proteins can diffuse on the negatively charged biopolymers, the unique molecular features of the biopolymers and of their natural substrates are essential for function.     

Bistability, bifurcations, and Waddington's epigenetic landscape

Waddington's epigenetic landscape is probably the most famous and most powerful metaphor in developmental biology. Cells, represented by balls, roll downhill through a landscape of bifurcating valleys. Each new valley represents a possible cell fate and the ridges between the valleys maintain the cell fate once it has been chosen. Here I examine models of two important developmental processes - cell-fate induction and lateral inhibition - and ask whether the landscapes for these models at least qualitatively resemble Waddington's picture. For cell-fate induction, the answer is no. The commitment of a cell to a new fate corresponds to the disappearance of a valley from the landscape, not the splitting of one valley into two, and it occurs through a type of bifurcation - a saddle-node bifurcation - that possesses an intrinsic irreversibility that is missing from Waddington's picture. Lateral inhibition, a symmetrical cell-cell competition process, corresponds better to Waddington's picture, with one valley reversibly splitting into two through a pitchfork bifurcation. I propose an alternative epigenetic landscape that has numerous valleys and ridges right from the start, with the process of cell-fate commitment corresponding to the irreversible disappearance of some of these valleys and ridges, via cell-fate induction, complemented by the creation of new valleys and ridges through processes like cell-cell competition.     

Astroglial-Induced In Vitro Angiogenesis: Requirements for RNA and Protein Synthesis

Astrocytes are believed to affect microvascular endothelial cell differentiation in brain and retina. Bovine retinal microvessel endothelial cells formed capillary-like structures when cocultured with C₆ astroglial cells or in the absence of C₆ cells in response to the reconstituted basement membrane protein Matrigel. Using quantitative computer-assisted image analysis, the requirements for RNA and protein synthesis in these two complementary models of in vitro microvessel morphogenesis were examined. Astroglial-dependent capillary-like structure formation was inhibited by up to 87% in a dose-dependent fashion by cycloheximide (0.01–0.1 μg/ml), puromycin (0.1–0.25 μg/ml), and actinomycin D (0.01– 0.025 μg/ml). In contrast, the astroglial-independent process in response to Matrigel was not affected by these metabolic inhibitors. These findings suggest that capillary-like structures form in response to astroglial cells in two distinct sequential stages. The first consists of inductive astroglial-endothelial interactions requiring both RNA and protein synthesis. This initiates endogenous endothelial morphogenic events that do not appear to require RNA or protein synthesis, consistent with posttranslational regulatory mechanisms. The first astroglial-dependent step is relevant to the regulation of microvessel formation in brain and retina, whereas the second may represent a morphogenic pathway common to micro-vessel formation in many tissues.     

A Simple Self-Maintaining Metabolic System: Robustness,Autocatalysis, Bistability

A living organism must not only organize itself from within; it must also maintain its organization in the face of changes in its environment and degradation of its components. We show here that a simple (M,R)-system consisting of three interlocking catalytic cycles, with every catalyst produced by the system itself, can both establish a non-trivial steady state and maintain this despite continuous loss of the catalysts by irreversible degradation. As long as at least one catalyst is present at a sufficient concentration in the initial state, the others can be produced and maintained. The system shows bistability, because if the amount of catalyst in the initial state is insufficient to reach the non-trivial steady state the system collapses to a trivial steady state in which all fluxes are zero. It is also robust, because if one catalyst is catastrophically lost when the system is in steady state it can recreate the same state. There are three elementary flux modes, but none of them is an enzyme-maintaining mode, the entire network being necessary to maintain the two catalysts.     

The Thermodynamics of Nucleotide Binding to Protein

Abstract

A detailed understanding of the mechanism of enzyme action requires a correspondingly detailed knowledge of the structures of the intermediates and transition states on the catalytic pathway, as well as the kinetics and thermodynamics of their interconversion. Cryoenzymology, the use of subzero temperatures and fluid cryosolvents, has the potential to supply this type of information. In this article recent investigations illustrating the advantages of cryoenzymology are reviewed. The major advantage lies in the ability to accumulate and stabilize productive enzyme—substrate intermediates for sufficient lengths of time to allow the collection of high resolution structural data, e.g. by X-ray diffraction. In addition, intermediates which are not detectable under normal conditions, due to too short lifetimes and/or low concentrations, may be detected at low temperatures, in some cases through changes in the rate-limiting step. The method seems of rather general applicability, judging by the number of different types of enzymes, including oligomeric and membrane-associated ones, which have successfully been studied using cryoenzymology. In some cases, at least, good agreement between observations at subzero temperatures and normal conditions has been found, demonstrating the relevance of the technique. Potential limitations of the technique, as well as questions regarding the effects on the protein structure, are also discussed.     

Binding Thermodynamics of Ferredoxin:NADP Reductase: Two Different Protein Substrates and One Energetics

The thermodynamics of the formation of binary and ternary complexes between Anabaena PCC 7119 FNR and its substrates, NADP⁺ and Fd, or Fld, has been studied by ITC. Despite structural dissimilarities, the main difference between Fd and Fld binding to FNR relates to hydrophobicity, reflected in different binding heat capacity and number of water molecules released from the interface. At pH 8, the formation of the binary complexes is both enthalpically and entropically driven, accompanied by the protonation of at least one ionizable group. His²⁹⁹ FNR has been identified as the main responsible for the proton exchange observed. However, at pH 10, where no protonation occurs and intrinsic binding parameters can be obtained, the formation of the binary complexes is entropically driven, with negligible enthalpic contribution. Absence of the FMN cofactor in Fld does not alter significantly the strength of the interaction, but considerably modifies the enthalpic and entropic contributions, suggesting a different binding mode. Ternary complexes show negative cooperativity (6-fold and 11-fold reduction in binding affinity, respectively), and an increase in the enthalpic contribution (more favorable) and a decrease in the entropic contribution (less favorable), with regard to the binary complexes energetics.     

Coupled Protein Diffusion and Folding in the Cell

When a protein unfolds in the cell, its diffusion coefficient is affected by its increased hydrodynamic radius and by interactions of exposed hydrophobic residues with the cytoplasmic matrix, including chaperones. We characterize protein diffusion by photobleaching whole cells at a single point, and imaging the concentration change of fluorescent-labeled protein throughout the cell as a function of time. As a folded reference protein we use green fluorescent protein. The resulting region-dependent anomalous diffusion is well characterized by 2-D or 3-D diffusion equations coupled to a clustering algorithm that accounts for position-dependent diffusion. Then we study diffusion of a destabilized mutant of the enzyme phosphoglycerate kinase (PGK) and of its stable control inside the cell. Unlike the green fluorescent protein control''s diffusion coefficient, PGK''s diffusion coefficient is a non-monotonic function of temperature, signaling ‘sticking’ of the protein in the cytosol as it begins to unfold. The temperature-dependent increase and subsequent decrease of the PGK diffusion coefficient in the cytosol is greater than a simple size-scaling model suggests. Chaperone binding of the unfolding protein inside the cell is one plausible candidate for even slower diffusion of PGK, and we test the plausibility of this hypothesis experimentally, although we do not rule out other candidates.     

Transmembrane Protein Diffusion in Gel-Supported Dual-Leaflet Membranes

Tools to measure transmembrane-protein diffusion in lipid bilayer membranes have advanced in recent decades, providing a need for predictive theoretical models that account for interleaflet leaflet friction on tracer mobility. Here we address the fully three-dimensional flows driven by a (nonprotruding) transmembrane protein embedded in a dual-leaflet membrane that is supported above and below by soft porous supports (e.g., hydrogel or extracellular matrix), each of which has a prescribed permeability and solvent viscosity. For asymmetric configurations, i.e., supports with contrasting permeability, as realized for cells in contact with hydrogel scaffolds or culture media, the diffusion coefficient can reflect interleaflet friction. Reasonable approximations, for sufficiently large tracers on low-permeability supports, are furnished by a recent phenomenological theory from the literature. Interpreting literature data, albeit for hard-supported membranes, provides a theoretical basis for the phenomenological Stokes drag law as well as strengthening assertions that nonhydrodynamic interactions are important in supported bilayer systems, possibly leading to overestimates of the membrane/leaflet viscosity. Our theory provides a theoretical foundation for future experimental studies of tracer diffusion in gel-supported membranes.     

Bistability in gene transcription: interplay of messenger RNA, protein, and nonprotein coding RNA

The author proposes a kinetic model describing the interplay of messenger ribonucleic acid (mRNA), protein, produced via translation of this RNA, and nonprotein coding RNA (ncRNA). The model includes association of mRNA and ncRNA and regulation of the ncRNA production by protein. In the case of positive feedback between the production of protein and ncRNA, the steady state of the system is found to be unique. For negative feedback, the model predicts in the mean-field case either unique steady state or bistable kinetics. With incorporation of fluctuations, the bistability is manifested in the form of kinetic bursts provided that the number of reactants is low. Basically, the model describes the simplest biological switch operating with participation of ncRNA. Although the results obtained are applicable to ncRNSs in general, the presentation is focused primarily on microRNAs (miRNAs) which form a large important subclass of ncRNAs and are thought to regulate up to one third of all human genes.     

Bistability in apoptosis: roles of bax, bcl-2, and mitochondrial permeability transition pores

We propose a mathematical model for mitochondria-dependent apoptosis, in which kinetic cooperativity in formation of the apoptosome is a key element ensuring bistability. We examine the role of Bax and Bcl-2 synthesis and degradation rates, as well as the number of mitochondrial permeability transition pores (MPTPs), on the cell response to apoptotic stimuli. Our analysis suggests that cooperative apoptosome formation is a mechanism for inducing bistability, much more robust than that induced by other mechanisms, such as inhibition of caspase-3 by the inhibitor of apoptosis (IAP). Simulations predict a pathological state in which cells will exhibit a monostable cell survival if Bax degradation rate is above a threshold value, or if Bax expression rate is below a threshold value. Otherwise, cell death or survival occur depending on initial caspase-3 levels. We show that high expression rates of Bcl-2 can counteract the effects of Bax. Our simulations also demonstrate a monostable (pathological) apoptotic response if the number of MPTPs exceeds a threshold value. This study supports our contention, based on mathematical modeling, that cooperativity in apoptosome formation is critically important for determining the healthy responses to apoptotic stimuli, and helps define the roles of Bax, Bcl-2, and MPTP vis-à-vis apoptosome formation.     

Protein Thermodynamics Can Be Predicted Directly from Biological Growth Rates

Life on Earth is capable of growing from temperatures well below freezing to above the boiling point of water, with some organisms preferring cooler and others hotter conditions. The growth rate of each organism ultimately depends on its intracellular chemical reactions. Here we show that a thermodynamic model based on a single, rate-limiting, enzyme-catalysed reaction accurately describes population growth rates in 230 diverse strains of unicellular and multicellular organisms. Collectively these represent all three domains of life, ranging from psychrophilic to hyperthermophilic, and including the highest temperature so far observed for growth (122°C). The results provide credible estimates of thermodynamic properties of proteins and obtain, purely from organism intrinsic growth rate data, relationships between parameters previously identified experimentally, thus bridging a gap between biochemistry and whole organism biology. We find that growth rates of both unicellular and multicellular life forms can be described by the same temperature dependence model. The model results provide strong support for a single highly-conserved reaction present in the last universal common ancestor (LUCA). This is remarkable in that it means that the growth rate dependence on temperature of unicellular and multicellular life forms that evolved over geological time spans can be explained by the same model.     

Thermodynamics of Conformational Transitions in a Disordered Protein Backbone Model

Conformational entropy is expected to contribute significantly to the thermodynamics of structural transitions in intrinsically disordered proteins or regions in response to protein/ligand binding, posttranslational modifications, and environmental changes. We calculated the backbone (dihedral) conformational entropy of oligoglycine $\left({\text{Gly}}_N\right)$, a protein backbone mimic and model intrinsically disordered region, as a function of chain length ($N=3$, 4, 5, 10, and 15) from simulations using three different approaches. The backbone conformational entropy scales linearly with chain length with a slope consistent with the entropy of folding of well-structured proteins. The entropic contributions of second-order dihedral correlations are predominantly through intraresidue ?-ψ pairs, suggesting that oligoglycine may be thermodynamically modeled as a system of independent glycine residues. We find the backbone conformational entropy to be largely independent of global structural parameters, like the end-to-end distance and radius of gyration. We introduce a framework referred to herein as “ensemble confinement” to estimate the loss (gain) of conformational free energy and its entropic component when individual residues are constrained to (released from) particular regions of the ?-ψ map. Quantitatively, we show that our protein backbone model resists ordering/folding with a significant, unfavorable ensemble confinement free energy because of the loss of a substantial portion of the absolute backbone entropy. Proteins can couple this free-energy reservoir to distal binding events as a regulatory mechanism to promote or suppress binding.     

Bistability,Spatial Interaction,and the Distribution of Tropical Forests and Savannas

Recent work has indicated that tropical forest and savanna can be alternative stable states under a range of climatic conditions. However, dynamical systems theory suggests that in case of strong spatial interactions between patches of forest and savanna, a boundary between both states is only possible at conditions in which forest and savanna are equally stable, called the ‘Maxwell point.’ Frequency distributions of MODIS tree-cover data at 250 m resolution were used to estimate such Maxwell points with respect to the amount and seasonality of rainfall in both South America and Africa. We tested on a 0.5° scale whether there is a larger probability of local coexistence of forests and savannas near the estimated Maxwell points. Maxwell points for South America and Africa were estimated at 1760 and 1580 mm mean annual precipitation and at Markham’s Seasonality Index values of 50 and 24 %. Although the probability of local coexistence was indeed highest around these Maxwell points, local coexistence was not limited to the Maxwell points. We conclude that critical transitions between forest and savanna may occur when climatic changes exceed a critical value. However, we also conclude that spatial interactions between patches of forest and savanna may reduce the hysteresis that can be observed in isolated patches, causing more predictable forest-savanna boundaries than continental-scale analyses of tree cover indicate. This effect could be less pronounced in Africa than in South America, where the forest-savanna boundary is substantially affected by rainfall seasonality.