Flow and diffusion of high-stakes test scores

We apply visualization and modeling methods for convective and diffusive flows to public school mathematics test scores from Texas. We obtain plots that show the most likely future and past scores of students, the effects of random processes such as guessing, and the rate at which students appear in and disappear from schools. We show that student outcomes depend strongly upon economic class, and identify the grade levels where flows of different groups diverge most strongly. Changing the effectiveness of instruction in one grade naturally leads to strongly nonlinear effects on student outcomes in subsequent grades.     

Dissipative self-assembly of particles interacting through time-oscillatory potentials

Dissipative self-assembly is the emergence of order within a system due to the continuous input of energy. This form of nonequilibrium self-organization allows the creation of structures that are inaccessible in equilibrium self-assembly. However, design strategies for dissipative self-assembly are limited by a lack of fundamental understanding of the process. This work proposes a novel route for dissipative self-assembly via the oscillation of interparticle potentials. It is demonstrated that in the limit of fast potential oscillations the structure of the system is exactly described by an effective potential that is the time average of the oscillatory potential. This effective potential depends on the shape of the oscillations and can lead to effective interactions that are physically inaccessible in equilibrium. As a proof of concept, Brownian dynamics simulations were performed on a binary mixture of particles coated by weak acids and weak bases under externally controlled oscillations of pH. Dissipative steady-state structures were formed when the period of the pH oscillations was smaller than the diffusional timescale of the particles, whereas disordered oscillating structures were observed for longer oscillation periods. Some of the dissipative structures (dimers, fibers, and honeycombs) cannot be obtained in equilibrium (fixed pH) simulations for the same system of particles. The transition from dissipative self-assembled structures for fast oscillations to disordered oscillating structures for slow oscillations is characterized by a maximum in the energy dissipated per oscillation cycle. The generality of the concept is demonstrated in a second system with oscillating particle sizes.Dissipative or dynamic self-assembly is the formation of order due to the continuous input of energy into the system and dissipation of energy by the system into the environment (1). If the input of energy is stopped, dissipative structures are destroyed as the system evolves toward equilibrium; therefore, these structures exist only far from equilibrium. Dissipative self-assembled structures are unique due to their ability to adapt to environmental changes. Consider, for example, a school of fish where each individual dynamically interacts with its neighbors and adjusts its position and velocity accordingly (2). Due to its dynamical nature, the school of fish responds as a whole when a predator threatens one of its individuals. This complex behavior is impossible for a static assembly. Nature excels in using dissipative structures to minimize wasted energy. For example, a swarm of bees can change its size and density to regulate its internal temperature, and a flock of Canada geese reduces energy dissipation due to aerodynamic drag by flying in a V-shaped formation (2).Synthetic dissipative assemblies are restricted to a small number of examples, such as magnetic spinners at the air–water interface (1), magnetic droplets on surperhydrophobic surfaces (3), lanes of colloidal particles under the influence of external fields (4, 5), clusters of active colloids (6), and swarms of self-propelled particles (7). One reason for the scarcity of examples of synthetic dissipative self-assembly (in comparison with equilibrium self-assembly) is the lack of general design strategies. In equilibrium self-assembly, there is an optimal balance of the physical and chemical interactions in the system that dictates the formation of ordered structures from preexisting building blocks (8–10). The structure of these building blocks can be engineered to control their interactions and, thus, determine the outcome of equilibrium self-assembly. For example, the molecular architecture of block copolymers, which self-assemble according to the balance between enthalpic interactions and the conformational entropy of the chains, controls their equilibrium morphology (11). The structure of dissipative systems, on the other hand, depends not only on the relative strength of the physical and chemical interactions among building blocks, but also on dynamical variables, such as diffusion constants, chemical reaction rates, and time-dependent changes of external parameters, which make the effective particle interactions time dependent.The goal of this work is to demonstrate and analyze a novel general strategy for dissipative self-assembly via the oscillation of interparticle forces controlled by an external variable. We derive the general result that for fast enough oscillations the dissipative self-assembly follows an equilibrium-like distribution with an effective interparticle potential. These interactions are the time average of the oscillating potentials. Namely (as shown in SI Text), the probability of a given configuration, {r⇀i}, in nonequilibrium steady state for a fast oscillating potential is Pneq({r⇀i})∝⁡exp[−β〈U({r⇀i})〉] with 〈U({r⇀i})〉=(1/τ)∫0τU({r⇀i};t)dt being the average interaction potential over the period of the oscillation τ. Whereas dissipative structures follow a Boltzmann distribution dictated by the time-averaged potentials, these interparticle potentials can be obtained only far from equilibrium. As a case study, we performed computer simulations on a model system of positively and negatively charged particles whose charges depend on the pH of the solution, which is externally oscillated. In previous work on light-switchable particles (12, 13) the time between light pulses was larger than the characteristic equilibration timescale; thus, the system relaxed to its equilibrium state between pulses. In contrast, we are interested in the regime where the switching time of the interparticle interactions and the characteristic timescale for equilibration are commensurate, such that the system is always out of equilibrium. We show that this condition is achieved in our system when the period of the oscillation is similar to or shorter than the diffusional timescale of the particles. In that case, the particles form dissipative structures that cannot be obtained in a simulation by equilibrium self-assembly at fixed pH. We characterized the transition between ordered dissipative structures at high oscillation frequencies and disordered oscillating structures at low oscillation frequencies and showed that this transition corresponds to a maximum of the energy dissipated per oscillation cycle. The generality of our results is also demonstrated for a different time-dependent potential where the sizes of the particles oscillate in time (details are shown in SI Text). Dissipative self-assembly via the oscillation of interparticle interactions has the potential to deliver self-assembled structures that are unavailable close to thermodynamic equilibrium and, therefore, to open previously unidentified routes in bottom–up nanofabrication.The simulated systems are composed of two types of particles, a and b, each of which represents a pH-responsive colloid (Fig. 1A). a-type and b-type particles have charges of opposite signs; the magnitudes of these charges depend on the pH of the system. We model the dependence of the charge of each particle type, z_i (with i = a or b) on the pH of the system with the well-known expression for acid–base equilibrium,zi=±z011+10±(pH−pKa).[1]Open in a separate windowFig. 1.Model system for dissipative self-assembly of pH-responsive particles. (A) The model system is composed of equal numbers of a-type and b-type particles: a-type particles model pH-responsive negatively charged colloids with pK_a = 5 (e.g., carboxylate-coated colloids), which have a −z₀ charge at pH 7 and zero charge at pH 3; b-type particles model pH-responsive positively charged colloids with pK_a = 5 (e.g., pyridine-coated colloids), which have a +z₀ charge at pH 3 and zero charge at pH 7. (B) Charge of the colloids as a function of pH (determined with Eq. 1).For simplicity, we assume that a-type and b-type particles have the same maximum absolute charge (z₀) and the same pK_a (we used pK_a = 5 in all simulations). We also neglect the effects of the local environment on the acid–base equilibrium [i.e., charge regulation (14, 15)], hydrodynamic interactions, the effect of the substrate, and many-body interactions (16), because these effects do not influence our general conclusions on dissipative self-assembly and because implementing them in our simulations would result in a prohibitive computational cost. Fig. 1B shows the pH dependence of the charge of each particle. Particles of type a have a negative charge –z₀ at pH 7 and are uncharged at pH 3 (particle a models, for instance, a carboxylate-coated colloid). Particles of type b have a positive +z₀ charge at pH 3 and are uncharged at pH 7 (particle b models, for example, an amino- or pyridine-coated particle). The particles in our simulations interact via the combination of a short-range repulsive potential that models excluded volume interactions between the cores of the particles and a long-range screened electrostatic potential (Methods). The screened electrostatic potential is the Yukawa potential (4, 17) given byuijYuk(r)=ziz0zjz0Cre−(r/λD),[2]where λ_D is the solution Debye length and C is a constant that determines the strength of the electrostatic potential in the system (Methods). We simulated the systems of particles using Brownian dynamics (BD) in a 2D box with periodic boundary conditions either at constant pH (i.e., static interparticle potential) or by oscillating the pH between 3 and 7 with a period τ. We use dimensionless variables: The distances are measured in units of σ (diameter of the colloid), the energies in k_BT, and the time in units of the characteristic diffusion timescale, t_d = σ²/D (where D is the diffusion coefficient).     

Anomalous heating in a colloidal system

We report anomalous heating in a colloidal system, an experimental observation of the inverse Mpemba effect, where for two initial temperatures lower than the temperature of the thermal bath, the colder of the two systems heats up faster when coupled to the same thermal bath. For an overdamped, Brownian colloidal particle moving in a tilted double-well potential, we find a nonmonotonic dependence of the heating times on the initial temperature of the system. Entropic effects make the inverse Mpemba effect generically weaker—harder to observe—than the usual Mpemba effect (anomalous cooling). We also observe a strong version of anomalous heating, where a cold system heats up exponentially faster than systems prepared under slightly different conditions.

Can an initially cold system heat up faster than an initially cool system that is otherwise nominally identical? Naively, one would assume that a slowly heating object relaxes to the temperature of its surroundings exponentially, passing through all the intermediate temperatures. A system that is initially at a cold temperature should then take longer to heat than a system initially at a cool temperature. However, for rapid heating, a system may evolve toward equilibrium so that its intermediate states are not in thermal equilibrium and are not characterized by a unique temperature. In such cases, the possibility of anomalously fast heating has recently been predicted and confirmed in numerical studies of an Ising antiferromagnet (1). Further numerical studies suggest that these effects may be seen in a wide variety of systems, including fluids with inelastic (2–4) and elastic (5, 6) collisions and spin glasses (7).Although anomalous heating is a recent prediction, an analogous anomaly for cooling and freezing has been noted in observations of water dating back to 350 BC (8). Its first systematic study was done in 1969 by Mpemba and Osborne, who concluded that hot water could begin to freeze in a time shorter than that required for cold water (9). This phenomenon has since been dubbed the Mpemba effect and was followed up with further experiments on water (10–16), accompanied by some controversy, tracing back to the difficulty of obtaining reproducible results (17, 18). Proposed mechanisms for the effect include evaporation (10, 19, 20), convection currents (21–23), dissolved gases and solutes (11, 14, 21), supercooling (12, 13), and hydrogen bonds (24, 25).In an effort to understand the Mpemba effect in more generic terms, Lu and Raz introduced a theoretical picture that related the effect to the geometry of system dynamics in a state space whose elements are defined by the amplitudes of eigenmodes of linear dynamical systems (1). A fast quench can then lead a system to follow a nonequilibrium path through state space to equilibrium that is shorter than the path traced out by a slowly cooling system. In recent work, we showed that this kind of Mpemba effect is present in a system consisting of a colloidal particle immersed in water and subject to a carefully designed potential (26). From this point of view, the dynamics of cooling and heating obey similar principles, and anomalous heating represents an inverse Mpemba effect. Yet, despite a formal similarity between the cases of heating and cooling (1, 27), anomalous heating has not previously been seen experimentally, neither in systems that exhibited the anomalous cooling effect (10–16, 26, 28–30) nor in any other system.Here we present experimental evidence for the inverse Mpemba effect. We also observe a strong version (31) of the effect, where, for a carefully chosen initial temperature, a system heats up exponentially faster than systems that were initially at different temperatures. Surprisingly, as we shall see, subtle differences between high- and low-temperature limits generically make the inverse effect more difficult to observe experimentally. Moreover, the mechanism for the inverse effect that we find to be relevant in our experiments does not depend on the presence of metastability (32), which played a crucial role in the forward cases explored in previous experiments.     

Role of CaMKIIδ phosphorylation of the cardiac ryanodine receptor in the force frequency relationship and heart failure

The force frequency relationship (FFR), first described by Bowditch 139 years ago as the observation that myocardial contractility increases proportionally with increasing heart rate, is an important mediator of enhanced cardiac output during exercise. Individuals with heart failure have defective positive FFR that impairs their cardiac function in response to stress, and the degree of positive FFR deficiency correlates with heart failure progression. We have identified a mechanism for FFR involving heart rate dependent phosphorylation of the major cardiac sarcoplasmic reticulum calcium release channel/ryanodine receptor (RyR2), at Ser2814, by calcium/calmodulin–dependent serine/threonine kinase–δ (CaMKIIδ). Mice engineered with an RyR2-S2814A mutation have RyR2 channels that cannot be phosphorylated by CaMKIIδ, and exhibit a blunted positive FFR. Ex vivo hearts from RyR2-S2814A mice also have blunted positive FFR, and cardiomyocytes isolated from the RyR2-S2814A mice exhibit impaired rate-dependent enhancement of cytosolic calcium levels and fractional shortening. The cardiac RyR2 macromolecular complexes isolated from murine and human failing hearts have reduced CaMKIIδ levels. These data indicate that CaMKIIδ phosphorylation of RyR2 plays an important role in mediating positive FFR in the heart, and that defective regulation of RyR2 by CaMKIIδ-mediated phosphorylation is associated with the loss of positive FFR in failing hearts.     

Structures of the junctophilin/voltage-gated calcium channel interface reveal hot spot for cardiomyopathy mutations

Junctophilins (JPH) are a class of proteins found at junctions between the plasma membrane and the endoplasmic or sarcoplasmic reticulum, allowing for communications between proteins embedded in different membranes. JPHs have been proposed to interact with lipids as well as several ion channels, allowing for specialized communication between them. The JPH3 isoform is the target for repeats that cause Huntington’s disease-like 2, whereas JPH2 is a hot spot for mutations linked to cardiomyopathy. Here we present crystal structures of two JPH isoforms, which resemble a twisted skeleton with ribs formed by membrane occupation recognition nexus repeats, and a backbone built by a long α-helix. We captured the structure of a complex between JPH2 and a C-terminal binding site in the L-type calcium channel (Ca_V1.1) and show that this interaction is required for clustering of these channels and for robust muscle excitation–contraction coupling. Over 80 sequence variants linked to cardiomyopathy are found in different structurally important regions of JPH2, most of which affect stabilizing interactions. A subset directly affects the interaction with the L-type calcium channel. In parallel, sequence variants in the L-type calcium channel, linked to cardiac arrhythmia, also affect critical interactions.

Junctions between the plasma membrane and the endoplasmic reticulum (ER) or sarcoplasmic reticulum (SR) are found in multiple cell types and allow for specialized communication between proteins embedded in these different membranes. Junctophilins (JPH) are key to enabling the formation of such junctions, by virtue of a C-terminal transmembrane helix, located in the ER or SR membrane, and an N-terminal domain containing MORN (membrane occupation recognition nexus) motifs, thought to interact with phospholipids in the plasma membrane (1, 2). As such, JPHs play critical roles in diverse signaling processes, often allowing functional or mechanical cross-talk between ion channels embedded in different membranes.Four isoforms (JPH1–JPH4) are encoded in the human genome, with JPH1 primarily expressed in skeletal muscle, JPH2 in skeletal, cardiac, and smooth muscle, and JPH3/4 mostly found in the brain (3) and in sensory neurons (4). Additionally, JPHs have been found in multiple cell types, including pancreatic β cells (5) and T cells (6). In muscle tissue, JPHs allow for the communication between L-type voltage-gated calcium channels (Ca_V), located in the transverse-tubule (T-tubule) membrane, and ryanodine receptors (RyRs) in the SR membrane. In cardiac myocytes, a depolarization of the plasma membrane activates the Ca_V1.2 isoform, and the influx of Ca²⁺ then triggers opening of RyR2, in a process known as Ca²⁺-induced Ca²⁺ release (7). In skeletal muscle, direct mechanical coupling is thought to occur between the corresponding Ca_V1.1 and RyR1 isoforms, although any direct contacts between these two proteins remain to be elucidated (8, 9). In both scenarios, the coupling requires proximity between the T-tubule and SR membranes, for which JPHs are critical. JPHs have also been suggested to directly bind both Ca_Vs and RyRs, as well as other ion channels including Ca²⁺-activated potassium channels (10–12) and KCNQ1 (13).The importance of JPHs is underscored by the various disorders associated with them. JPH1 has been identified as a modifier of Charcot-Marie-Tooth disease (14). JPH2 is a hot spot for mutations linked to hypertrophic cardiomyopathy (HCM) (15–17), and repeats in JPH3 have been found to cause Huntington disease-like 2 (HDL-2) (18). In addition, cardiac stress results in activation of calpain, which cleaves JPH2 and drives heart failure progression (19–24). Cleaved fragments of JPH2 have also been shown to migrate to the nucleus, where, depending on the fragment type, they either attenuate (22) or promote (21) cellular remodeling. To date, no high-resolution structural information is available for any JPH isoform, hampering insights into its basic functions and disease mechanisms.In this study, we describe high-resolution structures of two JPH isoforms, reveal how JPHs bind the C-terminal region of Ca_V1.1 via a groove formed by the MORN repeats, how this association is important for normal excitation–contraction coupling, and how disease-associated mutations may affect this process.     

Sequence physical properties encode the global organization of protein structure space

It is demonstrated that, properly represented, the amino acid composition of protein sequences contains the information necessary to delineate the global properties of protein structure space. A numerical representation of amino acid sequence in terms of a set of property factors is used, and the values of those property factors are averaged over individual sequences and then over sets of sequences belonging to structurally defined groups. These sequence sets then can be viewed as points in a 10-dimensional space, and the organization of that space, determined only by sequence properties, is similar at both local and global scales to that of the space of protein structures determined previously.     

Clean Electrochemical Synthesis of Pd–Pt Bimetallic Dendrites with High Electrocatalytic Performance for the Oxidation of Formic Acid

Pd–Pt bimetallic catalysts with a dendritic morphology were in situ synthesized on the surface of a carbon paper via the facile and surfactant-free two step electrochemical method. The effects of the frequency and modification time of the periodic square-wave potential (PSWP) on the morphology of the Pd–Pt bimetallic catalysts were investigated. The obtained Pd–Pt bimetallic catalysts with a dendritic morphology displayed an enhanced catalytic activity of 0.77 A mg⁻¹, almost 2.5 times that of the commercial Pd/C catalyst reported in the literature (0.31 A mg⁻¹) in acidic media. The enhanced catalytic activity of the Pd–Pt bimetallic catalysts with a dendritic morphology towards formic acid oxidation reaction (FAOR) was not only attributed to the large number of atomic defects at the edges of dendrites, but also ascribed to the high utilization of active sites resulting from the “clean” electrochemical preparation method. Besides, during chronoamperometric testing, the current density of the dendritic Pd–Pt bimetallic catalysts for a period of 3000 s was 0.08 A mg⁻¹, even four times that of the commercial Pd/C catalyst reported in the literature (about 0.02 A mg⁻¹).     

Detergent-free isolation,characterization, and functional reconstitution of a tetrameric K+ channel: The power of native nanodiscs

A major obstacle in the study of membrane proteins is their solubilization in a stable and active conformation when using detergents. Here, we explored a detergent-free approach to isolating the tetrameric potassium channel KcsA directly from the membrane of Escherichia coli, using a styrene-maleic acid copolymer. This polymer self-inserts into membranes and is capable of extracting membrane patches in the form of nanosize discoidal proteolipid particles or “native nanodiscs.” Using circular dichroism and tryptophan fluorescence spectroscopy, we show that the conformation of KcsA in native nanodiscs is very similar to that in detergent micelles, but that the thermal stability of the protein is higher in the nanodiscs. Furthermore, as a promising new application, we show that quantitative analysis of the co-isolated lipids in purified KcsA-containing nanodiscs allows determination of preferential lipid–protein interactions. Thin-layer chromatography experiments revealed an enrichment of the anionic lipids cardiolipin and phosphatidylglycerol, indicating their close proximity to the channel in biological membranes and supporting their functional relevance. Finally, we demonstrate that KcsA can be reconstituted into planar lipid bilayers directly from native nanodiscs, which enables functional characterization of the channel by electrophysiology without first depriving the protein of its native environment. Together, these findings highlight the potential of the use of native nanodiscs as a tool in the study of ion channels, and of membrane proteins in general.Integral membrane proteins (MPs) are an abundant class of proteins that play key roles in a wide range of essential cellular processes (1). To facilitate their study in vitro, detergent molecules are commonly used to extract MPs out of their native lipid–bilayer environment (2). However, the use of detergents has some inherent disadvantages. Most importantly, even though there are promising developments to improve their properties (3, 4), the insufficient mimicking of a lipid bilayer by detergent micelles often leads to destabilization and rapid loss of function of the incorporated protein (5). For many functional and structural studies, it is thus necessary to reconstitute the MP into a more stabilizing environment; for example, by replacing the detergent with amphipathic polymers (amphipols) (6) or incorporating the MP into lipid nanodiscs with a surrounding protein scaffold (7). Both approaches have proven to be valuable tools for the study of structural and functional properties of MPs (8, 9); however, a limitation remains, as transfer of MPs into any of these systems requires initial solubilization by detergent.Recently, a detergent-free approach has been described using amphipathic styrene-maleic acid copolymers (SMAs) as an alternative to solubilize MPs directly from biological membranes in the form of nanodiscs, referred to as “Lipodisq” or SMA lipid particles (10–13) (Fig. 1). The mechanism of action of SMA differs fundamentally from that of detergents: instead of disrupting the lipid bilayer completely, SMA spontaneously self-inserts and extracts intact membrane patches in the form of discoidal particles that are stabilized by a SMA annulus (14, 15). Because these nanodiscs conserve a spatially delimited native biomembrane including MPs, we term them “native nanodiscs.” One of the main advantages of this system is the straightforward extraction protocol without the need for detergent. It has been shown that the SMA polymer is capable of directly extracting native nanodiscs containing large functional protein complexes from yeast (12), bacterial proteins involved in cell division (16) and photosynthesis (17), and several members of the ABC transporter family (13). The isolation of these proteins from a variety of different organisms suggests a general applicability of SMA solubilization for all MPs, irrespective of their expression host or native organism.Open in a separate windowFig. 1.(A) Chemical structure of SMA polymers at neutral pH. For this study, a polymer with an average SMA ratio of n:m = 2:1 was used. (B) Schematic representation of a native nanodisc containing a KcsA tetramer (blue) and native lipids (green). The outer hydrophobic surface of the lipids is shielded by SMA (orange).To further explore the potential of native nanodiscs, we used the SMA polymer to isolate an oligomeric bacterial membrane protein: the tetrameric potassium channel from Streptomyces lividans (KcsA) (18), expressed in Escherichia coli. KcsA is an ideal model protein for such studies because it is well-characterized and because reconstitution studies have shown that both its function and stability are strongly affected by lipid composition (19–21). In this work, we apply SMA to prepare and purify native nanodiscs with KcsA to compare the conformational properties and stability of the protein with those in detergent micelles. In addition, we use native nanodiscs to investigate preferential lipid–protein interactions by analyzing the composition of small patches of native membrane that are copurified with the protein. Finally, we study the functional properties of KcsA on reconstitution from native nanodiscs into a planar lipid bilayer system. Our results underscore the huge potential of SMA as a membrane-solubilizing agent, as well as the use of native nanodiscs as a membrane-mimetic system for biophysical studies on ion channels, and MPs in general.     

Locating the transition from periodic oscillations to spatiotemporal chaos in the wake of invasion

In systems with cyclic dynamics, invasions often generate periodic spatiotemporal oscillations, which undergo a subsequent transition to chaos. The periodic oscillations have the form of a wavetrain and occur in a band of constant width. In applications, a key question is whether one expects spatiotemporal data to be dominated by regular or irregular oscillations or to involve a significant proportion of both. This depends on the width of the wavetrain band. Here, we present mathematical theory that enables the direct calculation of this width. Our method synthesizes recent developments in stability theory and computation. It is developed for only 1 equation system, but because this is a normal form close to a Hopf bifurcation, the results can be applied directly to a wide range of models. We illustrate this by considering a classic example from ecology: wavetrains in the wake of the invasion of a prey population by predators.     

Structural and energetic analysis of metastable intermediate states in the E1P–E2P transition of Ca2+-ATPase

Sarcoplasmic reticulum (SR) Ca²⁺-ATPase transports two Ca²⁺ ions from the cytoplasm to the SR lumen against a large concentration gradient. X-ray crystallography has revealed the atomic structures of the protein before and after the dissociation of Ca²⁺, while biochemical studies have suggested the existence of intermediate states in the transition between E1P⋅ADP⋅2Ca²⁺ and E2P. Here, we explore the pathway and free energy profile of the transition using atomistic molecular dynamics simulations with the mean-force string method and umbrella sampling. The simulations suggest that a series of structural changes accompany the ordered dissociation of ADP, the A-domain rotation, and the rearrangement of the transmembrane (TM) helices. The luminal gate then opens to release Ca²⁺ ions toward the SR lumen. Intermediate structures on the pathway are stabilized by transient sidechain interactions between the A- and P-domains. Lipid molecules between TM helices play a key role in the stabilization. Free energy profiles of the transition assuming different protonation states suggest rapid exchanges between Ca²⁺ ions and protons when the Ca²⁺ ions are released toward the SR lumen.

Sarcoplasmic reticulum Ca²⁺-ATPase (SR Ca²⁺-ATPase or SERCA1a) is a representative P-type ATPase that transports Ca²⁺ ions against a 10⁴ times concentration gradient across the SR membrane. The transport mechanism was originally described by E1/E2 theory, whereby the protein alternates between Ca²⁺ high-affinity E1 and low-affinity E2 states. A more-detailed reaction cycle requires multiple steps, including the binding/dissociation of Ca²⁺, H⁺-counter transport, ATP-binding and hydrolysis, phosphorylation/dephosphorylation of Asp351, and the dissociation of ADP and Pi (1–3) (SI Appendix, Fig. S1). Structurally, the Ca²⁺-ATPase consists of three cytoplasmic domains (actuator; A, nucleotide-binding; N, and phosphorylation; P) and 10 transmembrane (TM) helices (M1-M10) (4, 5). Two Ca²⁺-binding sites are located in M4-M6 and M8 (6), while a nucleotide, ATP or ADP, is bound at the N–P domain interface (7). Functional interconnections between the cytoplasmic domains and TM helices are necessary in the reaction cycle (8, 9).Molecular mechanisms underlying Ca²⁺ uptake by the ATPase have been investigated in biochemical experiments as well as structural studies. In particular, crystal structures of the Ca²⁺-ATPase, which represent different physiological states in the cycle (SI Appendix, Fig. S1), have provided essential information for understanding structure–function relationships (8, 9). Each crystal structure well explains the results of mutagenesis (3, 10), limited proteolysis studies (11, 12), and other biochemical experiments. Comparisons between multiple crystal structures provide direct evidence on how conformational changes of the Ca²⁺-ATPase take place from one step to another in the cycle. For instance, crystal structures that represent E1P⋅ADP⋅2Ca²⁺ and E2P (Fig. 1 A and B) reveal important conformational changes to release Ca²⁺ toward the SR lumen: 1) the A-domain rotates ∼90°; 2) the threonine–glycine–glutamate–serine (TGES) loop in the A-domain reaches the phosphorylated Asp351 in the P-domain (13–15); 3) M1-M6 are rearranged to open the luminal gate for the dissociation of Ca²⁺. Despite the increasing structural information, there are still unresolved questions. A series of biochemical studies suggested the existence of two intermediate states, E1P⋅2Ca²⁺ and E2P⋅2Ca²⁺. However, atomistic structures and their energetics in these intermediate states would be required to understand their functional roles.Open in a separate windowFig. 1.Structures of SR Ca²⁺-ATPase embedded in a DOPC membrane in E1P⋅ADP⋅2Ca²⁺ (PDB ID: 2ZBD) (A) and E2P (PDB ID: 2ZBE) (B). The three cytoplasmic domains (A, N, and P) are colored in red, purple, and green, respectively. (C) A structural transition pathway predicted using the mean-force string method is projected onto a two-dimensional map along with the two distance RMSDs (dRMS) from the representative structures in MD simulations of E1P and E2P_dp. In the simulation, Glu908 at the Ca²⁺-binding sites is protonated to mimic the same protonation states of E1P. Only the atomic coordinates that are involved in the collective variables (CVs) are used for dRMS calculations. The five substates (SSs) are defined along the pathway via the fixed radius clustering method (1 to 17: red; 18 to 27: yellow; 28 to 35: green; 36 to 51: cyan; and 52 to 64: blue). Among the 64 images, 5 images (10, 23, 31, 44, and 57) are selected as five representative SSs.There are several computational tools to predict conformational transition pathways of proteins, such as morphing (16), normal mode analysis (17), or molecular dynamics (MD) simulation based on coarse-grained or atomistic models (18–21). However, large conformational changes of the Ca²⁺-ATPase happen on the milliseconds or slower time scales, which are not accessible in brute-force MD simulations (18–21) even when using MD-specialized supercomputers, such as Anton/Anton 2 (22, 23) or MDGRAPE-4A (24). In this study, we perform atomistic MD simulations with an enhanced conformational sampling method to investigate the conformational pathway and free energy profile in the transition between E1P⋅ADP⋅2Ca²⁺ and E2P. We utilize the mean-force string method (25) for obtaining one of the most probable transition pathways. The free energy profile along the pathway is then calculated with umbrella sampling (26). The same approach has been previously applied to adenylate kinase in solution (27) and multidrug transporter AcrB (28) and the ABC heme transporter (29) in biological membranes. A similar method, the string method with swarm trajectories (30), has been applied to several membrane proteins (31, 32). Das et al. applied the method to four conformational transitions of the Ca²⁺-ATPase, including the same step examined in the current study (33).In the current simulation study, we intend to compare the simulation results with those of existing structural and biochemical studies. In particular, the two intermediate states (E1P⋅2Ca²⁺ and E2P⋅2Ca²⁺) and the Ca²⁺-ATPase–lipid interactions in the E1P–E2P transition are examined using the simulation trajectories. The predicted interactions between phospholipids and basic sidechains of Ca²⁺-ATPase are compared with recent X-ray crystallography studies (34). We also investigate the effect of protonation states in the E1P–E2P transitions from atomistic MD simulations, which is difficult via experimental studies. By integrating structural, biochemical, and computational results, we shed light on the structural and energetic features of the E1P–E2P transition of the Ca²⁺-ATPase in unprecedented detail.     

Continuous variable responses and signal gating form kinetic bases for pulsatile insulin signaling and emergence of resistance

Understanding kinetic control of biological processes is as important as identifying components that constitute pathways. Insulin signaling is central for almost all metazoans, and its perturbations are associated with various developmental disorders, metabolic diseases, and aging. While temporal phosphorylation changes and kinetic constants have provided some insights, constant or variable parameters that establish and maintain signal topology are poorly understood. Here, we report kinetic parameters that encode insulin concentration and nutrient-dependent flow of information using iterative experimental and mathematical simulation-based approaches. Our results illustrate how dynamics of distinct phosphorylation events collectively contribute to selective kinetic gating of signals and maximum connectivity of the signaling cascade under normo-insulinemic but not hyper-insulinemic states. In addition to identifying parameters that provide predictive value for maintaining the balance between metabolic and growth-factor arms, we posit a kinetic basis for the emergence of insulin resistance. Given that pulsatile insulin secretion during a fasted state precedes a fed response, our findings reveal rewiring of insulin signaling akin to memory and anticipation, which was hitherto unknown. Striking disparate temporal behavior of key phosphorylation events that destroy the topology under hyper-insulinemic states underscores the importance of unraveling regulatory components that act as bandwidth filters. In conclusion, besides providing fundamental insights, our study will help in identifying therapeutic strategies that conserve coupling between metabolic and growth-factor arms, which is lost in diseases and conditions of hyper-insulinemia.

Signaling cascades are essential for regulating cellular processes, and decades of work have unraveled molecular and biochemical mechanisms that constitute them. However, kinetic parameters that define emergent properties of signaling networks and therefore predict regulatory nodes are poorly understood. While independent experimental and mathematical approaches have provided valuable insights (1–6), studies that capture dynamics and complexities of signaling architecture vis-à-vis physiological variations in input strengths are far fewer. Not only would these reveal fundamental kinetic considerations that determine signal topology but also inform about reactions/components that could emerge as therapeutic targets.Evolutionarily conserved insulin signaling (IS) is essential for cellular/organismal metabolism and growth (7–9). Aberrant IS is associated both causally and consequentially with growth abnormalities, inflammation, accelerated aging, and diseases including metabolic disorders and cancer (10–13). Genetic perturbations and omics-based studies have elucidated importance of key phosphorylation events in response to insulin stimulation (14–16). Recent reports have provided crucial insights into physical protein interactome, temporal changes in phospho-proteome, and kinetic constants, viz. half-maximal time to reach peak response and half-maximal effective concentration (EC₅₀) (17, 18). However, kinetic parameters that govern network properties of IS as a function of normo-insulinemic and hyper-insulinemic states, which could collectively determine physiological and pathophysiological outcomes, is still lacking.Our current understanding largely stems from studies, which have used either supraphysiological or static concentrations of insulin (19–21). This is in contrast to the physiological setting wherein circulating insulin concentrations vary drastically from being low-pulsatile (∼0.1 nM) to high-biphasic (∼1.0 nM) in fasted and fed states, respectively (22). Moreover, kinetic criteria that either encode fasted-to-fed transitions or drive pathological manifestations of IS, as in diabetes and obesity (23, 24), are unknown. Since IS can be broadly divided into metabolic and growth-factor arms (25), if/how the flow of information is stratified and maintained under normal and hyper-insulinemic states remains to be unraveled.Mathematical approaches to model cellular signaling have gained traction in the recent past to understand the dynamics and also to provide predictive parameters that define topology of signaling network (26–29). Earlier such attempts to determine kinetics of IS have largely employed “averaged” measures to define the behavior of the system (3, 17). Notably, given the fluctuations in insulin levels and inherent noise in signaling, there are no reports that have computed kinetic parameters, which capture emergent properties of IS. Specifically, while there have been simulation-based approaches to define dose-to-duration effects and kinetic insulation on synthetic signaling networks (30), such principles have not been applied to complex biological cascades.In this current study, we unravel network properties of IS under physiological concentrations of insulin and reveal kinetic basis for emergence of memory and resistance. Our study utilizes parameters such as kinetic barriers and connectedness in the network to address how signaling topology is maintained. Notably, we describe the importance of dynamic range and pulsatility in signaling, which generates memory as well as couples the metabolic and growth-factor arms.     

Molecular switch architecture determines response properties of signaling pathways

Many intracellular signaling pathways are composed of molecular switches, proteins that transition between two states—on and off. Typically, signaling is initiated when an external stimulus activates its cognate receptor that, in turn, causes downstream switches to transition from off to on using one of the following mechanisms: activation, in which the transition rate from the off state to the on state increases; derepression, in which the transition rate from the on state to the off state decreases; and concerted, in which activation and derepression operate simultaneously. We use mathematical modeling to compare these signaling mechanisms in terms of their dose–response curves, response times, and abilities to process upstream fluctuations. Our analysis elucidates several operating principles for molecular switches. First, activation increases the sensitivity of the pathway, whereas derepression decreases sensitivity. Second, activation generates response times that decrease with signal strength, whereas derepression causes response times to increase with signal strength. These opposing features allow the concerted mechanism to not only show dose–response alignment, but also to decouple the response time from stimulus strength. However, these potentially beneficial properties come at the expense of increased susceptibility to upstream fluctuations. We demonstrate that these operating principles also hold when the models are extended to include additional features, such as receptor removal, kinetic proofreading, and cascades of switches. In total, we show how the architecture of molecular switches govern their response properties. We also discuss the biological implications of our findings.

Several molecules involved in intracellular signaling pathways act as molecular switches. These are proteins that can be temporarily modified to transition between two conformations, one corresponding to an on (active) state and another to an off (inactive) state. Two prominent examples of such switches are proteins that are modified by phosphorylation and dephosphorylation and GTPases that bind nucleotides. For phosphorylation–dephosphorylation cycles, it is common for the covalent addition of a phosphate by a kinase to cause activation of the modified protein. A phosphatase removes the phosphate to turn the protein off. In the GTPase cycle, the protein is on when bound to guanosine triphosphate (GTP) and off when bound to guanosine diphosphate (GDP). The transition from the GDP-bound state to the GTP-bound state requires nucleotide exchange, whereas the transition from the GTP-bound to the GDP-bound state is achieved via hydrolysis of the γ phosphate on GTP. The basal rates of nucleotide exchange and hydrolysis are often small. These reaction rates are increased severalfold by Guanine Exchange Factors (GEFs) and GTPase Accelerating Proteins (GAPs), respectively (1, 2).A signaling pathway is often initiated upon recognition of a stimulus by its cognate receptor, which then activates a downstream switch. In principle, a switch may be turned on by three mechanisms: (a) activation, by increasing the transition rate from the off state to the on state; (b) derepression, by decreasing the transition rate from the on state to the off state; and (c) concerted activation and derepression. Examples of these three mechanisms are found in the GTPase cycles in different organisms. In animals, signaling through many pathways is initiated by G-protein-coupled receptors (GPCRs) that respond to a diverse set of external stimuli. These receptors act as GEFs to activate heterotrimeric G proteins (3–6). Thus, pathway activation relies upon increasing the transition rate from the off state to the on state. There are no GPCRs in plants and other bikonts; the nucleotide exchange occurs spontaneously, without requiring GEF activity (7–9). G proteins are kept in the off state by a repressor such as a GAP or some other protein that holds the self-activating G protein in its inactive state. In this scenario, the presence of a stimulus results in derepression, i.e., removal of the repressing activity (10–12). Concerted activation and dererpression occur in the GTPase cycle of the yeast mating-response pathway (13, 14), in which the inactive GPCRs recruit a GAP protein and act to repress, whereas active receptors have GEF activity and act to activate. Thus, perception of a stimulus leads to concerted activation and derepression by increasing GEF activity while decreasing GAP activity.These three mechanisms of signaling through molecular switches also occur in many other systems. For example, the activation mechanism described here is a simpler abstraction of a linear signaling cascade, a classical framework used to study general properties of signaling pathways (15–19), as well as to model specific signaling pathways (20–22). While derepression may seem like an unusual mechanism, it occurs in numerous important signaling pathways in plants (e.g., auxin, ethylene, gibberellin, and phytochrome), as well as gene regulation (23–27). In many of these cases, derepression occurs through a decrease in the degradation rate of a component instead of its deactivation rate. Concerted mechanisms are found in bacterial two-component systems, wherein the same component acts as kinase and phosphatase (28–35).Many previous studies have focused on the properties of a single switch mechanism without drawing comparisons between the three potential ways for initiating signaling. For example, the classical Goldbeter–Koshland model studied zero-order ultrasensitivity of an activation mechanism (15). Further analyses examined the effect of receptor numbers (36–38), feedback mechanisms (39, 40), and removal of active receptors via endocytosis and degradation (41, 42). Similarly, important properties of the concerted mechanism have been elucidated, such as its ability to perform ratiometric signaling (13, 14), to align dose responses at different stages of the signaling pathway (43), as well as its robustness (29, 44). The derepression mechanism is relatively less studied. Although there are models of G-signaling in Arabidopsis thaliana (45–47), these models have a large number of states and parameters and do not specifically examine distinct behaviors conferred by derepression.What are the evolutionary constraints that may favor activation over derepression and vice versa? Seminal studies have investigated this question for gene-regulatory networks (48–50). However, an analysis of differences in the functional characteristics of activation, derepression, and concerted mechanisms in the context of cell signaling is still lacking. To address this deficiency, we perform a systematic comparison of the three mechanisms using the following metrics: 1) dose–response, 2) response time, and 3) ability to suppress or filter stochastic fluctuations in upstream components. The rationale behind comparing dose–response curves is that they provide information about the input sensitivity range and the output dynamic range, both of which are of pharmacological importance. We supplement this comparison with response times, which provide information about the dynamics of the signaling activity. The third metric of comparison is motivated from the fact that signaling pathways are subject to intrinsic fluctuations that occur due to the stochastic nature of biochemical reactions (51–56).We construct and analyze both deterministic ordinary differential equation (ODE) models and stochastic models based on continuous-time Markov chains. We show that activation has the following two effects: It makes the switch response more sensitive than that of the receptor, and it speeds up the response with the stimulus strength. In contrast, derepression makes the switch response less sensitive than the receptor occupancy and slows down the response speed as stimulus strength increases. These counteracting behaviors of activation and derepression lead to intermediate sensitivity and intermediate response time for the concerted mechanism. In the special case of a perfect concerted mechanism (equal activation and repression), the dose–response curve of the pathway aligns with the receptor occupancy, and the response time does not depend upon the stimulus level. The noise comparison reveals that the concerted mechanism is more susceptible to fluctuations than the activation and derepression mechanisms, which perform similarly. We further show that these results qualitatively hold for more complex models, such as those incorporating receptor removal and proofreading. We finally discuss our findings to suggest reasons that might have led biological systems to evolve one of these mechanisms over the others, a question that has received considerable attention in the context of gene regulation (48–50).     

Calculation of Dynamic Viscosity in Concentrated Cementitious Suspensions: Probabilistic Approximation and Bayesian Analysis

We present a new focus for the Krieger–Dougherty equation from a probabilistic point of view. This equation allows the calculation of dynamic viscosity in suspensions of various types, like cement paste and self-compacting mortar/concrete. The physical meaning of the parameters that intervene in the equation (maximum packing fraction of particles and intrinsic viscosity), together with the random nature associated with these systems, make the application of the Bayesian analysis desirable. This analysis permits the transformation of parametric-deterministic models into parametric-probabilistic models, which improves and enriches their results. The initial limitations of the Bayesian methods, due to their complexity, have been overcome by numerical methods (Markov Chain Monte Carlo and Gibbs Sampling) and the development of specific software (OpenBUGS). Here we use it to compute the probability density functions that intervene in the Krieger–Dougherty equation applied to the calculation of viscosity in several cement pastes, self-compacting mortars, and self-compacting concretes. The dynamic viscosity calculations made with the Bayesian distributions are significantly better than those made with the theoretical values.     

Topologically protected states in one-dimensional continuous systems and Dirac points

We study a class of periodic Schrödinger operators on ℝ that have Dirac points. The introduction of an “edge” via adiabatic modulation of a periodic potential by a domain wall results in the bifurcation of spatially localized “edge states,” associated with the topologically protected zero-energy mode of an asymptotic one-dimensional Dirac operator. The bound states we construct can be realized as highly robust transverse-magnetic electromagnetic modes for a class of photonic waveguides with a phase defect. Our model captures many aspects of the phenomenon of topologically protected edge states for 2D bulk structures such as the honeycomb structure of graphene.Energy localization in surface modes or edge states at the interface between dissimilar media has been explored, going back to the 1930s, as a vehicle for localization and transport of energy (1–8). These phenomena can be exploited in, for example, quantum, electronic, or photonic device design. An essential property for applications is robustness; the localization properties of such surface states needs to be stable with respect to distortions of or imperfections along the interface.A class of structures, which has attracted great interest since about 2005, is topological insulators (9, 10). In certain energy ranges, such structures behave as insulators in their bulk (this is associated with an energy gap in the spectrum of the bulk Hamiltonian), but have boundary conducting states with energies in the bulk energy gap; these are states that propagate along the boundary and are localized transverse to the boundary. Some of these states may be topologically protected; they persist under deformations of the interface that preserve the bulk spectral gap, e.g., localized perturbations of the interface. In honeycomb structures, e.g., graphene, where a bulk gap is opened at a “Dirac point” by breaking time-reversal symmetry (10–14), protected edge states are unidirectional. Furthermore, these edge states do not backscatter in the presence of interface perturbations (3–5, 8). Chiral edge states, observed in the quantum Hall effect, are a well known instance of topological protected states in condensed matter physics. In tight-binding models, this property can be understood in terms of topological invariants associated with the band structure of the bulk periodic structure (15–20).In this article we introduce a one-dimensional continuum model, a Schrödinger equation with periodic potential modulated by a domain wall, in which we rigorously study the bifurcation of topologically protected edge states as a parameter lifts a Dirac point degeneracy (symmetry-protected linear band crossing). This model, which has many of the features of the above examples, is motivated by the study of photonic edge states in honeycomb structures in ref. 3. The bifurcation we study is governed by the existence of a topologically protected zero-energy eigenstate of a one-dimensional Dirac operator, ?? (Eq. 5). The zero mode of this operator plays a role in electronic excitations in coupled scalar–spinor fields (21) and polymer chains (22). There are numerous studies of edge states for tight-binding models (for example, refs. 7, 9, and 18). The present work considers the far less-explored setting of edge states in the underlying partial differential equations (13, 14). A version of this article with detailed rigorous proofs can be found in ref. 23.Finally, we remark that the topologically protected states we construct can be realized as highly robust transverse-magnetic (TM) electromagnetic guided modes of Maxwell’s equations for a class of photonic waveguides.     

Determination of the Kinetics and Thermodynamic Parameters of Lignocellulosic Biomass Subjected to the Torrefaction Process

The torrefaction process upgrades biomass characteristics and produces solid biofuels that are coal-like in their properties. Kinetics analysis is important for the determination of the appropriate torrefaction condition to obtain the best utilization possible. In this study, the kinetics (Friedman (FR) and Kissinger–Akahira–Sunose (KAS) isoconversional methods) of two final products of lignocellulosic feedstocks, miscanthus (Miscanthus x giganteus) and hops waste (Humulus Lupulus), were studied under different heating rates (10, 15, and 20 °C/min) using thermogravimetry (TGA) under air atmosphere as the main method to investigate. The results of proximate and ultimate analysis showed an increase in HHV values, carbon content, and fixed carbon content, followed by a decrease in the VM and O/C ratios for both torrefied biomasses, respectively. FTIR spectra confirmed the chemical changes during the torrefaction process, and they corresponded to the TGA results. The average E_α for torrefied miscanthus increased with the conversion degree for both models (25–254 kJ/mol for FR and 47–239 kJ/mol for the KAS model). The same trend was noticed for the torrefied hops waste samples; the values were within the range of 14–224 kJ/mol and 60–221 kJ/mol for the FR and KAS models, respectively. Overall, the E_a values for the torrefied biomass were much higher than for raw biomass, which was due to the different compositions of the torrefied material. Therefore, it can be concluded that both torrefied products can be used as a potential biofuel source.     

The Formation of 14H-LPSO in Mg–9Gd–2Y–2Zn–0.5Zr Alloy during Heat Treatment

There is a new long-period stacking ordered structure in Mg–RE–Zn magnesium alloys, namely the LPSO phase, which can effectively improve the yield strength, elongation, and corrosion resistance of Mg alloys. According to different types of Mg–RE–Zn alloy systems, two transformation modes are involved in the heat treatment transformation process. The first is the alloy without LPSO phase in the as-cast alloy, and the Mg_xRE phase changes to 14H-LPSO phase. The second is the alloy containing LPSO phase in the as-cast state, and the 14H-LPSO phase is obtained by the transformations of 6H, 18R, and 24R. The effects of different solution parameters on the second phase of Mg–9Gd–2Y–2Zn–0.5Zr alloy were studied by scanning electron microscopy (SEM), transmission electron microscopy (TEM), and X-ray diffraction (XRD). The precipitation mechanism of 14H-LPSO phase during solution treatment was further clarified. At a solution time of 13 h, the grain size increased rapidly initially and then decreased slightly with increasing solution temperature. The analysis of the volume fraction of the second phase and lattice constant showed that Gd and Y elements in the alloy precipitated from the matrix and formed 14H-LPSO phase after solution treatment at 490 °C for 13 h. At this time, the hardness of the alloy reached the maximum of 74.6 HV. After solution treatment at 500 °C for 13 h, the solid solution degree of the alloy increases, and the grain size and hardness of the alloy remain basically unchanged.     

Sol–Gel Synthesis of Endodontic Cements: Post-Synthesis Treatment to Improve Setting Performance and Bioactivity

The sol–gel process is a wet chemical technique that allows very fine control of the composition, microstructure, and final textural properties of materials, and has great potential for the synthesis of endodontic cements with improved properties. In this work, the influence of different sol–gel synthesis variables on the preparation of endodontic cement based on calcium silicate with Ca/Si stoichiometry equal to 3 was studied. Starting from the most optimal hydraulic composition selected, a novel second post-synthesis treatment using ethanol was essayed. The effects of the tested variables were analyzed by X-ray diffraction, infrared spectroscopy, scanning electron microscopy, nitrogen physisorption, and Gillmore needles to determine the setting time and simulated body fluid (SBF) immersion to measure the bioactive response in vitro. The results indicated that the sol–gel technique is effective in obtaining bioactive endodontic cements (BECs) with high content of the hydraulic compound tricalcium silicate (C3S) in its triclinic polymorph. The implementation of a novel post-synthesis treatment at room temperature using ethanol allows obtaining a final BEC product with a finer particle size and a higher CaCO₃ content, which results in an improved material in terms of setting time and bioactive response.