Ensemble Level Research Articles

Ensemble perspective for understanding temporal credit assignment.

Recurrent neural networks are widely used for modeling spatiotemporal sequences in both nature language processing and neural population dynamics. However, understanding the temporal credit assignment is hard. Here, we propose that each individual connection in the recurrent computation is modeled by a spike and slab distribution, rather than a precise weight value. We then derive the mean-field algorithm to train the network at the ensemble level. The method is then applied to classify handwritten digits when pixels are read in sequence, and to the multisensory integration task that is a fundamental cognitive function of animals. Our model reveals important connections that determine the overall performance of the network. The model also shows how spatiotemporal information is processed through the hyperparameters of the distribution, and moreover reveals distinct types of emergent neural selectivity. To provide a mechanistic analysis of the ensemble learning, we first derive an analytic solution of the learning at the infinitely large network limit. We then carry out a low-dimensional projection of both neural and synaptic dynamics, analyze symmetry breaking in the parameter space, and finally demonstrate the role of stochastic plasticity in the recurrent computation. Therefore, our study sheds light on mechanisms of how weight uncertainty impacts the temporal credit assignment in recurrent neural networks from the ensemble perspective.

Time-lapse single-molecule imaging revealed spatiotemporal antibody interaction dynamics in situ.

Antibody-antigen interactions are primarily characterized by ensemble-averaged affinity measurements outside the cellular environment. However, the highly heterogeneous and dynamic individual antibody behaviors in the cellular environment may influence antibodies to achieve specific functions not well understood at the ensemble level. Here we present single-molecule interaction microscopy (SMIM) as a simple and versatile strategy to explore antibody-antigen interactions in situ. SMIM combines single-molecule localization microscopy with time-lapse imaging, extending single-molecule imaging into sub-minute timescales. Our results indicated that antibodies interact with similar kinetics with both on- and off-targets at the sub-second timescale, while on-target interactions outnumbered off-target interactions at the sub-minute timescale. Furthermore, we observed that immunoglobulin G (IgG) antibodies and antibody fragments (F(ab’)2) display repetitive binding kinetics with their targets on the sub-minute timescale. By extended imaging in the sub-minute timescale, we achieved simultaneous, dual-target, superresolved antibody-antigen interaction maps. SMIM presents an easy-to-implement strategy that enables multiplexed investigation of single antibodies interacting in their native environment with information on the nanoscale topography of both on- and off-targets and temporal dynamics with the on-target.

Tackling the puzzle of protein reaction-diffusion inside living cells with sub-5-nm localization.

The interior of the cells where most proteins perform their function, is a mixture of thousands of components, but by no means is it a “well-mixed” reactor. While diffusion of proteins can both assist and hinder the formation of heterogeneous environments in cells, the reactions of proteins also affect their tumbling and diffusion. How are protein diffusion and reaction coupled in the living cell? Using Minflux, we can answer this question at the single-molecule level. Minflux provides imaging and tracking at a resolution of 2-3 nm in three dimensions, with minimal bleaching, and high enough speed to distinguish the diffusion of a protein bound vs. unbound in a complex or free vs. stuck onto surfaces inside the cell. Here we study a protein-RNA complex in live cells: U1A-SL2 RNA, whose binding affinity and dynamics have been well studied in vitro and at the ensemble level in human cells. To obtain the best super-resolution tracking in living cells, we first optimized the labeling dyes from twelve options; only one binding partner needs to be labeled at a time to detect changes in its diffusion. Bound and unbound protein populations can be differentiated and spatially located with respect to specific regions in the cell.

Membrane phospholipids induce moderate positive cooperativity in closed pacemaker channels.

Hyperpolarization-activated cyclic nucleotide-gated ion channels (HCN channels) play pivotal role in pacemaking activity in the heart and brain. Previous studies have shown the effects of phospholipids like PIP2 on voltage dependent activation of HCN channels. Similar lipid dependent effects on channel activity have also been reported for other ion channels at an ensemble level. However, there is a lack of information regarding how ligand binding to membrane proteins itself is affected by membrane phospholipids at a molecular level. Here, we probe cAMP binding to full length HCN1 channel reconstituted into nanodiscs containing soy polar lipids to mimic a membrane environment. HCN1 nanodiscs were immobilized on zero mode waveguides (ZMWs) and binding of fluorescently labelled cAMP (fcAMP) was monitored over time using total-internal-reflection-fluorescence microscopy (TIRF). Surprisingly, we observed a moderate positive cooperativity in fcAMP binding to the closed HCN1 channel. The observed bound probability distributions deviated from the expected binomial distribution from an identical and independent binding model. These results are significantly different from the cAMP binding to the closed HCN1 channel in detergent micelles.2 Our results shed new light on the contribution of membrane phospholipids to cooperativity in ligand binding to HCN channels.

Consolidation of cellular memory representations in superficial neocortex

Systems-level memory consolidation, a key concept in memory research, involves the conversion of memories that depend on the hippocampus for their formation into efficient hippocampus-independent forms, presumably encoded by cortico-cortical connections. Yet, little is understood about the nature of consolidated neural codes at the cellular ensemble level. Mice require an intact hippocampus for "virtual" spatial learning and to develop neocortical representations of thecorresponding experiences. We find that, whereas a novel virtual environment is neither learned nor represented in superficial cortex following severe damageto hippocampus, pre-operatively learned memories and their corresponding sparse and widespread neural ensemble representations in cortical layers II-III are preserved, a sine qua non of memory consolidation. These findings provide a new window for future study of the cellular mechanisms of memory consolidation.

Multiscale Electrochemistry of Lithium Manganese Oxide (LiMn2O4): From Single Particles to Ensembles and Degrees of Electrolyte Wetting.

Scanning electrochemical cell microscopy (SECCM) facilitates single particle measurements of battery materials using voltammetry at fast scan rates (1 V s-1), providing detailed insight into intrinsic particle kinetics, otherwise obscured by matrix effects. Here, we elucidate the electrochemistry of lithium manganese oxide (LiMn2O4) particles, using a series of SECCM probes of graded size to determine the evolution of electrochemical characteristics from the single particle to ensemble level. Nanometer scale control over the SECCM meniscus cell position and height further allows the study of variable particle/substrate electrolyte wetting, including comparison of fully wetted particles (where contact is also made with the underlying glassy carbon substrate electrode) vs partly wetted particles. We find ensembles of LiMn2O4 particles show voltammograms with much larger peak separations than those of single particles. In addition, if the SECCM meniscus is brought into contact with the substrate electrode, such that the particle-support contact changes from dry to wet, a further dramatic increase in peak separation is observed. Finite element method modeling of the system reveals the importance of finite electronic conductivity of the particles, contact resistance, surface kinetics, particle size, and contact area with the electrode surface in determining the voltammetric waveshape at fast scan rates, while the responses are relatively insensitive to Li+ diffusion coefficients over a range of typical values. The simulation results explain the variability in voltammetric responses seen at the single particle level and reveal some of the key factors responsible for the evolution of the response, from ensemble, contact, and wetting perspectives. The variables and considerations explored herein are applicable to any single entity (nanoscale) electrochemical study involving low conductivity materials and should serve as a useful guide for further investigations of this type. Overall, this study highlights the potential of multiscale measurements, where wetting, electronic contact, and ionic contact can be varied independently, to inform the design of practical composite electrodes.

HIDRA2: deep-learning ensemble sea level and storm tide forecasting in the presence of seiches – the case of the northern Adriatic

Abstract. We propose a new deep-learning architecture HIDRA2 for sea level and storm tide modeling, which is extremely fast to train and apply and outperforms both our previous network design HIDRA1 and two state-of-the-art numerical ocean models (a NEMO engine with sea level data assimilation and a SCHISM ocean modeling system), over all sea level bins and all forecast lead times. The architecture of HIDRA2 employs novel atmospheric, tidal and sea surface height (SSH) feature encoders as well as a novel feature fusion and SSH regression block. HIDRA2 was trained on surface wind and pressure fields from a single member of the European Centre for Medium-Range Weather Forecasts (ECMWF) atmospheric ensemble and on Koper tide gauge observations. An extensive ablation study was performed to estimate the individual importance of input encoders and data streams. Compared to HIDRA1, the overall mean absolute forecast error is reduced by 13 %, while in storm events it is lower by an even larger margin of 25 %. Consistent superior performance over HIDRA1 as well as over general circulation models is observed in both tails of the sea level distribution: low tail forecasting is relevant for marine traffic scheduling to ports of the northern Adriatic, while high tail accuracy helps coastal flood response. Power spectrum analysis indicates that HIDRA2 most accurately represents the energy density peak centered on the ground state sea surface eigenmode (seiche) and comes a close second to SCHISM in the energy band of the first excited eigenmode. To assign model errors to specific frequency bands covering diurnal and semi-diurnal tides and the two lowest basin seiches, spectral decomposition of sea levels during several historic storms is performed. HIDRA2 accurately predicts amplitudes and temporal phases of the Adriatic basin seiches, which is an important forecasting benefit due to the high sensitivity of the Adriatic storm tide level to the temporal lag between peak tide and peak seiche.

Composite ligand shells on gold nanoprisms - an ensemble and single particle study.

The attachment of thiolated molecules onto gold surfaces is one of the most extensively used and robust ligand exchange approaches to exploit the nanooptical features of nanoscale and nanostructured plasmonic materials. In this work, the impact of thiol adsorption on the optical properties of wet-chemically synthesized gold nanoprisms is studied both at the ensemble and single particle level to investigate the build-up of more complex ligand layers. Two prototypical ligands with different lengths have been investigated ((16-mercaptohexadecyl)trimethylammonium bromide - MTAB and thiolated polyethylene glycol - mPEG-SH). From ensemble experiments it is found that composite ligand layers are obtained by the sequential addition of the two thiols, and an island-like surface accumulation of the molecules can be anticipated. The single particle experiment derived chemical interface damping and resonance energy changes further support this and show additionally that when the two thiols are used simultaneously, a higher density, intermixed layer is formed. Hence, when working with more than a single type of ligand during surface modification, sequential adsorption is preferred for the combination of accessible essential surface functionalities, whereas for high overall loading the simultaneous use of the different ligand types is favourable.

Single-molecule characterization of a bright and photostable deep-red fluorescent squaraine-figure-eight (SF8) dye

Squaraine Figure Eight (SF8) dyes are a unique class of deep-red fluorescent dyes with self-threaded molecular architecture that provides structural rigidity while simultaneously encapsulating and protecting the emissive fluorochrome. Previous cell microscopy and bulk phase studies of SF8 dyes indicated order of magnitude enhancements in photostability over conventional pentamethine cyanine dyes such as Cy5. Studies conducted at the single molecule level now reveal that these ensemble level enhancements carry over to the single molecule level in terms of enhanced emission quantum yields, longer times to photobleaching, and enhanced total photon yields. When compared to Cy5, the SF8-based dye SF8(D4)2 possesses a three-fold larger single molecule emission quantum yield, exhibits order of magnitude longer average times before photobleaching, and exhibits twenty times larger photon yields. Additional features such as water solubility, fluorochrome encapsulation to protect it against nucleophilic attack, and selective biomarker targeting capability make SF8-based dyes promising candidates for biological labeling and microscopy applications and single molecule tracking.

Magnesium-Vacancy Optical Centers in Diamond.

We provide the first systematic characterization of the structural and photoluminescence properties of optically active centers fabricated upon implantation of 30-100 keV Mg+ ions in synthetic diamond. The structural configurations of Mg-related defects were studied by the electron emission channeling technique for short-lived, radioactive 27Mg implantations at the CERN-ISOLDE facility, performed both at room temperature and 800 °C, which allowed the identification of a major fraction of Mg atoms (∼30 to 42%) in sites which are compatible with the split-vacancy structure of the MgV complex. A smaller fraction of Mg atoms (∼13 to 17%) was found on substitutional sites. The photoluminescence emission was investigated both at the ensemble and individual defect level in the 5-300 K temperature range, offering a detailed picture of the MgV-related emission properties and revealing the occurrence of previously unreported spectral features. The optical excitability of the MgV center was also studied as a function of the optical excitation wavelength to identify the optimal conditions for photostable and intense emission. The results are discussed in the context of the preliminary experimental data and the theoretical models available in the literature, with appealing perspectives for the utilization of the tunable properties of the MgV center for quantum information processing applications.

Single-particle electrophoresis for studying the adsorption of cationic polymers onto anionic particles.

Understanding the adsorption of polymers onto particles is crucial for many technological and biomedical applications. Even though polymer adsorption on particles is a dynamic process, most experimental techniques can only study the adsorption indirectly, in equilibrium and on the ensemble level. New analysis methods are required to overcome these limitations. We investigated the use of single-particle electrophoresis to study the adsorption kinetics of cationic polymers onto anionic particles and compared the resulting data to a theoretical model. In this approach, the electrophoretic mobility of single polystyrene (PS) particles, exposed to different concentrations of poly(2-guanidinoethyl methacrylate), was measured as a function of time. The polymer adsorption leads to an electrophoretic mobility change of the PS particle over time, from the initial negative value to a positive value at equilibrium. By fitting the kinetics data to the Langmuir model, the adsorption rate, desorption rate and equilibrium constant were determined. Finally, the adsorption kinetics of several other polymers was investigated. This showed that the presented technique enables direct analysis and comparison of the kinetics of polymer adsorption on the single-particlelevel.

Activity Patterns of Individual Neurons and Ensembles Correlated with Retrieval of a Contextual Memory in the Dorsal CA1 of Mouse Hippocampus.

The hippocampus is crucial for retrieval of contextual memories. The activation of a subpopulation of neurons in the dorsal CA1 (dCA1) of the hippocampus is required for memory retrieval. Given that hippocampal neurons exhibit distinct patterns of response during memory retrieval, the activity patterns of individual neurons or ensembles may be critically involved in memory retrieval. However, this relation has been unclear. To investigate this question, we used an in vivo microendoscope calcium imaging technique to optically record neuronal activity in the dCA1 of male and female mice. We observed that a portion of dCA1 neurons increased their responses to the learned context after contextual fear conditioning (FC), resulting in overall increase in response of neuronal population compared with simple context exposure. Such increased response was specific to the conditioned context as it disappeared in neutral context. The magnitude of increase in neuronal responses by FC was proportional to memory strength during retrieval. The increases in activity preferentially occurred during the putative sharp wave ripple events and were not simply because of animal's movement and immobility. At the ensemble level, synchronous cell activity patterns were associated with memory retrieval. Accordingly, when such patterns were more similar between conditioned and neutral context, animals displayed proportionally more similar level of freezing. Together, these results indicate that increase in responses of individual neurons and synchronous cell activity patterns in the dCA1 neuronal network are critically involved in representing a contextual memory recall.SIGNIFICANCE STATEMENT Neurons in the dorsal CA1 of the hippocampus are crucial for memory retrieval. By using in vivo calcium imaging methods for recording neuronal activity, we demonstrate that dCA1 neurons increased their responses to the learned context specifically by FC and such changes correlated with memory strength during retrieval. Moreover, distinct synchronous cell activity patterns were formed by FC and involved in representing contextual memory retrieval. These findings reveal dynamic activity features of dCA1 neurons that are involved in contextual memory retrieval.

One-Dimensional Highly-Confined CsPbBr3 Nanorods with Enhanced Stability: Synthesis and Spectroscopy.

One-dimensional (1D) colloidal lead halide perovskites (LHPs) have potential as quantum emitters. Their study, however, has been hampered by their previous instability, leaving a gap in our understanding of structure-property relationships in colloidal LHPs with anisotropic shapes. Here, we synthesize stable, highly-confined 1D CsPbBr3 nanorods (NRs) and demonstrate their structural details and photoluminescence (PL) properties at both the ensemble and single particle levels. Using amino-terminated copolymers, we are able to stabilize and characterize 1D CsPbBr3 NRs utilizing transmission electron microscopy (TEM) and small angle scattering (SAS). Scanning transmission electron microscopy reveals that these NRs possess structural defects, including twists and inhomogeneity. Solution-phase photon correlation spectroscopy shows low biexciton-to-exciton quantum yield ratios (QYBX/QYX) and broad spectral line widths dominated by homogeneous broadening.

Harvesting a Wide Spectral Range of Electronic Coherences with Disordered Quasi‐Homo Dimeric Assemblies at Room Temperature

AbstractA wide variety of photoinduced electronic coherences are shown to be robust with respect to dephasing in ensembles of quasi‐homodimers assembled with sub‐nm ligands from colloidal 3 nm CdSe quantum dots (QDs) with controlled 9% size dispersion, both in solution and in solid‐state. Coherence periods ranging from 40 to 300 fs are consistently characterized by multidimensional electronic spectroscopy in the Vis range in solution and solid‐state samples. A theoretical model that includes size dispersion, spin orbit coupling, and crystal field splitting supports the assignment of electronic coherences. Further, this model provides a guide for optimizing the coherences by tuning the interplay between dimer electronic delocalization, optical activity, and size dispersion. The experimental persistence of many QD electronic coherences at the level of the size dispersed ensemble in the solid‐state and in solution opens the way for building versatile bottom‐up materials well suited to quantum technology applications.

Covariant nonequilibrium thermodynamics from Ito-Langevin dynamics

Using the recently developed covariant Ito-Langevin dynamics, we develop a nonequilibrium thermodynamic theory for small systems coupled to multiplicative noises. The theory is based on Ito calculus, and is fully covariant under time-independent nonlinear transformation of variables. Assuming instantaneous detailed balance, we derive expressions for various thermodynamic functions, including work, heat, entropy production, and free energy, both at ensemble level and at trajectory level, and prove the second law of thermodynamics for arbitrary nonequilibrium processes. We relate time-reversal asymmetry of path probability to entropy production, and derive its consequences such as fluctuation theorem and nonequilibrium work relation. For Langevin systems with additive noises, our theory is equivalent to the common theories of stochastic energetics and stochastic thermodynamics. Using concrete examples, we demonstrate that whenever kinetic coefficients or metric tensor depend on system variables, the common theories of stochastic thermodynamics and stochastic energetics should be replaced by our theory.

Multiple parameters shape the 3D chromatin structure of single nuclei at the doc locus in Drosophila

The spatial organization of chromatin at the scale of topologically associating domains (TADs) and below displays large cell-to-cell variations. Up until now, how this heterogeneity in chromatin conformation is shaped by chromatin condensation, TAD insulation, and transcription has remained mostly elusive. Here, we used Hi-M, a multiplexed DNA-FISH imaging technique providing developmental timing and transcriptional status, to show that the emergence of TADs at the ensemble level partially segregates the conformational space explored by single nuclei during the early development of Drosophila embryos. Surprisingly, a substantial fraction of nuclei display strong insulation even before TADs emerge. Moreover, active transcription within a TAD leads to minor changes to the local inter- and intra-TAD chromatin conformation in single nuclei and only weakly affects insulation to the neighboring TAD. Overall, our results indicate that multiple parameters contribute to shaping the chromatin architecture of single nuclei at the TAD scale.

Quantitative prediction of ensemble dynamics, shapes and contact propensities of intrinsically disordered proteins.

Intrinsically disordered proteins (IDPs) are highly dynamic systems that play an important role in cell signaling processes and their misfunction often causes human disease. Proper understanding of IDP function not only requires the realistic characterization of their three-dimensional conformational ensembles at atomic-level resolution but also of the time scales of interconversion between their conformational substates. Large sets of experimental data are often used in combination with molecular modeling to restrain or bias models to improve agreement with experiment. It is shown here for the N-terminal transactivation domain of p53 (p53TAD) and Pup, which are two IDPs that fold upon binding to their targets, how the latest advancements in molecular dynamics (MD) simulations methodology produces native conformational ensembles by combining replica exchange with series of microsecond MD simulations. They closely reproduce experimental data at the global conformational ensemble level, in terms of the distribution properties of the radius of gyration tensor, and at the local level, in terms of NMR properties including 15N spin relaxation, without the need for reweighting. Further inspection revealed that 10–20% of the individual MD trajectories display the formation of secondary structures not observed in the experimental NMR data. The IDP ensembles were analyzed by graph theory to identify dominant inter-residue contact clusters and characteristic amino-acid contact propensities. These findings indicate that modern MD force fields with residue-specific backbone potentials can produce highly realistic IDP ensembles sampling a hierarchy of nano- and picosecond time scales providing new insights into their biological function.

Dynamic Hippocampal CA2 Responses to Contextual Spatial Novelty.

Hippocampal place cells are functional units of spatial navigation and are present in all subregions: CA1, CA2, CA3, and CA4. Recent studies on CA2 have indicated its role in social and contextual memories, but its contribution to spatial novelty detection and encoding remains largely unknown. The current study aims to uncover how CA2 processes spatial novelty and to distinguish its functional role towards the same from CA1. Accordingly, a novel 3-day paradigm was designed where animals were introduced to a completely new environment on the first day, and on subsequent days, novel segments were inserted into the existing spatial environment while the other segments remained the same, allowing us to compare novel and familiar parts of the same closed-loop track on multiple days. We found that spatial novelty leads to dynamic and complex hippocampal place cell firings at both individual neuron and population levels. Place cells in both CA1 and CA2 had strong responses to novel segments, leading to higher average firing rates and increased pairwise cross correlations across all days. However, CA2 place cells that fired for novel areas had lower spatial information scores than CA1 place cells active in the same areas. At the ensemble level, CA1 only responded to spatial novelty on day 1, when the environment was completely novel, whereas CA2 responded to it on all days, each time novelty was introduced. Therefore, CA2 was more sensitive and responsive to novel spatial features even when introduced in a familiar environment, unlike CA1.

From Ensemble Electrochemistry to Nano‐Impact Electrochemistry: Altered Reaction Selectivity

AbstractSelective electrochemical production of valued chemicals is of significant importance but remains a great challenge in chemistry. Conventional approaches for enhancing reaction selectivity focus on the improvement of the catalysts themselves. In this work, we systematically studied the reaction kinetics and mass transport behavior of LaNiO3 nanocubes (LaNiO3 NCs) catalyzed hydrogen peroxide reduction reaction (HPRR) at ensemble and single nanoparticle levels using nano‐impact electrochemistry (NIE). We find that the selectivity of HPRR was altered at individual random‐walk nanoparticles as compared to their ensemble counterpart without changing the reaction kinetics, due to the significantly enhanced mass transport at single nanoparticles. This discovery offers the scope of new catalytic approaches for engineering electrochemical reactions in general.

From Ensemble Electrochemistry to Nano‐Impact Electrochemistry: Altered Reaction Selectivity

Selective electrochemical production of valued chemicals is of significant importance but remains a great challenge in chemistry. Conventional approaches for enhancing reaction selectivity focus on the improvement of the catalysts themselves. In this work, we systematically studied the reaction kinetics and mass transport behavior of LaNiO3 nanocubes (LaNiO3 NCs) catalyzed hydrogen peroxide reduction reaction (HPRR) at ensemble and single nanoparticle levels using nano-impact electrochemistry (NIE). We find that the selectivity of HPRR was altered at individual random-walk nanoparticles as compared to their ensemble counterpart without changing the reaction kinetics, due to the significantly enhanced mass transport at single nanoparticles. This discovery offers the scope of new catalytic approaches for engineering electrochemical reactions in general.