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The severity of the COVID-19 pandemic, caused by the SARS-CoV-2 coronavirus, calls for the urgent development of a vaccine. The primary immunological target is the SARS-CoV-2 spike (S) protein. S is exposed on the viral surface to mediate viral entry into the host cell. To identify possible antibody binding sites not shielded by glycans, we performed multi-microsecond molecular dynamics simulations of a 4.1 million atom system containing a patch of viral membrane with four full-length, fully glycosylated and palmitoylated S proteins. By mapping steric accessibility, structural rigidity, sequence conservation and generic antibody binding signatures, we recover known epitopes on S and reveal promising epitope candidates for vaccine development. We find that the extensive and inherently flexible glycan coat shields a surface area larger than expected from static structures, highlighting the importance of structural dynamics in epitope mapping.
Abstract
The primary immunological target of COVID-19 vaccines is the SARS-CoV-2 spike (S) protein. S is exposed on the viral surface and mediates viral entry into the host cell. To identify possible antibody binding sites, we performed multi-microsecond molecular dynamics simulations of a 4.1 million atom system containing a patch of viral membrane with four full-length, fully glycosylated and palmitoylated S proteins. By mapping steric accessibility, structural rigidity, sequence conservation, and generic antibody binding signatures, we recover known epitopes on S and reveal promising epitope candidates for structure-based vaccine design. We find that the extensive and inherently flexible glycan coat shields a surface area larger than expected from static structures, highlighting the importance of structural dynamics. The protective glycan shield and the high flexibility of its hinges give the stalk overall low epitope scores. Our computational epitope-mapping procedure is general and should thus prove useful for other viral envelope proteins whose structures have been characterized.
Author summary
The SARS-CoV-2 virus has caused a global health crisis. The spike protein exposed at its surface is key for infection and the primary antibody target. However, spike is covered by highly mobile glycan molecules that could impair antibody binding. To identify accessible epitopes, we performed molecular dynamics simulations of an atomistic model of glycosylated spike embedded in a membrane. By combining extensive simulations with bioinformatics analyses, we recovered known antibody binding sites and identified several epitope candidates as targets for further vaccine development.
Sparse coding is a popular approach to model natural images but has faced two main challenges: modelling low-level image components (such as edge-like structures and their occlusions) and modelling varying pixel intensities. Traditionally, images are modelled as a sparse linear superposition of dictionary elements, where the probabilistic view of this problem is that the coefficients follow a Laplace or Cauchy prior distribution. We propose a novel model that instead uses a spike-and-slab prior and nonlinear combination of components. With the prior, our model can easily represent exact zeros for e.g. the absence of an image component, such as an edge, and a distribution over non-zero pixel intensities. With the nonlinearity (the nonlinear max combination rule), the idea is to target occlusions; dictionary elements correspond to image components that can occlude each other. There are major consequences of the model assumptions made by both (non)linear approaches, thus the main goal of this paper is to isolate and highlight differences between them. Parameter optimization is analytically and computationally intractable in our model, thus as a main contribution we design an exact Gibbs sampler for efficient inference which we can apply to higher dimensional data using latent variable preselection. Results on natural and artificial occlusion-rich data with controlled forms of sparse structure show that our model can extract a sparse set of edge-like components that closely match the generating process, which we refer to as interpretable components. Furthermore, the sparseness of the solution closely follows the ground-truth number of components/edges in the images. The linear model did not learn such edge-like components with any level of sparsity. This suggests that our model can adaptively well-approximate and characterize the meaningful generation process.
An overt pro-inflammatory immune response is a key factor contributing to lethal pneumococcal infection in an influenza pre-infected host and represents a potential target for therapeutic intervention. However, there is a paucity of knowledge about the level of contribution of individual cytokines. Based on the predictions of our previous mathematical modeling approach, the potential benefit of IFN-γ- and/or IL-6-specific antibody-mediated cytokine neutralization was explored in C57BL/6 mice infected with the influenza A/PR/8/34 strain, which were subsequently infected with the Streptococcus pneumoniae strain TIGR4 on day 7 post influenza. While single IL-6 neutralization had no effect on respiratory bacterial clearance, single IFN-γ neutralization enhanced local bacterial clearance in the lungs. Concomitant neutralization of IFN-γ and IL-6 significantly reduced the degree of pneumonia as well as bacteremia compared to the control group, indicating a positive effect for the host during secondary bacterial infection. The results of our model-driven experimental study reveal that the predicted therapeutic value of IFN-γ and IL-6 neutralization in secondary pneumococcal infection following influenza infection is tightly dependent on the experimental protocol while at the same time paving the way toward the development of effective immune therapies.
The detailed biophysical mechanisms through which transcranial magnetic stimulation (TMS) activates cortical circuits are still not fully understood. Here we present a multi-scale computational model to describe and explain the activation of different pyramidal cell types in motor cortex due to TMS. Our model determines precise electric fields based on an individual head model derived from magnetic resonance imaging and calculates how these electric fields activate morphologically detailed models of different neuron types. We predict neural activation patterns for different coil orientations consistent with experimental findings. Beyond this, our model allows us to calculate activation thresholds for individual neurons and precise initiation sites of individual action potentials on the neurons’ complex morphologies. Specifically, our model predicts that cortical layer 3 pyramidal neurons are generally easier to stimulate than layer 5 pyramidal neurons, thereby explaining the lower stimulation thresholds observed for I-waves compared to D-waves. It also shows differences in the regions of activated cortical layer 5 and layer 3 pyramidal cells depending on coil orientation. Finally, it predicts that under standard stimulation conditions, action potentials are mostly generated at the axon initial segment of cortical pyramidal cells, with a much less important activation site being the part of a layer 5 pyramidal cell axon where it crosses the boundary between grey matter and white matter. In conclusion, our computational model offers a detailed account of the mechanisms through which TMS activates different cortical pyramidal cell types, paving the way for more targeted application of TMS based on individual brain morphology in clinical and basic research settings.
The detailed biophysical mechanisms through which transcranial magnetic stimulation (TMS) activates cortical circuits are still not fully understood. Here we present a multi-scale computational model to describe and explain the activation of different pyramidal cell types in motor cortex due to TMS. Our model determines precise electric fields based on an individual head model derived from magnetic resonance imaging and calculates how these electric fields activate morphologically detailed models of different neuron types. We predict neural activation patterns for different coil orientations consistent with experimental findings. Beyond this, our model allows us to calculate activation thresholds for individual neurons and precise initiation sites of individual action potentials on the neurons’ complex morphologies. Specifically, our model predicts that cortical layer 3 pyramidal neurons are generally easier to stimulate than layer 5 pyramidal neurons, thereby explaining the lower stimulation thresholds observed for I-waves compared to D-waves. It also shows differences in the regions of activated cortical layer 5 and layer 3 pyramidal cells depending on coil orientation. Finally, it predicts that under standard stimulation conditions, action potentials are mostly generated at the axon initial segment of cortical pyramidal cells, with a much less important activation site being the part of a layer 5 pyramidal cell axon where it crosses the boundary between grey matter and white matter. In conclusion, our computational model offers a detailed account of the mechanisms through which TMS activates different cortical pyramidal cell types, paving the way for more targeted application of TMS based on individual brain morphology in clinical and basic research settings.
The detailed biophysical mechanisms through which transcranial magnetic stimulation (TMS) activates cortical circuits are still not fully understood. Here we present a multi-scale computational model to describe and explain the activation of different cell types in motor cortex due to transcranial magnetic stimulation. Our model determines precise electric fields based on an individual head model derived from magnetic resonance imaging and calculates how these electric fields activate morphologically detailed models of different neuron types. We predict detailed neural activation patterns for different coil orientations consistent with experimental findings. Beyond this, our model allows us to predict activation thresholds for individual neurons and precise initiation sites of individual action potentials on the neurons’ complex morphologies. Specifically, our model predicts that cortical layer 3 pyramidal neurons are generally easier to stimulate than layer 5 pyramidal neurons, thereby explaining the lower stimulation thresholds observed for I-waves compared to D-waves. It also predicts differences in the regions of activated cortical layer 5 and layer 3 pyramidal cells depending on coil orientation. Finally, it predicts that under standard stimulation conditions, action potentials are mostly generated at the axon initial segment of corctial pyramidal cells, with a much less important activation site being the part of a layer 5 pyramidal cell axon where it crosses the boundary between grey matter and white matter. In conclusion, our computational model offers a detailed account of the mechanisms through which TMS activates different cortical cell types, paving the way for more targeted application of TMS based on individual brain morphology in clinical and basic research settings.
Treatments for amblyopia focus on vision therapy and patching of one eye. Predicting the success of these methods remains difficult, however. Recent research has used binocular rivalry to monitor visual cortical plasticity during occlusion therapy, leading to a successful prediction of the recovery rate of the amblyopic eye. The underlying mechanisms and their relation to neural homeostatic plasticity are not known. Here we propose a spiking neural network to explain the effect of short-term monocular deprivation on binocular rivalry. The model reproduces perceptual switches as observed experimentally. When one eye is occluded, inhibitory plasticity changes the balance between the eyes and leads to longer dominance periods for the eye that has been deprived. The model suggests that homeostatic inhibitory plasticity is a critical component of the observed effects and might play an important role in the recovery from amblyopia.
Top-down influences on ambiguous perception: the role of stable and transient states of the observer
(2014)
The world as it appears to the viewer is the result of a complex process of inference performed by the brain. The validity of this apparently counter-intuitive assertion becomes evident whenever we face noisy, feeble or ambiguous visual stimulation: in these conditions, the state of the observer may play a decisive role in determining what is currently perceived. On this background, ambiguous perception and its amenability to top-down influences can be employed as an empirical paradigm to explore the principles of perception. Here we offer an overview of both classical and recent contributions on how stable and transient states of the observer can impact ambiguous perception. As to the influence of the stable states of the observer, we show that what is currently perceived can be influenced (1) by cognitive and affective aspects, such as meaning, prior knowledge, motivation, and emotional content and (2) by individual differences, such as gender, handedness, genetic inheritance, clinical conditions, and personality traits and by (3) learning and conditioning. As to the impact of transient states of the observer, we outline the effects of (4) attention and (5) voluntary control, which have attracted much empirical work along the history of ambiguous perception. In the huge literature on the topic we trace a difference between the observer's ability to control dominance (i.e., the maintenance of a specific percept in visual awareness) and reversal rate (i.e., the switching between two alternative percepts). Other transient states of the observer that have more recently drawn researchers' attention regard (6) the effects of imagery and visual working memory. (7) Furthermore, we describe the transient effects of prior history of perceptual dominance. (8) Finally, we address the currently available computational models of ambiguous perception and how they can take into account the crucial share played by the state of the observer in perceiving ambiguous displays.
The way we perceive the visual world depends crucially on the state of the observer. In the present study we show that what we are holding in working memory (WM) can bias the way we perceive ambiguous structure from motion stimuli. Holding in memory the percept of an unambiguously rotating sphere influenced the perceived direction of motion of an ambiguously rotating sphere presented shortly thereafter. In particular, we found a systematic difference between congruent dominance periods where the perceived direction of the ambiguous stimulus corresponded to the direction of the unambiguous one and incongruent dominance periods. Congruent dominance periods were more frequent when participants memorized the speed of the unambiguous sphere for delayed discrimination than when they performed an immediate judgment on a change in its speed. The analysis of dominance time-course showed that a sustained tendency to perceive the same direction of motion as the prior stimulus emerged only in the WM condition, whereas in the attention condition perceptual dominance dropped to chance levels at the end of the trial. The results are explained in terms of a direct involvement of early visual areas in the active representation of visual motion in WM.
Tailoring of spin state energetics of transition metal complexes and even the correct prediction of the resulting spin state is still a challenging task, both for the experimentalist and the theoretician. Apart from the complexity in the solid state imposed by packing effects, molecular factors of the spin state ordering are required to be identified and quantified on equal rights. In this work we experimentally record the spin states and SCO energies within an eight-member substitution-series of N4O2 ligated iron(II) complexes both in the solid state (SQUID magnetometry and single-crystal X-ray crystallography) and in solution (VT-NMR). The experimental survey is complemented
by exhaustive theoretical modelling of the molecular and electronic structure of the open-chain N4O2 family and its macrocyclic N6 congeners through density-functional theory methods. Ligand topology is identified as the leading factor defining ground-state multiplicity of the corresponding iron(II) complexes. Invariably the low-spin state is sterically trapped in the macrocycles, whereas subtle substitution effects allow for a molecular fine tuning of the spin state in the open-chain ligands. Factorization of computed relative SCO energies holds promise for directed design of future SCO systems.
Dynamics of chaotic strings
(2011)
The main topic of this thesis is the investigation of dynamical properties of coupled Tchebycheff map networks. At every node of the network the dynamics is given by the iteration of a Tchebycheff map, which shows strongest possible chaotic behaviour. By applying a coupling between the various individual dynamics along the links of the network, a rich structure of complex dynamical patterns emerges. Accordingly, coupled chaotic map networks provide prototypical models for studying the interplay between local dynamics, network structure, and the emergent global dynamics. An exciting application of coupled Tchebycheff map lattices in quantum field theory has been proposed Beck in Spatio-temporal chaos and vacuum fluctuations of quantized fields' (2002). In this so-called chaotic string model, the coupled map lattice dynamics generates the noise needed for the Parisi-Wu approach of stochastic quantization. The remarkable obversation is that the respective dynamics seems to reproduce distinguished numerical values of coupling constants that coincide with those observed in the standard model of particle physic. The results of this thesis give insights into the chaotic string model and its network generalization from a dynamical point of view. This leads to a deeper understanding of the dynamics, which is essential for a critical discussion of possible physical embeddings. Apart from this specific application to particle physics, the investigated concepts like synchronization or a most random behaviour of the dynamics are of general interest for dynamical system theory and the science of complex networks. As a first approach, discrete symmetry transformations of the model are studied. These transformations are formulated in a general way in order to be also applicable to similar dynamics on bipartite network structures. An observable of main interest in the chaotic string model is the interaction energy. In Spatio-temporal chaos and vacuum fluctuations of quantized fields' (2002) it has been observed that certain chaotic string couplings, corresponding to a vanishing interaction energy, coincide with coupling constants of the standard model of elementary particle physics. Since the interaction energy is basically a spatial correlation measure, an interpretation of the respective dynamical states in terms of a most random behaviour is tempting. In order to distinguish certain states as most random', or evoke another dynamical principle, a deeper understanding of the dynamics essential. In the present thesis the dynamics is studied numerically via Lyapunov measures, spatial correlations, and ergodic properties. It is shown that the zeros of the interaction energy are distinguished only with respect to this specific observable, but not by a more general dynamical principle. The original chaotic string model is defined on a one-dimensional lattice (ring-network) as the underlying network topology. This thesis studies a modification of the model based on the introduction of tunable disorder. The effects of inhomogeneous coupling weights as well as small-world perturbations of the ring-network structure on the interaction energy are discussed. Synchronization properties of the chaotic string model and its network generalization are studied in later chapters of this thesis. The analysis is based on the master stability formalism, which relates the stability of the synchronized state to the spectral properties of the network. Apart from complete synchronization, where the dynamics at all nodes of the network coincide, also two-cluster synchronization on bipartite networks is studied. For both types of synchronization it is shown that depending on the type of coupling the synchronized dynamics can display chaotic as well as periodic or quasi-periodic behaviour. The semi-analytical calculations reveal that the respective synchronized states are often stable for a wide range of coupling values even for the ring-network, although the respective basins of attraction may inhabit only a small fraction of the phase space. To provide analytical results in closed form, for complete synchronization the stability of all fixed points and period-2 orbits of all chaotic string networks are determined analytically. The master stability formalism allows to treat the ring-network of the chaotic string model as a special case, but the results are valid for coupled Tchebycheff maps on arbitrary networks. For two-cluster synchronization on bipartite networks, selected fixed points and period-2 orbits are analyzed.
Perception is an active inferential process in which prior knowledge is combined with sensory input, the result of which determines the contents of awareness. Accordingly, previous experience is known to help the brain “decide” what to perceive. However, a critical aspect that has not been addressed is that previous experience can exert 2 opposing effects on perception: An attractive effect, sensitizing the brain to perceive the same again (hysteresis), or a repulsive effect, making it more likely to perceive something else (adaptation). We used functional magnetic resonance imaging and modeling to elucidate how the brain entertains these 2 opposing processes, and what determines the direction of such experience-dependent perceptual effects. We found that although affecting our perception concurrently, hysteresis and adaptation map into distinct cortical networks: a widespread network of higher-order visual and fronto-parietal areas was involved in perceptual stabilization, while adaptation was confined to early visual areas. This areal and hierarchical segregation may explain how the brain maintains the balance between exploiting redundancies and staying sensitive to new information. We provide a Bayesian model that accounts for the coexistence of hysteresis and adaptation by separating their causes into 2 distinct terms: Hysteresis alters the prior, whereas adaptation changes the sensory evidence (the likelihood function).
We propose to measure azimuthal correlations of heavy-flavor hadrons to address the status of thermalization at the partonic stage of light quarks and gluons in high-energy nuclear collisions. In particular, we show that hadronic interactions at the late stage cannot significantly disturb the initial back-to-back azimuthal correlations of DDbar pairs. Thus, a decrease or the complete absence of these initial correlations does indicate frequent interactions of heavy-flavor quarks and also light partons in the partonic stage, which are essential for the early thermalization of light partons.
Abstract We consider the phase structure of hadronic and hadron-quark models at finite temperature and density. The basis for the hadronic part is an extension of a flavor-SU(3) ? ? ? model. We study the effect on the phase diagram by adding additional hadronic resonances to the model. With the resulting equation of state we investigate heavy-ion c... collisions using hydrodynamical simulations. In a combined approach we include quarks and the Polyakov loop field in the calculation and study chiral symmetry restoration and the deconfinement transition.
The core of neutron stars consists of extremely dense matter at relatively low temperatures. In such an environment the appearance of exotic strongly interacting particles beyond nucleons appears quite natural. In this context we consider hybrid stars that, in addition to nucleons and hyperons, also contain quarks as further degrees of freedom. We investigate the impact of quarks on the properties of these compact stars. In addition, we discuss new constraints on such objects arising from the recently measured gravitational wave signal of two merging neutron stars.
The electrical and computational properties of neurons in our brains are determined by a rich repertoire of membrane-spanning ion channels and elaborate dendritic trees. However, the precise reason for this inherent complexity remains unknown. Here, we generated large stochastic populations of biophysically realistic hippocampal granule cell models comparing those with all 15 ion channels to their reduced but functional counterparts containing only 5 ion channels. Strikingly, valid parameter combinations in the full models were more frequent and more stable in the face of perturbations to channel expression levels. Scaling up the numbers of ion channels artificially in the reduced models recovered these advantages confirming the key contribution of the actual number of ion channel types. We conclude that the diversity of ion channels gives a neuron greater flexibility and robustness to achieve target excitability.
Dendritic morphology has been shown to have a dramatic impact on neuronal function. However, population features such as the inherent variability in dendritic morphology between cells belonging to the same neuronal type are often overlooked when studying computation in neural networks. While detailed models for morphology and electrophysiology exist for many types of single neurons, the role of detailed single cell morphology in the population has not been studied quantitatively or computationally. Here we use the structural context of the neural tissue in which dendritic trees exist to drive their generation in silico. We synthesize the entire population of dentate gyrus granule cells, the most numerous cell type in the hippocampus, by growing their dendritic trees within their characteristic dendritic fields bounded by the realistic structural context of (1) the granule cell layer that contains all somata and (2) the molecular layer that contains the dendritic forest. This process enables branching statistics to be linked to larger scale neuroanatomical features. We find large differences in dendritic total length and individual path length measures as a function of location in the dentate gyrus and of somatic depth in the granule cell layer. We also predict the number of unique granule cell dendrites invading a given volume in the molecular layer. This work enables the complete population-level study of morphological properties and provides a framework to develop complex and realistic neural network models.
High shares of intermittent renewable power generation in a European electricity system will require flexible backup power generation on the dominant diurnal, synoptic, and seasonal weather timescales. The same three timescales are already covered by today’s dispatchable electricity generation facilities, which are able to follow the typical load variations on the intra-day, intra-week, and seasonal timescales. This work aims to quantify the changing demand for those three backup flexibility classes in emerging large-scale electricity systems, as they transform from low to high shares of variable renewable power generation. A weather-driven modelling is used, which aggregates eight years of wind and solar power generation data as well as load data over Germany and Europe, and splits the backup system required to cover the residual load into three flexibility classes distinguished by their respective maximum rates of change of power output. This modelling shows that the slowly flexible backup system is dominant at low renewable shares, but its optimized capacity decreases and drops close to zero once the average renewable power generation exceeds 50% of the mean load. The medium flexible backup capacities increase for modest renewable shares, peak at around a 40% renewable share, and then continuously decrease to almost zero once the average renewable power generation becomes larger than 100% of the mean load. The dispatch capacity of the highly flexible backup system becomes dominant for renewable shares beyond 50%, and reach their maximum around a 70% renewable share. For renewable shares above 70% the highly flexible backup capacity in Germany remains at its maximum, whereas it decreases again for Europe. This indicates that for highly renewable large-scale electricity systems the total required backup capacity can only be reduced if countries share their excess generation and backup power.