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Recurrent cortical network dynamics plays a crucial role for sequential information processing in the brain. While the theoretical framework of reservoir computing provides a conceptual basis for the understanding of recurrent neural computation, it often requires manual adjustments of global network parameters, in particular of the spectral radius of the recurrent synaptic weight matrix. Being a mathematical and relatively complex quantity, the spectral radius is not readily accessible to biological neural networks, which generally adhere to the principle that information about the network state should either be encoded in local intrinsic dynamical quantities (e.g. membrane potentials), or transmitted via synaptic connectivity. We present two synaptic scaling rules for echo state networks that solely rely on locally accessible variables. Both rules work online, in the presence of a continuous stream of input signals. The first rule, termed flow control, is based on a local comparison between the mean squared recurrent membrane potential and the mean squared activity of the neuron itself. It is derived from a global scaling condition on the dynamic flow of neural activities and requires the separability of external and recurrent input currents. We gained further insight into the adaptation dynamics of flow control by using a mean field approximation on the variances of neural activities that allowed us to describe the interplay between network activity and adaptation as a two-dimensional dynamical system. The second rule that we considered, variance control, directly regulates the variance of neural activities by locally scaling the recurrent synaptic weights. The target set point of this homeostatic mechanism is dynamically determined as a function of the variance of the locally measured external input. This functional relation was derived from the same mean-field approach that was used to describe the approximate dynamics of flow control.
The effectiveness of the presented mechanisms was tested numerically using different external input protocols. The network performance after adaptation was evaluated by training the network to perform a time delayed XOR operation on binary sequences. As our main result, we found that flow control can reliably regulate the spectral radius under different input statistics, but precise tuning is negatively affected by interneural correlations. Furthermore, flow control showed a consistent task performance over a wide range of input strengths/variances. Variance control, on the other side, did not yield the desired spectral radii with the same precision. Moreover, task performance was less consistent across different input strengths.
Given the better performance and simpler mathematical form of flow control, we concluded that a local control of the spectral radius via an implicit adaptation scheme is a realistic alternative to approaches using classical “set point” homeostatic feedback controls of neural firing.
Author summary How can a neural network control its recurrent synaptic strengths such that network dynamics are optimal for sequential information processing? An important quantity in this respect, the spectral radius of the recurrent synaptic weight matrix, is a non-local quantity. Therefore, a direct calculation of the spectral radius is not feasible for biological networks. However, we show that there exist a local and biologically plausible adaptation mechanism, flow control, which allows to control the recurrent weight spectral radius while the network is operating under the influence of external inputs. Flow control is based on a theorem of random matrix theory, which is applicable if inter-synaptic correlations are weak. We apply the new adaption rule to echo-state networks having the task to perform a time-delayed XOR operation on random binary input sequences. We find that flow-controlled networks can adapt to a wide range of input strengths while retaining essentially constant task performance.
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.
The spike (S) protein of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is required for cell entry and is the major focus for vaccine development. We combine cryo electron tomography, subtomogram averaging and molecular dynamics simulations to structurally analyze S in situ. Compared to recombinant S, the viral S is more heavily glycosylated and occurs predominantly in a closed pre-fusion conformation. We show that the stalk domain of S contains three hinges that give the globular domain unexpected orientational freedom. We propose that the hinges allow S to scan the host cell surface, shielded from antibodies by an extensive glycan coat. The structure of native S contributes to our understanding of SARS-CoV-2 infection and the development of safe vaccines. The large scale tomography data set of SARS-CoV-2 used for this study is therefore sufficient to resolve structural features to below 5 Ångstrom, and is publicly available at EMPIAR-10453.