Neuronal spike timing adaptation described with a fractional leaky integrate-and-fire model.

The voltage trace of neuronal activities can follow multiple timescale dynamics that arise from correlated membrane conductances. Such processes can result in power-law behavior in which the membrane voltage cannot be characterized with a single time constant. The emergent effect of these membrane correlations is a non-Markovian process that can be modeled with a fractional derivative. A fractional derivative is a non-local process in which the value of the variable is determined by integrating a temporal weighted voltage trace, also called the memory trace. Here we developed and analyzed a fractional leaky integrate-and-fire model in which the exponent of the fractional derivative can vary from 0 to 1, with 1 representing the normal derivative. As the exponent of the fractional derivative decreases, the weights of the voltage trace increase. Thus, the value of the voltage is increasingly correlated with the trajectory of the voltage in the past. By varying only the fractional exponent, our model can reproduce upward and downward spike adaptations found experimentally in neocortical pyramidal cells and tectal neurons in vitro. The model also produces spikes with longer first-spike latency and high inter-spike variability with power-law distribution. We further analyze spike adaptation and the responses to noisy and oscillatory input. The fractional model generates reliable spike patterns in response to noisy input. Overall, the spiking activity of the fractional leaky integrate-and-fire model deviates from the spiking activity of the Markovian model and reflects the temporal accumulated intrinsic membrane dynamics that affect the response of the neuron to external stimulation.

Design of Antigen-Specific Antibody CDRH3 Sequences Using AI and Germline-Based Templates.

Antibody-antigen specificity is engendered and refined through a number of complex B cell processes, including germline gene recombination and somatic hypermutation. Here, we present an AI-based technology for de novo generation of antigen-specific antibody CDRH3 sequences using germline-based templates, and validate this technology through the generation of antibodies against SARS-CoV-2. AI-based processes that mimic the outcome, but bypass the complexity of natural antibody generation, can be efficient and effective alternatives to traditional experimental approaches for antibody discovery.

Antibody sequence determinants of viral antigen specificity.

Throughout life, humans experience repeated exposure to viral antigens through infection and vaccination, resulting in the generation of diverse, antigen-specific antibody repertoires. A paramount feature of antibodies that enables their critical contributions in counteracting recurrent and novel pathogens, and consequently fostering their utility as valuable targets for therapeutic and vaccine development, is the exquisite specificity displayed against their target antigens. Yet, there is still limited understanding of the determinants of antibody-antigen specificity, particularly as a function of antibody sequence. In recent years, experimental characterization of antibody repertoires has led to novel insights into fundamental properties of antibody sequences but has been largely decoupled from at-scale antigen specificity analysis. Here, using the LIBRA-seq technology, we generated a large data set mapping antibody sequence to antigen specificity for thousands of B cells, by screening the repertoires of a set of healthy individuals against 20 viral antigens representing diverse pathogens of biomedical significance. Analysis uncovered virus-specific patterns in variable gene usage, gene pairing, somatic hypermutation, as well as the presence of convergent antiviral signatures across multiple individuals, including the presence of public antibody clonotypes. Notably, our results showed that, for B-cell receptors originating from different individuals but leveraging an identical combination of heavy and light chain variable genes, there is a specific CDRH3 identity threshold above which B cells appear to exclusively share the same antigen specificity. This finding provides a quantifiable measure of the relationship between antibody sequence and antigen specificity and further defines experimentally grounded criteria for defining public antibody clonality.IMPORTANCEThe B-cell compartment of the humoral immune system plays a critical role in the generation of antibodies upon new and repeated pathogen exposure. This study provides an unprecedented level of detail on the molecular characteristics of antibody repertoires that are specific to each of the different target pathogens studied here and provides empirical evidence in support of a 70% CDRH3 amino acid identity threshold in pairs of B cells encoded by identical IGHV:IGL(K)V genes, as a means of defining public clonality and therefore predicting B-cell antigen specificity in different individuals. This is of exceptional importance when leveraging public clonality as a method to annotate B-cell receptor data otherwise lacking antigen specificity information. Understanding the fundamental rules of antibody-antigen interactions can lead to transformative new approaches for the development of antibody therapeutics and vaccines against current and emerging viruses.

Computational modeling of diffusion in the cerebellum.

Diffusion is a major transport mechanism in living organisms. In the cerebellum, diffusion is responsible for the propagation of molecular signaling involved in synaptic plasticity and metabolism, both intracellularly and extracellularly. In this chapter, we present an overview of the cerebellar structure and function. We then discuss the types of diffusion processes present in the cerebellum and their biological importance. We particularly emphasize the differences between extracellular and intracellular diffusion and the presence of tortuosity and anomalous diffusion in different parts of the cerebellar cortex. We provide a mathematical introduction to diffusion and a conceptual overview of various computational modeling techniques. We discuss their scope and their limit of application. Although our focus is the cerebellum, we have aimed at presenting the biological and mathematical foundations as general as possible to be applicable to any other area in biology in which diffusion is of importance.

FRACTIONAL INTEGRATION TOOLBOX.

The problems formulated in the fractional calculus framework often require numerical fractional integration/differentiation of large data sets. Several existing fractional control toolboxes are capable of performing fractional calculus operations, however, none of them can efficiently perform numerical integration on multiple large data sequences. We developed a Fractional Integration Toolbox (FIT), which efficiently performs fractional numerical integration/differentiation of the Riemann-Liouville type on large data sequences. The toolbox allows parallelization and is designed to be deployed on both CPU and GPU platforms.