A mathematical and computational model of the calcium dynamics in Caenorhabditis elegans ASH sensory neuron

A multiscale sensorimotor model of experience-dependent behavior in a minimal organism

To survive in ever-changing environments, living organisms need to continuously combine the ongoing external inputs they receive, representing present conditions, with their dynamical internal state, which includes influences of past experiences. It is still unclear in general, however 1) how this happens at the molecular and cellular levels and 2) how the corresponding molecular and cellular processes are integrated with the behavioral responses of the organism. Here, we address these issues by modeling mathematically a particular behavioral paradigm in a minimal model organism, namely chemotaxis in the nematode C. elegans. Specifically, we use a long-standing collection of elegant experiments on salt chemotaxis in this animal, in which the migration direction varies depending on its previous experience. Our model integrates the molecular, cellular, and organismal levels to reproduce the experimentally observed experience-dependent behavior. The model proposes specific molecular mechanisms for the encoding of current conditions and past experiences in key neurons associated with this response, predicting the behavior of various mutants associated with those molecular circuits.

A computational model to uncover the biophysical underpinnings of neural firing heterogeneity in dissociated hippocampal cultures

Calcium (Ca2+ ) imaging reveals a variety of correlated firing in cultures of dissociated hippocampal neurons, pinpointing the non-synaptic paracrine release of glutamate as a possible mediator for such firing patterns, although the biophysical underpinnings remain unknown. An intriguing possibility is that extracellular glutamate could bind metabotropic receptors linked with inositol trisphosphate (IP3 ) mediated release of Ca2+ from the endoplasmic reticulum of individual neurons, thereby modulating neural activity in combination with sarco/endoplasmic reticulum Ca2+ transport ATPase (SERCA) and voltage-gated Ca2+ channels (VGCC). However, the possibility that such release may occur in different neuronal compartments and can be inherently stochastic poses challenges in the characterization of such interplay between various Ca2+ channels. Here we deploy biophysical modeling in association with Monte Carlo parameter sampling to characterize such interplay and successfully predict experimentally observed Ca2+ patterns. The results show that the neurotransmitter level at the plasma membrane is the extrinsic source of heterogeneity in somatic Ca2+ transients. Our analysis, in particular, identifies the origin of such heterogeneity to an intrinsic differentiation of hippocampal neurons in terms of multiple cellular properties pertaining to intracellular Ca2+ signaling, such as VGCC, IP3 receptor, and SERCA expression. In the future, the biophysical model and parameter estimation approach used in this study can be upgraded to predict the response of a system of interconnected neurons.

Quantitative description of neuronal calcium dynamics in C. elegans' thermoreception

The dynamical mechanisms underlying thermoreception in the nematode C. elegans are studied with a mathematical model for the amphid finger-like ciliated (AFD) neurons. The equations, equipped with Arrhenius temperature factors, account for the worm's thermotaxis when seeking environments at its cultivation temperature, and for the AFD's calcium dynamics when exposed to both linearly ramping and oscillatory temperature stimuli. Calculations of the peak time for calcium responses during simulations of pulse-like temperature inputs are consistent with known behavioral time scales of C. elegans.

Modeling of olfactory transduction in AWCON neuron via coupled electrical-calcium dynamics

Amphid wing "C" (AWC) neurons are among the most important and studied neurons of the nematode Caenorhabditis elegans. In this work, we unify the existing electrical and intracellular calcium dynamics descriptions to obtain a biophysically accurate model of olfactory transduction in AWCON neurons. We study the membrane voltage and the intracellular calcium dynamics at different exposure times and odorant concentrations to grasp a complete picture of AWCON functioning. Moreover, we investigate the complex cascade of biochemical processes that allow AWC activation upon odor removal. We analyze the behavior of the different components of the models and, by suppressing them selectively, we extrapolate their contribution to the overall neuron response and study the resilience of the dynamical system. Our results are all in agreement with the available experimental data. Therefore, we provide an accurate mathematical and biophysical model for studying olfactory signal processing in C. elegans.

Primer on Mathematical Modeling in C. elegans

Recently, applications of mathematical and computational models to biological processes have helped investigators to systematically interpret data, test hypotheses built on experimental data, generate new hypotheses, and guide the design of new experiments, protocols, and synthetic biological systems. Availability of diverse quantitative data is a prerequisite for successful mathematical modeling. The ability to acquire high-quality quantitative data for a broad range of biological processes and perform precise perturbation makes C. elegans an ideal model system for such studies. In this primer, we examine the general procedure of modeling biological systems and demonstrate this process using the heat-shock response in C. elegans as a case study. Our goal is to facilitate the initial discussion between worm biologists and their potential collaborators from quantitative disciplines.

Modelling learning in C. elegans chemosensory and locomotive circuitry for T-maze navigation

Recently, a new type of Caenorhabditis elegans associative learning was reported, where nematodes learn to reach a target arm in an empty T‐maze, after they have successfully located reward (food) in the same side arm of a similar, baited, training maze. Here, we present a simplified mathematical model of C. elegans chemosensory and locomotive circuitry that replicates C. elegans navigation in a T‐maze and predicts the underlying mechanisms generating maze learning. Based on known neural circuitry, the model circuit responds to food‐released chemical cues by modulating motor neuron activity that drives simulated locomotion. We show that, through modulation of interneuron activity, such a circuit can mediate maze learning by acquiring a turning bias, even after a single training session. Simulated nematode maze navigation during training conditions in food‐baited mazes and during testing conditions in empty mazes is validated by comparing simulated behaviour with new experimental video data, extracted through the implementation of a custom‐made maze tracking algorithm. Our work provides a mathematical framework for investigating the neural mechanisms underlying this novel learning behaviour in C. elegans. Model results predict neuronal components involved in maze and spatial learning and identify target neurons and potential neural mechanisms for future experimental investigations into this learning behaviour.

Understanding doxorubicin associated calcium remodeling during triple-negative breast cancer treatment: an in silico study

Aim:

Triple-negative breast cancer (TNBC) is the most malignant subtype of breast cancer with high heterogeneity, rapid progression, and paucity of treatment options. The most effective chemotherapeutic drug used to treat TNBC is doxorubicin (Doxo) which is an anthracycline antibiotic. However, Doxo treatment alters cytosolic calcium dynamics leading to drug-resistance condition. The aim of this study is to capture the alterations in the activity of various calcium channels and pumps during Doxo treatment and their consequences on cytosolic calcium dynamics that ultimately result in drug resistance.

Methods:

In the present study, a mathematical model is proposed to capture the complex dynamical landscape of intracellular calcium during Doxo treatment. This study provides an insight into Doxo remodeling of calcium dynamics and associated drug-resistance effect. The model was first analyzed analytically and then explored through numerical simulation using techniques like global sensitivity analysis, parameter recalibration, etc.

Results:

The model is used to predict the potential combination therapy for Doxo that can overcome Doxo associated drug resistance. The results show targeting the dysregulated Ca²⁺ channels and pumps might provide efficient chemotherapy in TNBC. It was also observed that the indispensability of calcium influx rate is paramount in the Doxo drug resistance. Finally, three drugs were identified from existing literature that could be used as a combination therapy along with Doxo.

Conclusions:

The investigation highlights the importance of integrating the calcium signaling of various calcium regulating compounds for their effective anti-tumor effects deliverance along with chemotherapeutic agents. The results from this study might provide a new direction to the experimental biologists to explore different combination therapies with Doxo to enhance its anti-tumor effect.

Chemosensory signal transduction in Caenorhabditis elegans

Chemosensory neurons translate perception of external chemical cues, including odorants, tastants, and pheromones, into information that drives attraction or avoidance motor programs. In the laboratory, robust behavioral assays, coupled with powerful genetic, molecular and optical tools, have made Caenorhabditis elegans an ideal experimental system in which to dissect the contributions of individual genes and neurons to ethologically relevant chemosensory behaviors. Here, we review current knowledge of the neurons, signal transduction molecules and regulatory mechanisms that underlie the response of C. elegans to chemicals, including pheromones. The majority of identified molecules and pathways share remarkable homology with sensory mechanisms in other organisms. With the development of new tools and technologies, we anticipate that continued study of chemosensory signal transduction and processing in C. elegans will yield additional new insights into the mechanisms by which this animal is able to detect and discriminate among thousands of chemical cues with a limited sensory neuron repertoire.

Biophysical modeling of C. elegans neurons: Single ion currents and whole-cell dynamics of AWCon and RMD

C. elegans neuronal system constitutes the ideal framework for studying simple, yet realistic, neuronal activity, since the whole nervous system is fully characterized with respect to the exact number of neurons and the neuronal connections. Most recent efforts are devoted to investigate and clarify the signal processing and functional connectivity, which are at the basis of sensing mechanisms, signal transmission, and motor control. In this framework, a refined modelof whole neuron dynamics constitutes a key ingredient to describe the electrophysiological processes, both at thecellular and at the network scale. In this work, we present Hodgkin-Huxley-based models of ion channels dynamics black, built on data available both from C. elegans and from other organisms, expressing homologous channels. We combine these channel models to simulate the electrical activity oftwo among the most studied neurons in C. elegans, which display prototypical dynamics of neuronal activation, the chemosensory AWCON and the motor neuron RMD. Our model properly describes the regenerative responses of the two cells. We analyze in detail the role of ion currents, both in wild type and in in silico knockout neurons. Moreover, we specifically investigate the behavior of RMD, identifying a heterogeneous dynamical response which includes bistable regimes and sustained oscillations. We are able to assess the critical role of T-type calcium currents, carried by CCA-1 channels, and leakage currents in the regulation of RMD response. Overall, our results provide new insights in the activity of key C. elegans neurons. The developed mathematical framework constitute a basis for single-cell and neuronal networks analyses, opening new scenarios in the in silico modeling of C. elegans neuronal system.

OpenWorm: overview and recent advances in integrative biological simulation of Caenorhabditis elegans

The adoption of powerful software tools and computational methods from the software industry by the scientific research community has resulted in a renewed interest in integrative, large-scale biological simulations. These typically involve the development of computational platforms to combine diverse, process-specific models into a coherent whole. The OpenWorm Foundation is an independent research organization working towards an integrative simulation of the nematode Caenorhabditis elegans, with the aim of providing a powerful new tool to understand how the organism's behaviour arises from its fundamental biology. In this perspective, we give an overview of the history and philosophy of OpenWorm, descriptions of the constituent sub-projects and corresponding open-science management practices, and discuss current achievements of the project and future directions.This article is part of a discussion meeting issue 'Connectome to behaviour: modelling C. elegans at cellular resolution'.