Modelling and sensitivity analysis of the reactions involving receptor, G-protein and effector in vertebrate olfactory receptor neurons

Computational cardiac physiology for new modelers: Origins, foundations, and future

Mathematical models of the cardiovascular system have come a long way since they were first introduced in the early 19th century. Driven by a rapid development of experimental techniques, numerical methods, and computer hardware, detailed models that describe physical scales from the molecular level up to organs and organ systems have been derived and used for physiological research. Mathematical and computational models can be seen as condensed and quantitative formulations of extensive physiological knowledge and are used for formulating and testing hypotheses, interpreting and directing experimental research, and have contributed substantially to our understanding of cardiovascular physiology. However, in spite of the strengths of mathematics to precisely describe complex relationships and the obvious need for the mathematical and computational models to be informed by experimental data, there still exist considerable barriers between experimental and computational physiological research. In this review, we present a historical overview of the development of mathematical and computational models in cardiovascular physiology, including the current state of the art. We further argue why a tighter integration is needed between experimental and computational scientists in physiology, and point out important obstacles and challenges that must be overcome in order to fully realize the synergy of experimental and computational physiological research.

Combining hypothesis- and data-driven neuroscience modeling in FAIR workflows

Modeling in neuroscience occurs at the intersection of different points of view and approaches. Typically, hypothesis-driven modeling brings a question into focus so that a model is constructed to investigate a specific hypothesis about how the system works or why certain phenomena are observed. Data-driven modeling, on the other hand, follows a more unbiased approach, with model construction informed by the computationally intensive use of data. At the same time, researchers employ models at different biological scales and at different levels of abstraction. Combining these models while validating them against experimental data increases understanding of the multiscale brain. However, a lack of interoperability, transparency, and reusability of both models and the workflows used to construct them creates barriers for the integration of models representing different biological scales and built using different modeling philosophies. We argue that the same imperatives that drive resources and policy for data - such as the FAIR (Findable, Accessible, Interoperable, Reusable) principles - also support the integration of different modeling approaches. The FAIR principles require that data be shared in formats that are Findable, Accessible, Interoperable, and Reusable. Applying these principles to models and modeling workflows, as well as the data used to constrain and validate them, would allow researchers to find, reuse, question, validate, and extend published models, regardless of whether they are implemented phenomenologically or mechanistically, as a few equations or as a multiscale, hierarchical system. To illustrate these ideas, we use a classical synaptic plasticity model, the Bienenstock-Cooper-Munro rule, as an example due to its long history, different levels of abstraction, and implementation at many scales.

A Modular Workflow for Model Building, Analysis, and Parameter Estimation in Systems Biology and Neuroscience

Neuroscience incorporates knowledge from a range of scales, from single molecules to brain wide neural networks. Modeling is a valuable tool in understanding processes at a single scale or the interactions between two adjacent scales and researchers use a variety of different software tools in the model building and analysis process. Here we focus on the scale of biochemical pathways, which is one of the main objects of study in systems biology. While systems biology is among the more standardized fields, conversion between different model formats and interoperability between various tools is still somewhat problematic. To offer our take on tackling these shortcomings and by keeping in mind the FAIR (findability, accessibility, interoperability, reusability) data principles, we have developed a workflow for building and analyzing biochemical pathway models, using pre-existing tools that could be utilized for the storage and refinement of models in all phases of development. We have chosen the SBtab format which allows the storage of biochemical models and associated data in a single file and provides a human readable set of syntax rules. Next, we implemented custom-made MATLAB® scripts to perform parameter estimation and global sensitivity analysis used in model refinement. Additionally, we have developed a web-based application for biochemical models that allows simulations with either a network free solver or stochastic solvers and incorporating geometry. Finally, we illustrate convertibility and use of a biochemical model in a biophysically detailed single neuron model by running multiscale simulations in NEURON. Using this workflow, we can simulate the same model in three different simulators, with a smooth conversion between the different model formats, enhancing the characterization of different aspects of the model.

A physicochemical model of odor sampling

We present a general physicochemical sampling model for olfaction, based on established pharmacological laws, in which arbitrary combinations of odorant ligands and receptors can be generated and their individual and collective effects on odor representations and olfactory performance measured. Individual odor ligands exhibit receptor-specific affinities and efficacies; that is, they may bind strongly or weakly to a given receptor, and can act as strong agonists, weak agonists, partial agonists, or antagonists. Ligands interacting with common receptors compete with one another for dwell time; these competitive interactions appropriately simulate the degeneracy that fundamentally defines the capacities and limitations of odorant sampling. The outcome of these competing ligand-receptor interactions yields a pattern of receptor activation levels, thereafter mapped to glomerular presynaptic activation levels based on the convergence of sensory neuron axons. The metric of greatest interest is the mean discrimination sensitivity, a measure of how effectively the olfactory system at this level is able to recognize a small change in the physicochemical quality of a stimulus. This model presents several significant outcomes, both expected and surprising. First, adding additional receptors reliably improves the system’s discrimination sensitivity. Second, in contrast, adding additional ligands to an odorscene initially can improve discrimination sensitivity, but eventually will reduce it as the number of ligands increases. Third, the presence of antagonistic ligand-receptor interactions produced clear benefits for sensory system performance, generating higher absolute discrimination sensitivities and increasing the numbers of competing ligands that could be present before discrimination sensitivity began to be impaired. Finally, the model correctly reflects and explains the modest reduction in odor discrimination sensitivity exhibited by transgenic mice in which the specificity of glomerular targeting by primary olfactory neurons is partially disrupted.

We understand most sensory systems by comparing the responses of the system against objective external physical measurements. For example, we know that our ability to distinguish small changes in color is greater for some colors than for others, and that we can distinguish sounds more acutely when they are within the range of pitches used for speech. Similar principles presumably apply to the sense of smell, but odorous chemicals are harder to physically quantify than light or sound because they cannot be organized in terms of a straightforward physical variable like wavelength or frequency. That said, the physical properties of interactions between chemicals and cellular receptors (such as those in the olfactory system) are well understood. What we lack is a systematic framework within which these pharmacological principles can be organized to study odor sampling in the way that we have long studied visual and auditory sampling. We here propose and describe such a framework for odor sampling, and show that it successfully replicates some established but unexplained experimental results.

A computational model for gonadotropin releasing cells in the teleost fish medaka

Pituitary endocrine cells fire action potentials (APs) to regulate their cytosolic Ca²⁺ concentration and hormone secretion rate. Depending on animal species, cell type, and biological conditions, pituitary APs are generated either by TTX-sensitive Na⁺ currents (I_Na), high-voltage activated Ca²⁺ currents (I_Ca), or by a combination of the two. Previous computational models of pituitary cells have mainly been based on data from rats, where I_Na is largely inactivated at the resting potential, and spontaneous APs are predominantly mediated by I_Ca. Unlike in rats, spontaneous I_Na-mediated APs are consistently seen in pituitary cells of several other animal species, including several species of fish. In the current work we develop a computational model of gonadotropin releasing cells in the teleost fish medaka (Oryzias latipes). The model stands out from previous modeling efforts by being (1) the first model of a pituitary cell in teleosts, (2) the first pituitary cell model that fires sponateous APs that are predominantly mediated by I_Na, and (3) the first pituitary cell model where the kinetics of the depolarizing currents, I_Na and I_Ca, are directly fitted to voltage-clamp data. We explore the firing properties of the model, and compare it to the properties of previous models that fire I_Ca-based APs. We put a particular focus on how the big conductance K⁺ current (I_BK) modulates the AP shape. Interestingly, we find that I_BK can prolong AP duration in models that fire I_Ca-based APs, while it consistently shortens the duration of the predominantly I_Na-mediated APs in the medaka gonadotroph model. Although the model is constrained to experimental data from gonadotroph cells in medaka, it may likely provide insights also into other pituitary cell types that fire I_Na-mediated APs.

Excitable cells elicit electrical pulses called action potentials (APs), which are generated and shaped by a combination of ion channels in the cell membrane. Since one type of ion channels is permeable to Ca²⁺ ions, there is typically an influx of Ca²⁺ during an AP. Pituitary cells therefore use AP firing to regulate their cytosolic Ca²⁺ concentration, which in turn controls their hormone secretion rate. The amount of Ca²⁺ that enters during an AP depends strongly on how long it lasts, and it is therefore important to understand the mechanisms that control this. Pituitary APs are generally mediated by a combination of Ca²⁺ channels and Na⁺ channels, and the relative contributions of from the two vary between cell types, animal species and biological conditions. Previous computer models have predominantly been adapted to data from pituitary cells which tend to fire Ca²⁺-based APs. Here we develop a new model, adapted to data from pituitary cells in the fish medaka, which APs that are predominantly Na⁺-based, and compare its dynamical properties to the previous models that fire Ca²⁺-based APs.

Uncertainpy: A Python Toolbox for Uncertainty Quantification and Sensitivity Analysis in Computational Neuroscience

Computational models in neuroscience typically contain many parameters that are poorly constrained by experimental data. Uncertainty quantification and sensitivity analysis provide rigorous procedures to quantify how the model output depends on this parameter uncertainty. Unfortunately, the application of such methods is not yet standard within the field of neuroscience. Here we present Uncertainpy, an open-source Python toolbox, tailored to perform uncertainty quantification and sensitivity analysis of neuroscience models. Uncertainpy aims to make it quick and easy to get started with uncertainty analysis, without any need for detailed prior knowledge. The toolbox allows uncertainty quantification and sensitivity analysis to be performed on already existing models without needing to modify the model equations or model implementation. Uncertainpy bases its analysis on polynomial chaos expansions, which are more efficient than the more standard Monte-Carlo based approaches. Uncertainpy is tailored for neuroscience applications by its built-in capability for calculating characteristic features in the model output. The toolbox does not merely perform a point-to-point comparison of the "raw" model output (e.g., membrane voltage traces), but can also calculate the uncertainty and sensitivity of salient model response features such as spike timing, action potential width, average interspike interval, and other features relevant for various neural and neural network models. Uncertainpy comes with several common models and features built in, and including custom models and new features is easy. The aim of the current paper is to present Uncertainpy to the neuroscience community in a user-oriented manner. To demonstrate its broad applicability, we perform an uncertainty quantification and sensitivity analysis of three case studies relevant for neuroscience: the original Hodgkin-Huxley point-neuron model for action potential generation, a multi-compartmental model of a thalamic interneuron implemented in the NEURON simulator, and a sparsely connected recurrent network model implemented in the NEST simulator.

Mechanisms of regulation of olfactory transduction and adaptation in the olfactory cilium

Olfactory adaptation is a fundamental process for the functioning of the olfactory system, but the underlying mechanisms regulating its occurrence in intact olfactory sensory neurons (OSNs) are not fully understood. In this work, we have combined stochastic computational modeling and a systematic pharmacological study of different signaling pathways to investigate their impact during short-term adaptation (STA). We used odorant stimulation and electroolfactogram (EOG) recordings of the olfactory epithelium treated with pharmacological blockers to study the molecular mechanisms regulating the occurrence of adaptation in OSNs. EOG responses to paired-pulses of odorants showed that inhibition of phosphodiesterases (PDEs) and phosphatases enhanced the levels of STA in the olfactory epithelium, and this effect was mimicked by blocking vesicle exocytosis and reduced by blocking cyclic adenosine monophosphate (cAMP)-dependent protein kinase (PKA) and vesicle endocytosis. These results suggest that G-coupled receptors (GPCRs) cycling is involved with the occurrence of STA. To gain insights on the dynamical aspects of this process, we developed a stochastic computational model. The model consists of the olfactory transduction currents mediated by the cyclic nucleotide gated (CNG) channels and calcium ion (Ca²⁺)-activated chloride (CAC) channels, and the dynamics of their respective ligands, cAMP and Ca²⁺, and it simulates the EOG results obtained under different experimental conditions through changes in the amplitude and duration of cAMP and Ca²⁺ response, two second messengers implicated with STA occurrence. The model reproduced the experimental data for each pharmacological treatment and provided a mechanistic explanation for the action of GPCR cycling in the levels of second messengers modulating the levels of STA. All together, these experimental and theoretical results indicate the existence of a mechanism of regulation of STA by signaling pathways that control GPCR cycling and tune the levels of second messengers in OSNs, and not only by CNG channel desensitization as previously thought.

Common dynamical features of sensory adaptation in photoreceptors and olfactory sensory neurons

Sensory systems adapt, i.e., they adjust their sensitivity to external stimuli according to the ambient level. In this paper we show that single cell electrophysiological responses of vertebrate olfactory receptors and of photoreceptors to different input protocols exhibit several common features related to adaptation, and that these features can be used to investigate the dynamical structure of the feedback regulation responsible for the adaptation. In particular, we point out that two different forms of adaptation can be observed, in response to steps and to pairs of pulses. These two forms of adaptation appear to be in a dynamical trade-off: the more adaptation to a step is close to perfect, the slower is the recovery in adaptation to pulse pairs and viceversa. Neither of the two forms is explained by the dynamical models currently used to describe adaptation, such as the integral feedback model.

A dynamical feedback model for adaptation in the olfactory transduction pathway

Olfactory transduction exhibits two distinct types of adaptation, which we denote multipulse and step adaptation. In terms of measured transduction current, multipulse adaptation appears as a decrease in the amplitude of the second of two consecutive responses when the olfactory neuron is stimulated with two brief pulses. Step adaptation occurs in response to a sustained steplike stimulation and is characterized by a return to a steady-state current amplitude close to the prestimulus value, after a transient peak. In this article, we formulate a dynamical model of the olfactory transduction pathway, which includes the kinetics of the CNG channels, the concentration of Ca ions flowing through them, and the Ca-complexes responsible for the regulation. Based on this model, a common dynamical explanation for the two types of adaptation is suggested. We show that both forms of adaptation can be well described using different time constants for the kinetics of Ca ions (faster) and the kinetics of the feedback mechanisms (slower). The model is validated on experimental data collected in voltage-clamp conditions using different techniques and animal species.

Event timing in associative learning: from biochemical reaction dynamics to behavioural observations

Associative learning relies on event timing. Fruit flies for example, once trained with an odour that precedes electric shock, subsequently avoid this odour (punishment learning); if, on the other hand the odour follows the shock during training, it is approached later on (relief learning). During training, an odour-induced Ca⁺⁺ signal and a shock-induced dopaminergic signal converge in the Kenyon cells, synergistically activating a Ca⁺⁺-calmodulin-sensitive adenylate cyclase, which likely leads to the synaptic plasticity underlying the conditioned avoidance of the odour. In Aplysia, the effect of serotonin on the corresponding adenylate cyclase is bi-directionally modulated by Ca⁺⁺, depending on the relative timing of the two inputs. Using a computational approach, we quantitatively explore this biochemical property of the adenylate cyclase and show that it can generate the effect of event timing on associative learning. We overcome the shortage of behavioural data in Aplysia and biochemical data in Drosophila by combining findings from both systems.

System identification of Drosophila olfactory sensory neurons

The lack of a deeper understanding of how olfactory sensory neurons (OSNs) encode odors has hindered the progress in understanding the olfactory signal processing in higher brain centers. Here we employ methods of system identification to investigate the encoding of time-varying odor stimuli and their representation for further processing in the spike domain by Drosophila OSNs. In order to apply system identification techniques, we built a novel low-turbulence odor delivery system that allowed us to deliver airborne stimuli in a precise and reproducible fashion. The system provides a 1% tolerance in stimulus reproducibility and an exact control of odor concentration and concentration gradient on a millisecond time scale. Using this novel setup, we recorded and analyzed the in-vivo response of OSNs to a wide range of time-varying odor waveforms. We report for the first time that across trials the response of OR59b OSNs is very precise and reproducible. Further, we empirically show that the response of an OSN depends not only on the concentration, but also on the rate of change of the odor concentration. Moreover, we demonstrate that a two-dimensional (2D) Encoding Manifold in a concentration-concentration gradient space provides a quantitative description of the neuron's response. We then use the white noise system identification methodology to construct one-dimensional (1D) and two-dimensional (2D) Linear-Nonlinear-Poisson (LNP) cascade models of the sensory neuron for a fixed mean odor concentration and fixed contrast. We show that in terms of predicting the intensity rate of the spike train, the 2D LNP model performs on par with the 1D LNP model, with a root mean-square error (RMSE) increase of about 5 to 10%. Surprisingly, we find that for a fixed contrast of the white noise odor waveforms, the nonlinear block of each of the two models changes with the mean input concentration. The shape of the nonlinearities of both the 1D and the 2D LNP model appears to be, for a fixed mean of the odor waveform, independent of the stimulus contrast. This suggests that white noise system identification of Or59b OSNs only depends on the first moment of the odor concentration. Finally, by comparing the 2D Encoding Manifold and the 2D LNP model, we demonstrate that the OSN identification results depend on the particular type of the employed test odor waveforms. This suggests an adaptive neural encoding model for Or59b OSNs that changes its nonlinearity in response to the odor concentration waveforms.