In this paper we develop a new method for numerically approximating sensitivities in parameter-dependent ordinary differential equations (ODEs). Our approach, intended for situations where the standard forward and adjoint sensitivity analyses become too computationally costly for practical purposes, is based on the Peano-Baker series from control theory. Using this series, we construct a representation of the sensitivity matrix S and, from this representation, a numerical method for approximating S. We prove that, under standard regularity assumptions, the error of our method scales as O(Δtmax2), where Δtmax is the largest time step used when numerically solving the ODE. We illustrate the performance of the method in several numerical experiments, taken from both the systems biology setting and more classical dynamical systems. The experiments show the sought-after improvement in running time of our method compared to the forward sensitivity approach. In experiments involving a random linear system, the forward approach requires roughly n longer computational time, where n is the dimension of the parameter space, than our proposed method.

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.

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.

Interplay between the second messengers cAMP and Ca2+ is a hallmark of dynamic cellular processes. A common motif is the opposition of the Ca2+-sensitive phosphatase calcineurin and the major cAMP receptor, protein kinase A (PKA). Calcineurin dephosphorylates sites primed by PKA to bring about changes including synaptic long-term depression (LTD). AKAP79 supports signaling of this type by anchoring PKA and calcineurin in tandem. In this study, we discovered that AKAP79 increases the rate of calcineurin dephosphorylation of type II PKA regulatory subunits by an order of magnitude. Fluorescent PKA activity reporter assays, supported by kinetic modeling, show how AKAP79-enhanced calcineurin activity enables suppression of PKA without altering cAMP levels by increasing PKA catalytic subunit capture rate. Experiments with hippocampal neurons indicate that this mechanism contributes toward LTD. This non-canonical mode of PKA regulation may underlie many other cellular processes.

Since 2010, the Swedish e-Science Research Centre (SeRC) is funding and coordinating e-Science activities in a broad spectrum of scientific disciplines. After an initial 5-year phase that produced outstanding results, SeRC is increasingly focusing on fostering interactions between disciplines and has created so-called Multidisciplinary Collaborative Programs (MCPs). In these programs, domain researchers collaborate with e-Science methods and tool developers and e-Infrastructure providers. In this paper we give an overview of the initial phase of SeRC and present the new programs that started operating in 2019.

Motivation: Dynamical models describing intracellular phenomena are increasing in size and complexity as more information is obtained from experiments. These models are often over-parameterized with respect to the quantitative data used for parameter estimation, resulting in uncertainty in the individual parameter estimates as well as in the predictions made from the model. Here we combine Bayesian analysis with global sensitivity analysis (GSA) in order to give better informed predictions; to point out weaker parts of the model that are important targets for further experiments, as well as to give guidance on parameters that are essential in distinguishing different qualitative output behaviours. Results: We used approximate Bayesian computation (ABC) to estimate the model parameters from experimental data, as well as to quantify the uncertainty in this estimation (inverse uncertainty quantification), resulting in a posterior distribution for the parameters. This parameter uncertainty was next propagated to a corresponding uncertainty in the predictions (forward uncertainty propagation), and a GSA was performed on the predictions using the posterior distribution as the possible values for the parameters. This methodology was applied on a relatively large model relevant for synaptic plasticity, using experimental data from several sources. We could hereby point out those parameters that by themselves have the largest contribution to the uncertainty of the prediction as well as identify parameters important to separate between qualitatively different predictions. This approach is useful both for experimental design as well as model building.

Transient changes in striatal dopamine (DA) concentration are considered to encode a reward prediction error (RPE) in reinforcement learning tasks. Often, a phasic DA change occurs concomitantly with a dip in striatal acetylcholine (ACh), whereas other neuromodulators, such as adenosine (Adn), change slowly. There are abundant adenylyl cyclase (AC) coupled GPCRs for these neuromodulators in striatal medium spiny neurons (MSNs), which play important roles in plasticity. However, little is known about the interaction between these neuromodulators via GPCRs. The interaction between these transient neuromodulator changes and the effect on cAMP/PKA signaling via Golf- and Gi/o-coupled GPCR are studied here using quantitative kinetic modeling. The simulations suggest that, under basal conditions, cAMP/PKA signaling could be significantly inhibited in D1R+ MSNs via ACh/M4R/Gi/o and an ACh dip is required to gate a subset of D1R/Golf-dependent PKA activation. Furthermore, the interaction between ACh dip and DA peak, via D1R and M4R, is synergistic. In a similar fashion, PKA signaling in D2+ MSNs is under basal inhibition via D2R/Gi/o and a DA dip leads to a PKA increase by disinhibiting A2aR/Golf, but D2+ MSNs could also respond to the DA peak via other intracellular pathways. This study highlights the similarity between the two types of MSNs in terms of high basal AC inhibition by Gi/o and the importance of interactions between Gi/o and Golf signaling, but at the same time predicts differences between them with regard to the sign of RPE responsible for PKA activation.

An important aspect of homology modeling and protein design algorithms is the correct positioning of protein side chains on a fixed backbone. Homology modeling methods are necessary to complement large scale structural genomics projects. Recently it has been shown that in automatic protein design it is of the uttermost importance to find the global solution to the side chain positioning problem [1]. If a suboptimal solution is found the difference in free energy between different sequences will be smaller than the error of the side chain positioning. Several different algorithms have been developed to solve this problem. The most successful methods use a discrete representation of the conformational space. Today, the best methods to solve this problem, are based on the dead end elimination theorem. Here we introduce an alternative method. The problem is formulated as a linear integer program. This programming problem can then be solved by efficient polynomial time methods, using linear programming relaxation. If the solution to the relaxed problem is integral it corresponds to the global minimum energy conformation (GMEC). In our experimental results, the solution to the relaxed problem has always been integral.