Neural optimization: Understanding trade-offs with Pareto theory

Nervous systems, like any organismal structure, have been shaped by evolutionary processes to increase fitness. The resulting neural ’bauplan’ has to account for multiple objectives simultaneously, including computational function, as well as additional factors such as robustness to environmental changes and energetic limitations. Oftentimes these objectives compete, and quantification of the relative impact of individual optimization targets is non-trivial. Pareto optimality offers a theoretical framework to decipher objectives and trade-offs between them. We, therefore, highlight Pareto theory as a useful tool for the analysis of neurobiological systems from biophysically detailed cells to large-scale network structures and behavior. The Pareto approach can help to assess optimality, identify relevant objectives and their respective impact, and formulate testable hypotheses.     

Rampant False Detection of Adaptive Phenotypic Optimization by ParTI-Based Pareto Front Inference

Organisms face tradeoffs in performing multiple tasks. Identifying the optimal phenotypes maximizing the organismal fitness (or Pareto front) and inferring the relevant tasks allow testing phenotypic adaptations and help delineate evolutionary constraints, tradeoffs, and critical fitness components, so are of broad interest. It has been proposed that Pareto fronts can be identified from high-dimensional phenotypic data, including molecular phenotypes such as gene expression levels, by fitting polytopes (lines, triangles, tetrahedrons, and so on), and a program named ParTI was recently introduced for this purpose. ParTI has identified Pareto fronts and inferred phenotypes best for individual tasks (or archetypes) from numerous data sets such as the beak morphologies of Darwin’s finches and mRNA concentrations in human tumors, implying evolutionary optimizations of the involved traits. Nevertheless, the reliabilities of these findings are unknown. Using real and simulated data that lack evolutionary optimization, we here report extremely high false-positive rates of ParTI. The errors arise from phylogenetic relationships or population structures of the organisms analyzed and the flexibility of data analysis in ParTI that is equivalent to p-hacking. Because these problems are virtually universal, our findings cast doubt on almost all ParTI-based results and suggest that reliably identifying Pareto fronts and archetypes from high-dimensional phenotypic data are currently generally difficult.     

Systematic design for trait introgression projects

Key message

Using an Operations Research approach, we demonstrate design of optimal trait introgression projects with respect to competing objectives.

Abstract

We demonstrate an innovative approach for designing Trait Introgression (TI) projects based on optimization principles from Operations Research. If the designs of TI projects are based on clear and measurable objectives, they can be translated into mathematical models with decision variables and constraints that can be translated into Pareto optimality plots associated with any arbitrary selection strategy. The Pareto plots can be used to make rational decisions concerning the trade-offs between maximizing the probability of success while minimizing costs and time. The systematic rigor associated with a cost, time and probability of success (CTP) framework is well suited to designing TI projects that require dynamic decision making. The CTP framework also revealed that previously identified ‘best’ strategies can be improved to be at least twice as effective without increasing time or expenses.

     

The synaptic action of Degenerin/Epithelial sodium channels

Degenerin/Epithelial Sodium Channels (DEG/ENaCs) are a large family of animal-specific non-voltage gated ion channels, with enriched expression in neuronal and epithelial tissues. While neuronal DEG/ENaCs were originally characterized as sensory receptor channels, recent studies indicate that several DEG/ENaC family members are also expressed throughout the central nervous system. Human genome-wide association studies have linked DEG/ENaC-coding genes with several neurologic and psychiatric disorders, including epilepsy and panic disorder. In addition, studies in rodent models further indicate that DEG/ENaC activity in the brain contributes to many behaviors, including those related to anxiety and long-term memory. Although the exact neurophysiological functions of DEG/ENaCs remain mostly unknown, several key studies now suggest that multiple family members might exert their neuronal function via the direct modulation of synaptic processes. Here, we review and discuss recent findings on the synaptic functions of DEG/ENaCs in both vertebrate and invertebrate species, and propose models for their possible roles in synaptic physiology.     

Biodiversity mitigates trade-offs among species functional traits underpinning multiple ecosystem services

Biodiversity loss and its effects on humanity is of major global concern. While a growing body of literature confirms positive relationships between biodiversity and multiple ecological functions, the links between biodiversity, ecological functions and multiple ecosystem services is yet unclear. Studies of biodiversity–functionality relationships are mainly based on computer simulations or controlled field experiments using only few species. Here, we use a trait-based approach to integrate plant functions into an ecosystem service assessment to address impacts of restoration on species-rich grasslands over time. We found trade-offs among functions and services when analysing contributions from individual species. At the community level, these trade-offs disappeared for almost all services with time since restoration as an effect of increased species diversity and more evenly distributed species. Restoration to enhance biodiversity also in species-rich communities is therefore essential to secure higher functional redundancy towards disturbances and sustainable provision of multiple ecosystem services over time.     

Transporters of Neurotransmitters: Receptive, Transport, and Channel Functions

Based on possible unity of the evolutionary origin of some prokaryotic proteins with eukaryotic ion channels and receptors, this review analyzes interconnections between receptive, transport, and channel functions of integral proteins. This interconnection can be considered the best by the example of neurotransmitter transporters. Their role in chemical synapses and their possible participation in phenomena of synaptic plasticity are reviewed. There are discussed mechanisms of transporter functioning, such as the allosteric model and the model of activity by the principle of channel, as well as data about coupling by the transporters of reception of substrate and its transport with the substrate-activated channel of Cl^–-conductance and the ion leakage. The importance of the latter aspects of the neurotransmitter transporter functioning is usually underestimated in studying neuronal and glial electrogenesis.     

A divide-and-conquer approach to determine the Pareto frontier for optimization of protein engineering experiments

In developing improved protein variants by site-directed mutagenesis or recombination, there are often competing objectives that must be considered in designing an experiment (selecting mutations or breakpoints): stability versus novelty, affinity versus specificity, activity versus immunogenicity, and so forth. Pareto optimal experimental designs make the best trade-offs between competing objectives. Such designs are not "dominated"; that is, no other design is better than a Pareto optimal design for one objective without being worse for another objective. Our goal is to produce all the Pareto optimal designs (the Pareto frontier), to characterize the trade-offs and suggest designs most worth considering, but to avoid explicitly considering the large number of dominated designs. To do so, we develop a divide-and-conquer algorithm, Protein Engineering Pareto FRontier (PEPFR), that hierarchically subdivides the objective space, using appropriate dynamic programming or integer programming methods to optimize designs in different regions. This divide-and-conquer approach is efficient in that the number of divisions (and thus calls to the optimizer) is directly proportional to the number of Pareto optimal designs. We demonstrate PEPFR with three protein engineering case studies: site-directed recombination for stability and diversity via dynamic programming, site-directed mutagenesis of interacting proteins for affinity and specificity via integer programming, and site-directed mutagenesis of a therapeutic protein for activity and immunogenicity via integer programming. We show that PEPFR is able to effectively produce all the Pareto optimal designs, discovering many more designs than previous methods. The characterization of the Pareto frontier provides additional insights into the local stability of design choices as well as global trends leading to trade-offs between competing criteria.     

The neuronal calcium ion channel activity of constrained analogues of MONIRO-1

Structural modifications of the neuronal calcium channel blocker MONIRO-1, including constraining the phenoxyaniline portion of the molecule and replacing the guanidinium functionality with tertiary amines, led to compounds with significantly improved affinities for the endogenously expressed Ca_V2.2 channel in the SH-SY5Y neuroblastoma cell line. These analogues also showed promising activity towards the Ca_V3.2 channel, recombinantly expressed in HEK293T cells. Both of these ion channels have received attention as likely targets for the treatment of neuropathic pain. The dibenzoazepine and dihydrobenzodiazepine derivatives prepared in this study show an encouraging combination of neuronal calcium ion channel inhibitory potency, plasma stability and potential to cross the blood–brain-barrier.     

海马CA1区锥体细胞树突分级峰电位的模型分析

脑神经元复杂的树突树结构和电压激活离子通道赋予其复杂的信息整合功能。通过神经元形态的分枝结构模型和电压激活离子通道动力学模型 ,包括远端树突高密度A型K 通道 ,对海马CA1区锥体细胞树突的信息整合特性进行了仿真研究。结果表明 ,远端树突峰电位在很大范围内具有分级放大作用 ,在一定的刺激条件下峰电位的发起部位可在树突轴上移动 ,并且轴突反传动作电位幅度在远端树突会发生突然减小。     

Plant water uptake modelling: added value of cross-disciplinary approaches

In recent years, research interest in plant water uptake strategies has rapidly increased in many disciplines, such as hydrology, plant ecology and ecophysiology. Quantitative modelling approaches to estimate plant water uptake and spatiotemporal dynamics have significantly advanced through different disciplines across scales. Despite this progress, major limitations, for example, predicting plant water uptake under drought or drought impact at large scales, remain. These are less attributed to limitations in process understanding, but rather to a lack of implementation of cross-disciplinary insights into plant water uptake model structure. The main goal of this review is to highlight how the four dominant model approaches, that is, Feddes approach, hydrodynamic approach, optimality and statistical approaches, can be and have been used to create interdisciplinary hybrid models enabling a holistic system understanding that, among other things, embeds plant water uptake plasticity into a broader conceptual view of soil–plant feedbacks of water, nutrient and carbon cycling, or reflects observed drought responses of plant–soil feedbacks and their dynamics under, that is, drought. Specifically, we provide examples of how integration of Bayesian and hydrodynamic approaches might overcome challenges in interpreting plant water uptake related to different travel and residence times of different plant water sources or trade-offs between root system optimization to forage for water and nutrients during different seasons and phenological stages.     

Neuronal zinc regulation and the prion protein

Zinc, the most abundant trace metal in the brain, has numerous functions in health and disease. It is released into the synaptic cleft alongside glutamate and this connection between zinc and glutamatergic neurotransmission allows the ion to modulate overall excitability of the brain and influence synaptic plasticity. To maintain healthy synapses, extracellular zinc levels need to be tightly regulated. We recently reported that the cellular prion protein (PrP^C) can directly influence neuronal zinc concentrations by promoting zinc uptake via AMPA receptors. The octapeptide repeat region of PrP^C is involved in zinc sensing or scavenging and the AMPA receptor provides the channel for transport of the metal across the membrane, facilitated by a direct interaction between the N-terminal polybasic region of PrP^C and AMPA receptors. PrP^C has been evolutionarily linked to the Zrt/Irt-like protein (ZIP) metal ion transport family with the C-terminus of PrP^C sharing sequence similarities with the N-terminal extracellular domains of ZIP 5, 6 and 10. By incorporating the properties of ZIP transporters (both zinc sensing and zinc transport) into two existing neuronal proteins, (PrP^C as zinc sensor, AMPA receptor as zinc transporter), neuronal cells are enhancing their biological efficiency and functionality.     

The use of automated parameter searches to improve ion channel kinetics for neural modeling

The voltage and time dependence of ion channels can be regulated, notably by phosphorylation, interaction with phospholipids, and binding to auxiliary subunits. Many parameter variation studies have set conductance densities free while leaving kinetic channel properties fixed as the experimental constraints on the latter are usually better than on the former. Because individual cells can tightly regulate their ion channel properties, we suggest that kinetic parameters may be profitably set free during model optimization in order to both improve matches to data and refine kinetic parameters. To this end, we analyzed the parameter optimization of reduced models of three electrophysiologically characterized and morphologically reconstructed globus pallidus neurons. We performed two automated searches with different types of free parameters. First, conductance density parameters were set free. Even the best resulting models exhibited unavoidable problems which were due to limitations in our channel kinetics. We next set channel kinetics free for the optimized density matches and obtained significantly improved model performance. Some kinetic parameters consistently shifted to similar new values in multiple runs across three models, suggesting the possibility for tailored improvements to channel models. These results suggest that optimized channel kinetics can improve model matches to experimental voltage traces, particularly for channels characterized under different experimental conditions than recorded data to be matched by a model. The resulting shifts in channel kinetics from the original template provide valuable guidance for future experimental efforts to determine the detailed kinetics of channel isoforms and possible modulated states in particular types of neurons.     

Control of neuronal excitability by GSK-3beta: Epilepsy and beyond

Glycogen synthase kinase 3beta (GSK-3β) is an enzyme with a variety of cellular functions in addition to the regulation of glycogen metabolism. In the central nervous system, different intracellular signaling pathways converge on GSK-3β through a cascade of phosphorylation events that ultimately control a broad range of neuronal functions in the development and adulthood. In mice, genetically removing or increasing GSK-3β cause distinct functional and structural neuronal phenotypes and consequently affect cognition. Precise control of GSK-3β activity is important for such processes as neuronal migration, development of neuronal morphology, synaptic plasticity, excitability, and gene expression. Altered GSK-3β activity contributes to aberrant plasticity within neuronal circuits leading to neurological, psychiatric disorders, and neurodegenerative diseases. Therapeutically targeting GSK-3β can restore the aberrant plasticity of neuronal networks at least in animal models of these diseases. Although the complete repertoire of GSK-3β neuronal substrates has not been defined, emerging evidence shows that different ion channels and their accessory proteins controlling excitability, neurotransmitter release, and synaptic transmission are regulated by GSK-3β, thereby supporting mechanisms of synaptic plasticity in cognition. Dysregulation of ion channel function by defective GSK-3β activity sustains abnormal excitability in the development of epilepsy and other GSK-3β-linked human diseases.     

Marginal Models Via GLS: A Convenient Yet Neglected Tool for the Analysis of Correlated Data in the Behavioural Sciences

Behavioural research often produces data that have a complicated structure. For instance, data can represent repeated observations of the same individual and suffer from heteroscedasticity as well as other technical snags. The regression analysis of such data is often complicated by the fact that the observations (response variables) are mutually correlated. The correlation structure can be quite complex and might or might not be of direct interest to the user. In any case, one needs to take correlations into account (e.g. by means of random‐effect specification) in order to arrive at correct statistical inference (e.g. for construction of the appropriate test or confidence intervals). Over the last decade, such data have been more and more frequently analysed using repeated‐measures ANOVA and mixed‐effects models. Some researchers invoke the heavy machinery of mixed‐effects modelling to obtain the desired population‐level (marginal) inference, which can be achieved by using simpler tools – namely marginal models. This paper highlights marginal modelling (using generalized least squares [GLS] regression) as an alternative method. In various concrete situations, such marginal models can be based on fewer assumptions and directly generate estimates (population‐level parameters) which are of immediate interest to the behavioural researcher (such as population mean). Sometimes, they might be not only easier to interpret but also easier to specify than their competitors (e.g. mixed‐effects models). Using five examples from behavioural research, we demonstrate the use, advantages, limits and pitfalls of marginal and mixed‐effects models implemented within the functions of the ‘nlme’ package in R.     

Optimality principles for model-based prediction of human gait

Although humans have a large repertoire of potential movements, gait patterns tend to be stereotypical and appear to be selected according to optimality principles such as minimal energy. When applied to dynamic musculoskeletal models such optimality principles might be used to predict how a patient's gait adapts to mechanical interventions such as prosthetic devices or surgery. In this paper we study the effects of different performance criteria on predicted gait patterns using a 2D musculoskeletal model. The associated optimal control problem for a family of different cost functions was solved utilizing the direct collocation method. It was found that fatigue-like cost functions produced realistic gait, with stance phase knee flexion, as opposed to energy-related cost functions which avoided knee flexion during the stance phase. We conclude that fatigue minimization may be one of the primary optimality principles governing human gait.     

Fast assessment of structural models of ion channels based on their predicted current–voltage characteristics

Computational prediction of protein structures is a difficult task, which involves fast and accurate evaluation of candidate model structures. We propose to enhance single‐model quality assessment with a functionality evaluation phase for proteins whose quantitative functional characteristics are known. In particular, this idea can be applied to evaluation of structural models of ion channels, whose main function ‐ conducting ions ‐ can be quantitatively measured with the patch‐clamp technique providing the current–voltage characteristics. The study was performed on a set of KcsA channel models obtained from complete and incomplete contact maps. A fast continuous electrodiffusion model was used for calculating the current–voltage characteristics of structural models. We found that the computed charge selectivity and total current were sensitive to structural and electrostatic quality of models. In practical terms, we show that evaluating predicted conductance values is an appropriate method to eliminate models with an occluded pore or with multiple erroneously created pores. Moreover, filtering models on the basis of their predicted charge selectivity results in a substantial enrichment of the candidate set in highly accurate models. Tests on three other ion channels indicate that, in addition to being a proof of the concept, our function‐oriented single‐model quality assessment method can be directly applied to evaluation of structural models of some classes of protein channels. Finally, our work raises an important question whether a computational validation of functionality should be included in the evaluation process of structural models, whenever possible. Proteins 2016; 84:217–231. © 2015 Wiley Periodicals, Inc.     

Confidence scores for prediction models

In medical statistics, many alternative strategies are available for building a prediction model based on training data. Prediction models are routinely compared by means of their prediction performance in independent validation data. If only one data set is available for training and validation, then rival strategies can still be compared based on repeated bootstraps of the same data. Often, however, the overall performance of rival strategies is similar and it is thus difficult to decide for one model. Here, we investigate the variability of the prediction models that results when the same modelling strategy is applied to different training sets. For each modelling strategy we estimate a confidence score based on the same repeated bootstraps. A new decomposition of the expected Brier score is obtained, as well as the estimates of population average confidence scores. The latter can be used to distinguish rival prediction models with similar prediction performances. Furthermore, on the subject level a confidence score may provide useful supplementary information for new patients who want to base a medical decision on predicted risk. The ideas are illustrated and discussed using data from cancer studies, also with high-dimensional predictor space.     

Opinion: an integrated approach to classifying neuronal phenotypes

Characterizing the functional phenotypes of neurons is essential for understanding how genotypes can be related to the neural basis of behaviour. Traditional classifications of neurons by single features (such as morphology or firing behaviour) are increasingly inadequate for reflecting functional phenotypes, as they do not integrate functions across different neuronal types. Here, we describe a set of rules for identifying and predicting functional phenotypes that combine morphology, intrinsic ion channel species and their distributions in dendrites, and functional properties. This more comprehensive neuronal classification should be an improvement on traditional classifications for relating genotype to functional phenotype.     

Molecular dynamics study of the KcsA potassium channel

The structural, dynamical, and thermodynamic properties of a model potassium channel are studied using molecular dynamics simulations. We use the recently unveiled protein structure for the KcsA potassium channel from Streptomyces lividans. Total and free energy profiles of potassium and sodium ions reveal a considerable preference for the larger potassium ions. The selectivity of the channel arises from its ability to completely solvate the potassium ions, but not the smaller sodium ions. Self-diffusion of water within the narrow selectivity filter is found to be reduced by an order of magnitude from bulk levels, whereas the wider hydrophobic section of the pore maintains near-bulk self-diffusion. Simulations examining multiple ion configurations suggest a two-ion channel. Ion diffusion is found to be reduced to approximately (1)/(3) of bulk diffusion within the selectivity filter. The reduced ion mobility does not hinder the passage of ions, as permeation appears to be driven by Coulomb repulsion within this multiple ion channel.     

The geometry of the Pareto front in biological phenotype space

When organisms perform a single task, selection leads to phenotypes that maximize performance at that task. When organisms need to perform multiple tasks, a trade‐off arises because no phenotype can optimize all tasks. Recent work addressed this question, and assumed that the performance at each task decays with distance in trait space from the best phenotype at that task. Under this assumption, the best‐fitness solutions (termed the Pareto front) lie on simple low‐dimensional shapes in trait space: line segments, triangles and other polygons. The vertices of these polygons are specialists at a single task. Here, we generalize this finding, by considering performance functions of general form, not necessarily functions that decay monotonically with distance from their peak. We find that, except for performance functions with highly eccentric contours, simple shapes in phenotype space are still found, but with mildly curving edges instead of straight ones. In a wide range of systems, complex data on multiple quantitative traits, which might be expected to fill a high‐dimensional phenotype space, is predicted instead to collapse onto low‐dimensional shapes; phenotypes near the vertices of these shapes are predicted to be specialists, and can thus suggest which tasks may be at play.