Dynamical aspects of behavior generation under constraints

Dynamic adaptation is a key feature of brains helping to maintain the quality of their performance in the face of increasingly difficult constraints. How to achieve high-quality performance under demanding real-time conditions is an important question in the study of cognitive behaviors. Animals and humans are embedded in and constrained by their environments. Our goal is to improve the understanding of the dynamics of the interacting brain–environment system by studying human behaviors when completing constrained tasks and by modeling the observed behavior. In this article we present results of experiments with humans performing tasks on the computer under variable time and resource constraints. We compare various models of behavior generation in order to describe the observed human performance. Finally we speculate on mechanisms how chaotic neurodynamics can contribute to the generation of flexible human behaviors under constraints.     

Structure determination of a Galectin-3-carbohydrate complex using paramagnetism-based NMR constraints

The determination of the location and conformation of a natural ligand bound to a protein receptor is often a first step in the rational design of molecules that can modulate receptor function. NMR observables, including NOEs, often provide the basis for these determinations. However, when ligands are carbohydrates, interactions mediated by extensive hydrogen-bonding networks often reduce or eliminate NOEs between ligand and protein protons. In these cases, it is useful to look to other distance- and orientation-dependent observables that can constrain the geometry of ligand-protein complexes. Here we illustrate the use of paramagnetism-based NMR constraints, including pseudo-contact shifts (PCS) and field-induced residual dipolar couplings (RDCs). When a paramagnetic center can be attached to the protein, field-induced RDCs and PCS reflect only bound-state properties of the ligand, even when averages over small fractions of bound states and large fractions of free states are observed. The effects can also be observed over a long range, making it possible to attach a paramagnetic center to a remote part of the protein. The system studied here is a Galectin-3-lactose complex. A lanthanide-binding peptide showing minimal flexibility with respect to the protein was integrated into the C terminus of an expression construct for the Galectin-3-carbohydrate-binding domain. Dysprosium ion, which has a large magnetic susceptibility anisotropy, was complexed to the peptide, making it possible to observe both PCSs and field-induced RDCs for the protein and the ligand. The structure determined from these constraints shows agreement with a crystal structure of a Galectin-3-N-acetyllactosamine complex.     

Rectifying postures reconstructed from joint angles to meet constraints.

Postures are often described and modeled using angles between body segments rather than joint coordinates. Models can be used to predict these angles as a function of anthropometry and postural requirements. Postural representation, however, requires the joint coordinates. The use of conventional forward kinematics to derive joint coordinates from predicted angles may violate task constraints, such as the placement of a hand on a target or a foot on a pedal. Errors arise because the anthropometry or other motion characteristics of a subject, for which the prediction is to be made, may differ from the data from which the prediction model was derived. We describe how to rectify model-predicted postures to exactly satisfy such task constraints. We require that the model used for predicting the angles also produce estimates of the variation in these predictions. We show how to alter the initial angle predictions, with the amount of perturbation at each angle dependent on the accuracy of its estimation, so as to exactly satisfy the joint coordinate constraints. Finally, we show in an empirical example that this correction usually produces better overall predictions of posture than those obtained initially.     

Multicriteria optimization of biochemical systems by linear programming: application to production of ethanol by Saccharomyces cerevisiae

In this study we present a method for simultaneous optimization of several metabolic responses of biochemical pathways. The method, based on the use of the power law formalism to obtain a linear system in logarithmic coordinates, is applied to ethanol production by Saccharomyces cerevisiae. Starting from an experimentally based kinetic model, we translated it to its power law equivalent. With this new model representation, we then applied the multiobjective optimization method. Our intent was to maximize ethanol production and minimize each of the internal metabolite concentrations. To ensure cell viability, all optimizations were carried out under imposed constraints. The different solutions obtained, which correspond to alternative patterns of enzyme overexpression, were implemented in the original model. We discovered few discrepancies between the S-system-optimized steady state and the corresponding optimized state in the original kinetic model, thus demonstrating the suitability of the S-system representation as the basis for the optimization procedure. In all optimized solutions, the ATP level reached its maximum and any increase in its activity positively affected the optimization process. This work illustrates that in any optimization study no single criteria is of general application being the multiobjective and constrained task the proper way to address it. It is concluded that the proposed multiobjective method can serve to carry out, in a single study, the general pattern of behavior of a given metabolic system with regard to its control and optimization.     

Factors promoting maternal trophic egg provisioning in non-eusocial animals

The adaptive function of trophic egg-laying is generally regarded as extended parental investment to the offspring. However, the evolutionary factors promoting trophic egg-laying are still unclear, because the amount of maternal investment per offspring should be ideally equal between smaller offspring with trophic eggs and larger offspring without any additional investment. Several authors have suggested that trophic egg-laying should evolve only when egg size is constrained, but this hypothesis has not been evaluated. We investigated the evolutionary mechanisms of trophic egg-laying by two different approaches. First, we evaluated morphological constraints on egg size in two sibling ladybird species, Harmonia axyridis, which is known to produce trophic eggs, and H. yedoensis. Second, we theoretically predicted the optimal proportion of trophic eggs to total eggs and egg size in relation to environmental heterogeneity, predictability of environmental quality, and investment efficiency of trophic egg consumption. The intra- and interspecific morphological comparisons suggest that morphological constraints on the evolutionary determination of egg size are weak at best in the two ladybird species. Moreover, we theoretically showed that small egg size and trophic egg-laying are favoured in heterogeneous environments when mothers cannot adjust egg size plastically. We also showed that even a small reduction in investment efficiency makes a trophic egg strategy unlikely, despite relatively high environmental predictability. We conclude that trophic egg provisioning may be a flexible maternal adaptation to a highly heterogeneous environment rather than a response to a morphological constraint on egg size.     

Tracking the motion of hidden segments using kinematic constraints and Kalman filtering

Motion capture for biomechanical applications involves in almost all cases sensors or markers that are applied to the skin of the body segments of interest. This paper deals with the problem of estimating the movement of connected skeletal segments from 3D position data of markers attached to the skin. The use of kinematic constraints has been shown previously to reduce the error in estimated segment movement that are due to skin and muscles moving with respect to the underlying segment. A kinematic constraint reduces the number of degrees of freedom between two articulating segments. Moreover, kinematic constraints can help reveal the movement of some segments when the 3D marker data otherwise are insufficient. Important cases include the human ankle complex and the phalangeal segments of the horse, where the movement of small segments is almost completely hidden from external observation by joint capsules and ligaments. This paper discusses the use of an extended Kalman filter for tracking a system of connected segments. The system is modeled using rigid segments connected by simplified joint models. The position and orientation of the mechanism are specified by a set of generalized coordinates corresponding to the mechanism's degrees of motion. The generalized coordinates together with their first time derivatives can be used as the state vector of a state space model governing the kinematics of the mechanism. The data collected are marker trajectories from skin-mounted markers, and the state vector is related to the position of the markers through a nonlinear function. The Jacobian of this function is derived. The practical use of the method is demonstrated on a model of the distal part of the limb of the horse. Monte Carlo simulations of marker data for a two-segment system connected by a joint with three degrees of freedom indicate that the proposed method gives significant improvement over a method, which does not make use of the joint constraint, but the method requires that the model is a good approximation of the true mechanism. Applying the method to data on the movement of the four distal-most segments of the horse's limb shows good between trial consistency and small differences between measured marker positions and marker positions predicted by the model.     

Bayesian inference for stationary points in Gaussian process regression models for event-related potentials analysis

Stationary points embedded in the derivatives are often critical for a model to be interpretable and may be considered as key features of interest in many applications. We propose a semiparametric Bayesian model to efficiently infer the locations of stationary points of a nonparametric function, which also produces an estimate of the function. We use Gaussian processes as a flexible prior for the underlying function and impose derivative constraints to control the function's shape via conditioning. We develop an inferential strategy that intentionally restricts estimation to the case of at least one stationary point, bypassing possible mis-specifications in the number of stationary points and avoiding the varying dimension problem that often brings in computational complexity. We illustrate the proposed methods using simulations and then apply the method to the estimation of event-related potentials derived from electroencephalography (EEG) signals. We show how the proposed method automatically identifies characteristic components and their latencies at the individual level, which avoids the excessive averaging across subjects that is routinely done in the field to obtain smooth curves. By applying this approach to EEG data collected from younger and older adults during a speech perception task, we are able to demonstrate how the time course of speech perception processes changes with age.     

Computational reconstruction of multidomain proteins using atomic force microscopy data

Classical structural biology techniques face a great challenge to determine the structure at the atomic level of large and flexible macromolecules. We present a novel methodology that combines high-resolution AFM topographic images with atomic coordinates of proteins to assemble very large macromolecules or particles. Our method uses a two-step protocol: atomic coordinates of individual domains are docked beneath the molecular surface of the large macromolecule, and then each domain is assembled using a combinatorial search. The protocol was validated on three test cases: a simulated system of antibody structures; and two experimentally based test cases: Tobacco mosaic virus, a rod-shaped virus; and Aquaporin Z, a bacterial membrane protein. We have shown that AFM-intermediate resolution topography and partial surface data are useful constraints for building macromolecular assemblies. The protocol is applicable to multicomponent structures connected in the polypeptide chain or as disjoint molecules. The approach effectively increases the resolution of AFM beyond topographical information down to atomic-detail structures.     

A Network Approach to Analyzing Highly Recombinant Malaria Parasite Genes

The var genes of the human malaria parasite Plasmodium falciparum present a challenge to population geneticists due to their extreme diversity, which is generated by high rates of recombination. These genes encode a primary antigen protein called PfEMP1, which is expressed on the surface of infected red blood cells and elicits protective immune responses. Var gene sequences are characterized by pronounced mosaicism, precluding the use of traditional phylogenetic tools that require bifurcating tree-like evolutionary relationships. We present a new method that identifies highly variable regions (HVRs), and then maps each HVR to a complex network in which each sequence is a node and two nodes are linked if they share an exact match of significant length. Here, networks of var genes that recombine freely are expected to have a uniformly random structure, but constraints on recombination will produce network communities that we identify using a stochastic block model. We validate this method on synthetic data, showing that it correctly recovers populations of constrained recombination, before applying it to the Duffy Binding Like-α (DBLα) domain of var genes. We find nine HVRs whose network communities map in distinctive ways to known DBLα classifications and clinical phenotypes. We show that the recombinational constraints of some HVRs are correlated, while others are independent. These findings suggest that this micromodular structuring facilitates independent evolutionary trajectories of neighboring mosaic regions, allowing the parasite to retain protein function while generating enormous sequence diversity. Our approach therefore offers a rigorous method for analyzing evolutionary constraints in var genes, and is also flexible enough to be easily applied more generally to any highly recombinant sequences.     

Electro/magnetoencephalography beamforming with spatial restrictions based on sparsity

We present a source localization method for electroencephalographic (EEG) and magnetoencephalographic (MEG) data which is based on an estimate of the sparsity obtained through the eigencanceler (EIG), which is a spatial filter whose weights are constrained to lie in the noise subspace. The EIG provides rejection of directional interferences while minimizing noise contributions and maintaining specified beam pattern constraints. In our case, the EIG is used to estimate the sparsity of the signal as a function of the position, then we use this information to spatially restrict the neural sources to locations out of the sparsity maxima. As proof of the concept, we incorporate this restriction in the “classical” linearly constrained minimum variance (LCMV) source localization approach in order to enhance its performance. We present numerical examples to evaluate the proposed method using realistically simulated EEG/MEG data for different signal-to-noise (SNR) conditions and various levels of correlation between sources, as well as real EEG/MEG measurements of median nerve stimulation. Our results show that the proposed method has the potential of reducing the bias on the search of neural sources in the classical approach, as well as making it more effective in localizing correlated sources.     

A Method for Molecular Dynamics on Curved Surfaces

Dynamics simulations of constrained particles can greatly aid in understanding the temporal and spatial evolution of biological processes such as lateral transport along membranes and self-assembly of viruses. Most theoretical efforts in the field of diffusive transport have focused on solving the diffusion equation on curved surfaces, for which it is not tractable to incorporate particle interactions even though these play a crucial role in crowded systems. We show here that it is possible to take such interactions into account by combining standard constraint algorithms with the classical velocity Verlet scheme to perform molecular dynamics simulations of particles constrained to an arbitrarily curved surface. Furthermore, unlike Brownian dynamics schemes in local coordinates, our method is based on Cartesian coordinates, allowing for the reuse of many other standard tools without modifications, including parallelization through domain decomposition. We show that by applying the schemes to the Langevin equation for various surfaces, we obtain confined Brownian motion, which has direct applications to many biological and physical problems. Finally we present two practical examples that highlight the applicability of the method: 1) the influence of crowding and shape on the lateral diffusion of proteins in curved membranes; and 2) the self-assembly of a coarse-grained virus capsid protein model.     

Conscientious objection in healthcare: How much discretionary space best supports good medicine?

Daniel Sulmasy has recently argued that good medicine depends on physicians having a wide discretionary space in which they can act on their consciences. The only constraints Sulmasy believes we should place on physicians’ discretionary space are those defined by a form of tolerance he derives from Locke, whereby people can publicly act in accordance with their personal religious and moral beliefs as long as their actions are not destructive to society. Sulmasy also claims that those who would reject physicians’ right to conscientious objection eliminate discretionary space, thus undermining good medicine and unnecessarily limiting religious freedom. I argue that, although Sulmasy is correct that some discretionary space is necessary for good medicine, he is wrong in thinking that proscribing conscientious objection entails eliminating discretionary space. I illustrate this using Julian Savulescu and Udo Schuklenk’s system for restricting conscientious objections as a counter‐example. I then argue that a narrow discretionary space constrained by professional ideals will promote good medicine better than Sulmasy’s wider discretionary space constrained by his conception of tolerance. Sulmasy’s version of discretionary space would have us tolerate actions that are at odds with aspects of good medicine, including aspects that Sulmasy himself explicitly values, such as fiduciary duty. Therefore, if we want the degree of religious freedom in the public sphere that Sulmasy favours then we must decide whether it is worth the cost to the healthcare system.     

Pan-genome study of Thermococcales reveals extensive genetic diversity and genetic evidence of thermophilic adaption

Thermococcales has a strong adaptability to extreme environments, which is of profound interest in explaining how complex life forms emerge on earth. However, their gene composition, thermal stability and evolution in hyperthermal environments are still little known. Here, we characterized the pan-genome architecture of 30 Thermococcales species to gain insight into their genetic properties, evolutionary patterns and specific metabolisms adapted to niches. We revealed an open pan-genome of Thermococcales comprising 6070 gene families that tend to increase with the availability of additional genomes. The genome contents of Thermococcales were flexible, with a series of genes experienced gene duplication, progressive divergence, or gene gain and loss events exhibiting distinct functional features. These archaea had concise types of heat shock proteins, such as HSP20, HSP60 and prefoldin, which were constrained by strong purifying selection that governed their conservative evolution. Furthermore, purifying selection forced genes involved in enzyme, motility, secretion system, defence system and chaperones to differ in functional constraints and their disparity in the rate of evolution may be related to adaptation to specific niche. These results deepened our understanding of genetic diversity and adaptation patterns of Thermococcales, and provided valuable research models for studying the metabolic traits of early life forms.     

Constraints and selection: insights from microsporogenesis in Asparagales

Developmental constraints have been proposed to interfere with natural selection in limiting the available set of potential adaptations. Whereas this concept has long been debated on theoretical grounds, it has been investigated empirically only in a few studies. In this article, we evaluate the importance of developmental constraints during microsporogenesis (male meiosis in plants), with an emphasis on phylogenetic patterns in Asparagales. Different developmental constraints were tested by character reshuffling or by simulated distributions. Among the different characteristics of microsporogenesis, only cell wall formation appeared as constrained. We show that constraints may also result from biases in the correlated occurrence of developmental steps (e.g., lack of successive cytokinesis when wall formation is centripetal). We document such biases and their potential outcomes, notably the establishment of intermediate stages, which allow development to bypass such constraints. These insights are discussed with regard to potential selection on pollen morphology.     

Constrained multiple sequence alignment tool development and its application to RNase family alignment

In this paper, we design a heuristic algorithm of computing a constrained multiple sequence alignment (CMSA for short) for guaranteeing that the generated alignment satisfies the user-specified constraints that some particular residues should be aligned together. If the number of residues needed to be aligned together is a constant alpha, then the time-complexity of our CMSA algorithm for aligning K sequences is O(alphaKn(4)), where n is the maximum of the lengths of sequences. In addition, we have built up such a CMSA software system and made several experiments on the RNase sequences, which mainly function in catalyzing the degradation of RNA molecules. The resulting alignments illustrate the practicability of our method.     

Further structural optimization of cis-(6-benzhydryl-piperidin-3-yl)-benzylamine and 1,4-diazabicyclo[3.3.1]nonane derivatives by introducing an exocyclic hydroxyl group: interaction with dopamine, serotonin, and norepinephrine transporters

Our earlier effort to develop constrained analogues of flexible piperidine derivatives for monoamine transporters led to the development of a series of 3,6-disubstituted piperidine derivatives, and a series of 4,8-disubstituted 1,4-diazabicyclo[3.3.1]nonane derivatives. In further structure-activity relationship (SAR) studies on these constrained derivatives, several novel analogues were developed where an exocyclic hydroxyl group was introduced on the N-alkyl-aryl side chain. All synthesized derivatives were tested for their affinities for the dopamine transporter (DAT), serotonin (5-HT) transporter (SERT), and norepinephrine transporter (NET) in the brain by measuring their potency in inhibiting the uptake of [(3)H]DA, [(3)H]5-HT, and [(3)H]NE, respectively. Compounds were also tested for their binding potency at the DAT by their ability to inhibit binding of [(3)H]WIN 35,428. The results indicated that position of the hydroxyl group on the N-alkyl side chain is important along with the length of the side chain. In general, hydroxyl derivatives derived from more constrained bicyclic diamines exhibited greater selectivity for interaction with DAT compared to the corresponding 3,6-disubstituted diamines. In the current series of molecules, compound 11b with N-propyl side chain with the hydroxyl group attached in the benzylic position was the most potent and selective for DAT (K(i)=8.63nM; SERT/DAT=172 and NET/DAT=48.4).     

A Self-Organizing Algorithm for Modeling Protein Loops

Protein loops, the flexible short segments connecting two stable secondary structural units in proteins, play a critical role in protein structure and function. Constructing chemically sensible conformations of protein loops that seamlessly bridge the gap between the anchor points without introducing any steric collisions remains an open challenge. A variety of algorithms have been developed to tackle the loop closure problem, ranging from inverse kinematics to knowledge-based approaches that utilize pre-existing fragments extracted from known protein structures. However, many of these approaches focus on the generation of conformations that mainly satisfy the fixed end point condition, leaving the steric constraints to be resolved in subsequent post-processing steps. In the present work, we describe a simple solution that simultaneously satisfies not only the end point and steric conditions, but also chirality and planarity constraints. Starting from random initial atomic coordinates, each individual conformation is generated independently by using a simple alternating scheme of pairwise distance adjustments of randomly chosen atoms, followed by fast geometric matching of the conformationally rigid components of the constituent amino acids. The method is conceptually simple, numerically stable and computationally efficient. Very importantly, additional constraints, such as those derived from NMR experiments, hydrogen bonds or salt bridges, can be incorporated into the algorithm in a straightforward and inexpensive way, making the method ideal for solving more complex multi-loop problems. The remarkable performance and robustness of the algorithm are demonstrated on a set of protein loops of length 4, 8, and 12 that have been used in previous studies.     

Two- and Higher Point Correlation Functions in Proteins

Abstract

A method is presented for a more efficient sampling of the configurational space of proteins as compared to conventional sampling techniques such as molecular dynamics. The method is based on the large conformational changes in proteins revealed by the “essential dynamics” analysis. A form of constrained dynamics is performed, forcing the system to move along some of the essential coordinates. This results in a broader sampling of the essential subspace than in a comparable conventional molecular dynamics simulation without constraints. The new sampling method (essential dynamics sampling) was applied to the histidine-containing phosphocarrier protein HPr. The results indicate that the essential dynamics sampling method produces physically allowed structures, as estimated by the evaluation of many geometrical properties. In addition, a study of the motions in the essential subspace reveals a diffusion-like behavior.