Regimes and mechanisms of transient amplification in abstract and biological neural networks

Neuronal networks encode information through patterns of activity that define the networks’ function. The neurons’ activity relies on specific connectivity structures, yet the link between structure and function is not fully understood. Here, we tackle this structure-function problem with a new conceptual approach. Instead of manipulating the connectivity directly, we focus on upper triangular matrices, which represent the network dynamics in a given orthonormal basis obtained by the Schur decomposition. This abstraction allows us to independently manipulate the eigenspectrum and feedforward structures of a connectivity matrix. Using this method, we describe a diverse repertoire of non-normal transient amplification, and to complement the analysis of the dynamical regimes, we quantify the geometry of output trajectories through the effective rank of both the eigenvector and the dynamics matrices. Counter-intuitively, we find that shrinking the eigenspectrum’s imaginary distribution leads to highly amplifying regimes in linear and long-lasting dynamics in nonlinear networks. We also find a trade-off between amplification and dimensionality of neuronal dynamics, i.e., trajectories in neuronal state-space. Networks that can amplify a large number of orthogonal initial conditions produce neuronal trajectories that lie in the same subspace of the neuronal state-space. Finally, we examine networks of excitatory and inhibitory neurons. We find that the strength of global inhibition is directly linked with the amplitude of amplification, such that weakening inhibitory weights also decreases amplification, and that the eigenspectrum’s imaginary distribution grows with an increase in the ratio between excitatory-to-inhibitory and excitatory-to-excitatory connectivity strengths. Consequently, the strength of global inhibition reveals itself as a strong signature for amplification and a potential control mechanism to switch dynamical regimes. Our results shed a light on how biological networks, i.e., networks constrained by Dale’s law, may be optimised for specific dynamical regimes.     

Surfection: a new platform for transfected cell arrays

Efficient high-throughput expression of genes in mammalian cells can facilitate large-scale functional genomic studies. Towards this aim, we developed a simple yet powerful method to deliver genes into cells by cationic polymers on the surface of substrates. Transfection can be achieved by directly contacting nucleic acid–cell mixtures with the cationic substrates, e.g. polyethylenimine/collagen-coated wells. This single-step matrix-surface- mediated transfection method, termed ‘surfection’, can efficiently deliver multiple plasmids into cells and can successfully assay siRNA-mediated gene silencing. This technology represents the easiest method to transfer combinations of genes in large-scale arrays, and is a versatile tool for live-cell imaging and cell-based drug screening.     

Enhanced Growth of Endothelial Precursor Cells on PCG-Matrix Facilitates Accelerated,Fibrosis-Free,Wound Healing: A Diabetic Mouse Model

Diabetes mellitus (DM)-induced endothelial progenitor cell (EPC) dysfunction causes impaired wound healing, which can be rescued by delivery of large numbers of ‘normal’ EPCs onto such wounds. The principal challenges herein are (a) the high number of EPCs required and (b) their sustained delivery onto the wounds. Most of the currently available scaffolds either serve as passive devices for cellular delivery or allow adherence and proliferation, but not both. This clearly indicates that matrices possessing both attributes are ‘the need of the day’ for efficient healing of diabetic wounds. Therefore, we developed a system that not only allows selective enrichment and expansion of EPCs, but also efficiently delivers them onto the wounds. Murine bone marrow-derived mononuclear cells (MNCs) were seeded onto a PolyCaprolactone-Gelatin (PCG) nano-fiber matrix that offers a combined advantage of strength, biocompatibility wettability; and cultured them in EGM2 to allow EPC growth. The efficacy of the PCG matrix in supporting the EPC growth and delivery was assessed by various in vitro parameters. Its efficacy in diabetic wound healing was assessed by a topical application of the PCG-EPCs onto diabetic wounds. The PCG matrix promoted a high-level attachment of EPCs and enhanced their growth, colony formation, and proliferation without compromising their viability as compared to Poly L-lactic acid (PLLA) and Vitronectin (VN), the matrix and non-matrix controls respectively. The PCG-matrix also allowed a sustained chemotactic migration of EPCs in vitro. The matrix-effected sustained delivery of EPCs onto the diabetic wounds resulted in an enhanced fibrosis-free wound healing as compared to the controls. Our data, thus, highlight the novel therapeutic potential of PCG-EPCs as a combined ‘growth and delivery system’ to achieve an accelerated fibrosis-free healing of dermal lesions, including diabetic wounds.     

A Two-Stage Algorithm for Origin-Destination Matrices Estimation Considering Dynamic Dispersion Parameter for Route Choice

This paper proposes a two-stage algorithm to simultaneously estimate origin-destination (OD) matrix, link choice proportion, and dispersion parameter using partial traffic counts in a congested network. A non-linear optimization model is developed which incorporates a dynamic dispersion parameter, followed by a two-stage algorithm in which Generalized Least Squares (GLS) estimation and a Stochastic User Equilibrium (SUE) assignment model are iteratively applied until the convergence is reached. To evaluate the performance of the algorithm, the proposed approach is implemented in a hypothetical network using input data with high error, and tested under a range of variation coefficients. The root mean squared error (RMSE) of the estimated OD demand and link flows are used to evaluate the model estimation results. The results indicate that the estimated dispersion parameter theta is insensitive to the choice of variation coefficients. The proposed approach is shown to outperform two established OD estimation methods and produce parameter estimates that are close to the ground truth. In addition, the proposed approach is applied to an empirical network in Seattle, WA to validate the robustness and practicality of this methodology. In summary, this study proposes and evaluates an innovative computational approach to accurately estimate OD matrices using link-level traffic flow data, and provides useful insight for optimal parameter selection in modeling travelers’ route choice behavior.     

Generative models of rich clubs in Hebbian neuronal networks and large-scale human brain networks

Rich clubs arise when nodes that are ‘rich’ in connections also form an elite, densely connected ‘club’. In brain networks, rich clubs incur high physical connection costs but also appear to be especially valuable to brain function. However, little is known about the selection pressures that drive their formation. Here, we take two complementary approaches to this question: firstly we show, using generative modelling, that the emergence of rich clubs in large-scale human brain networks can be driven by an economic trade-off between connection costs and a second, competing topological term. Secondly we show, using simulated neural networks, that Hebbian learning rules also drive the emergence of rich clubs at the microscopic level, and that the prominence of these features increases with learning time. These results suggest that Hebbian learning may provide a neuronal mechanism for the selection of complex features such as rich clubs. The neural networks that we investigate are explicitly Hebbian, and we argue that the topological term in our model of large-scale brain connectivity may represent an analogous connection rule. This putative link between learning and rich clubs is also consistent with predictions that integrative aspects of brain network organization are especially important for adaptive behaviour.     

Improved Estimation and Interpretation of Correlations in Neural Circuits

Ambitious projects aim to record the activity of ever larger and denser neuronal populations in vivo. Correlations in neural activity measured in such recordings can reveal important aspects of neural circuit organization. However, estimating and interpreting large correlation matrices is statistically challenging. Estimation can be improved by regularization, i.e. by imposing a structure on the estimate. The amount of improvement depends on how closely the assumed structure represents dependencies in the data. Therefore, the selection of the most efficient correlation matrix estimator for a given neural circuit must be determined empirically. Importantly, the identity and structure of the most efficient estimator informs about the types of dominant dependencies governing the system. We sought statistically efficient estimators of neural correlation matrices in recordings from large, dense groups of cortical neurons. Using fast 3D random-access laser scanning microscopy of calcium signals, we recorded the activity of nearly every neuron in volumes 200 μm wide and 100 μm deep (150–350 cells) in mouse visual cortex. We hypothesized that in these densely sampled recordings, the correlation matrix should be best modeled as the combination of a sparse graph of pairwise partial correlations representing local interactions and a low-rank component representing common fluctuations and external inputs. Indeed, in cross-validation tests, the covariance matrix estimator with this structure consistently outperformed other regularized estimators. The sparse component of the estimate defined a graph of interactions. These interactions reflected the physical distances and orientation tuning properties of cells: The density of positive ‘excitatory’ interactions decreased rapidly with geometric distances and with differences in orientation preference whereas negative ‘inhibitory’ interactions were less selective. Because of its superior performance, this ‘sparse+latent’ estimator likely provides a more physiologically relevant representation of the functional connectivity in densely sampled recordings than the sample correlation matrix.     

Different genomic relationship matrices for single-step analysis using phenotypic,pedigree and genomic information

Background

The incorporation of genomic coefficients into the numerator relationship matrix allows estimation of breeding values using all phenotypic, pedigree and genomic information simultaneously. In such a single-step procedure, genomic and pedigree-based relationships have to be compatible. As there are many options to create genomic relationships, there is a question of which is optimal and what the effects of deviations from optimality are.

Methods

Data of litter size (total number born per litter) for 338,346 sows were analyzed. Illumina PorcineSNP60 BeadChip genotypes were available for 1,989. Analyses were carried out with the complete data set and with a subset of genotyped animals and three generations pedigree (5,090 animals). A single-trait animal model was used to estimate variance components and breeding values. Genomic relationship matrices were constructed using allele frequencies equal to 0.5 (G05), equal to the average minor allele frequency (GMF), or equal to observed frequencies (GOF). A genomic matrix considering random ascertainment of allele frequencies was also used (GOF*). A normalized matrix (GN) was obtained to have average diagonal coefficients equal to 1. The genomic matrices were combined with the numerator relationship matrix creating H matrices.

Results

In G05 and GMF, both diagonal and off-diagonal elements were on average greater than the pedigree-based coefficients. In GOF and GOF*, the average diagonal elements were smaller than pedigree-based coefficients. The mean of off-diagonal coefficients was zero in GOF and GOF*. Choices of G with average diagonal coefficients different from 1 led to greater estimates of additive variance in the smaller data set. The correlation between EBV and genomic EBV (n = 1,989) were: 0.79 using G05, 0.79 using GMF, 0.78 using GOF, 0.79 using GOF*, and 0.78 using GN. Accuracies calculated by inversion increased with all genomic matrices. The accuracies of genomic-assisted EBV were inflated in all cases except when GN was used.

Conclusions

Parameter estimates may be biased if the genomic relationship coefficients are in a different scale than pedigree-based coefficients. A reasonable scaling may be obtained by using observed allele frequencies and re-scaling the genomic relationship matrix to obtain average diagonal elements of 1.     

A spectral theory for Wright’s inbreeding coefficients and related quantities

Wright’s inbreeding coefficient, F_ST, is a fundamental measure in population genetics. Assuming a predefined population subdivision, this statistic is classically used to evaluate population structure at a given genomic locus. With large numbers of loci, unsupervised approaches such as principal component analysis (PCA) have, however, become prominent in recent analyses of population structure. In this study, we describe the relationships between Wright’s inbreeding coefficients and PCA for a model of K discrete populations. Our theory provides an equivalent definition of F_ST based on the decomposition of the genotype matrix into between and within-population matrices. The average value of Wright’s F_ST over all loci included in the genotype matrix can be obtained from the PCA of the between-population matrix. Assuming that a separation condition is fulfilled and for reasonably large data sets, this value of F_ST approximates the proportion of genetic variation explained by the first (K − 1) principal components accurately. The new definition of F_ST is useful for computing inbreeding coefficients from surrogate genotypes, for example, obtained after correction of experimental artifacts or after removing adaptive genetic variation associated with environmental variables. The relationships between inbreeding coefficients and the spectrum of the genotype matrix not only allow interpretations of PCA results in terms of population genetic concepts but extend those concepts to population genetic analyses accounting for temporal, geographical and environmental contexts.     

Large scale analysis of the mutational landscape in HT-SELEX improves aptamer discovery

High-Throughput (HT) SELEX combines SELEX (Systematic Evolution of Ligands by EXponential Enrichment), a method for aptamer discovery, with massively parallel sequencing technologies. This emerging technology provides data for a global analysis of the selection process and for simultaneous discovery of a large number of candidates but currently lacks dedicated computational approaches for their analysis. To close this gap, we developed novel in-silico methods to analyze HT-SELEX data and utilized them to study the emergence of polymerase errors during HT-SELEX. Rather than considering these errors as a nuisance, we demonstrated their utility for guiding aptamer discovery. Our approach builds on two main advancements in aptamer analysis: AptaMut—a novel technique allowing for the identification of polymerase errors conferring an improved binding affinity relative to the ‘parent’ sequence and AptaCluster—an aptamer clustering algorithm which is to our best knowledge, the only currently available tool capable of efficiently clustering entire aptamer pools. We applied these methods to an HT-SELEX experiment developing aptamers against Interleukin 10 receptor alpha chain (IL-10RA) and experimentally confirmed our predictions thus validating our computational methods.     

Tracking Time Evolution of Collective Attention Clusters in Twitter: Time Evolving Nonnegative Matrix Factorisation

Micro-blogging services, such as Twitter, offer opportunities to analyse user behaviour. Discovering and distinguishing behavioural patterns in micro-blogging services is valuable. However, it is difficult and challenging to distinguish users, and to track the temporal development of collective attention within distinct user groups in Twitter. In this paper, we formulate this problem as tracking matrices decomposed by Nonnegative Matrix Factorisation for time-sequential matrix data, and propose a novel extension of Nonnegative Matrix Factorisation, which we refer to as Time Evolving Nonnegative Matrix Factorisation (TENMF). In our method, we describe users and words posted in some time interval by a matrix, and use several matrices as time-sequential data. Subsequently, we apply Time Evolving Nonnegative Matrix Factorisation to these time-sequential matrices. TENMF can decompose time-sequential matrices, and can track the connection among decomposed matrices, whereas previous NMF decomposes a matrix into two lower dimension matrices arbitrarily, which might lose the time-sequential connection. Our proposed method has an adequately good performance on artificial data. Moreover, we present several results and insights from experiments using real data from Twitter.     

Neurokernel: An Open Source Platform for Emulating the Fruit Fly Brain

We have developed an open software platform called Neurokernel for collaborative development of comprehensive models of the brain of the fruit fly Drosophila melanogaster and their execution and testing on multiple Graphics Processing Units (GPUs). Neurokernel provides a programming model that capitalizes upon the structural organization of the fly brain into a fixed number of functional modules to distinguish between these modules’ local information processing capabilities and the connectivity patterns that link them. By defining mandatory communication interfaces that specify how data is transmitted between models of each of these modules regardless of their internal design, Neurokernel explicitly enables multiple researchers to collaboratively model the fruit fly’s entire brain by integration of their independently developed models of its constituent processing units. We demonstrate the power of Neurokernel’s model integration by combining independently developed models of the retina and lamina neuropils in the fly’s visual system and by demonstrating their neuroinformation processing capability. We also illustrate Neurokernel’s ability to take advantage of direct GPU-to-GPU data transfers with benchmarks that demonstrate scaling of Neurokernel’s communication performance both over the number of interface ports exposed by an emulation’s constituent modules and the total number of modules comprised by an emulation.     

Model Development for Risk Assessment of Driving on Freeway under Rainy Weather Conditions

Rainy weather conditions could result in significantly negative impacts on driving on freeways. However, due to lack of enough historical data and monitoring facilities, many regions are not able to establish reliable risk assessment models to identify such impacts. Given the situation, this paper provides an alternative solution where the procedure of risk assessment is developed based on drivers’ subjective questionnaire and its performance is validated by using actual crash data. First, an ordered logit model was developed, based on questionnaire data collected from Freeway G15 in China, to estimate the relationship between drivers’ perceived risk and factors, including vehicle type, rain intensity, traffic volume, and location. Then, weighted driving risk for different conditions was obtained by the model, and further divided into four levels of early warning (specified by colors) using a rank order cluster analysis. After that, a risk matrix was established to determine which warning color should be disseminated to drivers, given a specific condition. Finally, to validate the proposed procedure, actual crash data from Freeway G15 were compared with the safety prediction based on the risk matrix. The results show that the risk matrix obtained in the study is able to predict driving risk consistent with actual safety implications, under rainy weather conditions.     

Shock Treatment: Using Immersive Digital Realism to Restage and Re-examine Milgram’s ‘Obedience to Authority’ Research

Attempts to revisit Milgram’s ‘Obedience to Authority’ (OtA) paradigm present serious ethical challenges. In recent years new paradigms have been developed to circumvent these challenges but none involve using Milgram’s own procedures and asking naïve participants to deliver the maximum level of shock. This was achieved in the present research by using Immersive Digital Realism (IDR) to revisit the OtA paradigm. IDR is a dramatic method that involves a director collaborating with professional actors to develop characters, the strategic withholding of contextual information, and immersion in a real-world environment. 14 actors took part in an IDR study in which they were assigned to conditions that restaged Milgrams’s New Baseline (‘Coronary’) condition and four other variants. Post-experimental interviews also assessed participants’ identification with Experimenter and Learner. Participants’ behaviour closely resembled that observed in Milgram’s original research. In particular, this was evidenced by (a) all being willing to administer shocks greater than 150 volts, (b) near-universal refusal to continue after being told by the Experimenter that “you have no other choice, you must continue” (Milgram’s fourth prod and the one most resembling an order), and (c) a strong correlation between the maximum level of shock that participants administered and the mean maximum shock delivered in the corresponding variant in Milgram’s own research. Consistent with an engaged follower account, relative identification with the Experimenter (vs. the Learner) was also a good predictor of the maximum shock that participants administered.     

A matrix of 3,4-diaminobenzophenone for the analysis of oligonucleotides by matrix-assisted laser desorption/ionization time-of-flight mass spectrometry

A new matrix of 3,4-diaminobenzophenone (DABP) was demonstrated to be advantageous in the analysis of oligonucleotides by matrix-assisted laser desorption/ionization time-of-flight mass spectrometry. With DABP as a matrix, intact oligonucleotide ions can be readily produced with lower laser powers, resulting in better detection limits, less fragmentation and fewer alkali metal ion adducts compared with the results obtained with conventional matrices. Importantly, minimal fragmentation and fewer alkali metal ion adducts were seen even at low concentrations of oligonucleotides. It was also found that samples prepared with DABP are highly homogenous and therefore reducing the need for finding ‘sweet’ spots in MALDI. In addition, excellent shot-to-shot reproducibility, resolution and signal-to-noise ratio were seen with DABP as the matrix.     

New Approaches for Calculating Moran’s Index of Spatial Autocorrelation

Spatial autocorrelation plays an important role in geographical analysis; however, there is still room for improvement of this method. The formula for Moran’s index is complicated, and several basic problems remain to be solved. Therefore, I will reconstruct its mathematical framework using mathematical derivation based on linear algebra and present four simple approaches to calculating Moran’s index. Moran’s scatterplot will be ameliorated, and new test methods will be proposed. The relationship between the global Moran’s index and Geary’s coefficient will be discussed from two different vantage points: spatial population and spatial sample. The sphere of applications for both Moran’s index and Geary’s coefficient will be clarified and defined. One of theoretical findings is that Moran’s index is a characteristic parameter of spatial weight matrices, so the selection of weight functions is very significant for autocorrelation analysis of geographical systems. A case study of 29 Chinese cities in 2000 will be employed to validate the innovatory models and methods. This work is a methodological study, which will simplify the process of autocorrelation analysis. The results of this study will lay the foundation for the scaling analysis of spatial autocorrelation.     

Methods to estimate breeding values in honey bees

Background

Efficient methodologies based on animal models are widely used to estimate breeding values in farm animals. These methods are not applicable in honey bees because of their mode of reproduction. Observations are recorded on colonies, which consist of a single queen and thousands of workers that descended from the queen mated to 10 to 20 drones. Drones are haploid and sperms are copies of a drone’s genotype. As a consequence, Mendelian sampling terms of full-sibs are correlated, such that the covariance matrix of Mendelian sampling terms is not diagonal.

Results

In this paper, we show how the numerator relationship matrix and its inverse can be obtained for honey bee populations. We present algorithms to derive the covariance matrix of Mendelian sampling terms that accounts for correlated terms. The resulting matrix is a block-diagonal matrix, with a small block for each full-sib family, and is easy to invert numerically. The method allows incorporating the within-colony distribution of progeny from drone-producing queens and drones, such that estimates of breeding values weigh information from relatives appropriately. Simulation shows that the resulting estimated breeding values are unbiased predictors of true breeding values. Benefits for response to selection, compared to an existing approximate method, appear to be limited (~5%). Benefits may however be greater when estimating genetic parameters.

Conclusions

This work shows how the relationship matrix and its inverse can be developed for honey bee populations, and used to estimate breeding values and variance components.     

siRNA-mediated off-target gene silencing triggered by a 7 nt complementation

A growing body of evidence suggests that siRNA could generate off-target effects through different mechanisms. However, the full impact of off-target gene regulation on phenotypic induction and accordingly on data interpretation in the context of large-scale siRNA library screen has not been reported. Here we report on off-target gene silencing effects observed in a large-scale knockdown experiment designed to identify novel regulators of the HIF-1 pathway. All of the three ‘top hits’ from our screen have been demonstrated to result from off-target gene silencing. Two of the three ‘siRNA hits’ were found to directly trigger down-regulation of hif-1α mRNA through a 7 nt motif, AGGCAGT, that is present in both the hif-1α mRNA and the siRNAs. Further analysis revealed that the generation of off-target gene silencing via this 7 nt motif depends on the characteristics of the target mRNA, including the sequence context surrounding the complementary region, the position of the complementary region in the mRNA and the copy number of the complementary region. Interestingly, the off-target siRNA against hif-1α was also shown to trigger mRNA degradation with high probability of other genes that possess multiple copies of the AGGCAGT motif in the 3′-untranslated region. Lessons learned from this study will be a valuable asset to aid in designing siRNAs with more stringent target selectivity and improving ‘hits-follow-up’ strategies for future large-scale knockdown experiments.     

BALSA: Bayesian algorithm for local sequence alignment

The Smith–Waterman algorithm yields a single alignment, which, albeit optimal, can be strongly affected by the choice of the scoring matrix and the gap penalties. Additionally, the scores obtained are dependent upon the lengths of the aligned sequences, requiring a post-analysis conversion. To overcome some of these shortcomings, we developed a Bayesian algorithm for local sequence alignment (BALSA), that takes into account the uncertainty associated with all unknown variables by incorporating in its forward sums a series of scoring matrices, gap parameters and all possible alignments. The algorithm can return both the joint and the marginal optimal alignments, samples of alignments drawn from the posterior distribution and the posterior probabilities of gap penalties and scoring matrices. Furthermore, it automatically adjusts for variations in sequence lengths. BALSA was compared with SSEARCH, to date the best performing dynamic programming algorithm in the detection of structural neighbors. Using the SCOP databases PDB40D-B and PDB90D-B, BALSA detected 19.8 and 41.3% of remote homologs whereas SSEARCH detected 18.4 and 38% at an error rate of 1% errors per query over the databases, respectively.