Spatiotemporal multi-resolution approximation of the Amari type neural field model

Neural fields are spatially continuous state variables described by integro-differential equations, which are well suited to describe the spatiotemporal evolution of cortical activations on multiple scales. Here we develop a multi-resolution approximation (MRA) framework for the integro-difference equation (IDE) neural field model based on semi-orthogonal cardinal B-spline wavelets. In this way, a flexible framework is created, whereby both macroscopic and microscopic behavior of the system can be represented simultaneously. State and parameter estimation is performed using the expectation maximization (EM) algorithm. A synthetic example is provided to demonstrate the framework

Loss of UGP2 in brain leads to a severe epileptic encephalopathy, emphasizing that bi-allelic isoform-specific start-loss mutations of essential genes can cause genetic diseases.

Developmental and/or epileptic encephalopathies (DEEs) are a group of devastating genetic disorders, resulting in early-onset, therapy-resistant seizures and developmental delay. Here we report on 22 individuals from 15 families presenting with a severe form of intractable epilepsy, severe developmental delay, progressive microcephaly, visual disturbance and similar minor dysmorphisms. Whole exome sequencing identified a recurrent, homozygous variant (chr2:64083454A > G) in the essential UDP-glucose pyrophosphorylase (UGP2) gene in all probands. This rare variant results in a tolerable Met12Val missense change of the longer UGP2 protein isoform but causes a disruption of the start codon of the shorter isoform, which is predominant in brain. We show that the absence of the shorter isoform leads to a reduction of functional UGP2 enzyme in neural stem cells, leading to altered glycogen metabolism, upregulated unfolded protein response and premature neuronal differentiation, as modeled during pluripotent stem cell differentiation in vitro. In contrast, the complete lack of all UGP2 isoforms leads to differentiation defects in multiple lineages in human cells. Reduced expression of Ugp2a/Ugp2b in vivo in zebrafish mimics visual disturbance and mutant animals show a behavioral phenotype. Our study identifies a recurrent start codon mutation in UGP2 as a cause of a novel autosomal recessive DEE syndrome. Importantly, it also shows that isoform-specific start-loss mutations causing expression loss of a tissue-relevant isoform of an essential protein can cause a genetic disease, even when an organism-wide protein absence is incompatible with life. We provide additional examples where a similar disease mechanism applies

Weak Spatial and Temporal Population Genetic Structure in the Rosy Apple Aphid, Dysaphis plantaginea, in French Apple Orchards

We used eight microsatellite loci and a set of 20 aphid samples to investigate the spatial and temporal genetic structure of rosy apple aphid populations from 13 apple orchards situated in four different regions in France. Genetic variability was very similar between orchard populations and between winged populations collected before sexual reproduction in the fall and populations collected from colonies in the spring. A very small proportion of individuals (∼2%) had identical multilocus genotypes. Genetic differentiation between orchards was low (FST<0.026), with significant differentiation observed only between orchards from different regions, but no isolation by distance was detected. These results are consistent with high levels of genetic mixing in holocyclic Dysaphis plantaginae populations (host alternation through migration and sexual reproduction). These findings concerning the adaptation of the rosy apple aphid have potential consequences for pest management

Population based models of cortical drug response: insights from anaesthesia

A great explanatory gap lies between the molecular pharmacology of psychoactive agents and the neurophysiological changes they induce, as recorded by neuroimaging modalities. Causally relating the cellular actions of psychoactive compounds to their influence on population activity is experimentally challenging. Recent developments in the dynamical modelling of neural tissue have attempted to span this explanatory gap between microscopic targets and their macroscopic neurophysiological effects via a range of biologically plausible dynamical models of cortical tissue. Such theoretical models allow exploration of neural dynamics, in particular their modification by drug action. The ability to theoretically bridge scales is due to a biologically plausible averaging of cortical tissue properties. In the resulting macroscopic neural field, individual neurons need not be explicitly represented (as in neural networks). The following paper aims to provide a non-technical introduction to the mean field population modelling of drug action and its recent successes in modelling anaesthesia

Cortical Resonance Frequencies Emerge from Network Size and Connectivity

Neural oscillations occur within a wide frequency range with different brain regions exhibiting resonance-like characteristics at specific points in the spectrum. At the microscopic scale, single neurons possess intrinsic oscillatory properties, such that is not yet known whether cortical resonance is consequential to neural oscillations or an emergent property of the networks that interconnect them. Using a network model of loosely-coupled Wilson-Cowan oscillators to simulate a patch of cortical sheet, we demonstrate that the size of the activated network is inversely related to its resonance frequency. Further analysis of the parameter space indicated that the number of excitatory and inhibitory connections, as well as the average transmission delay between units, determined the resonance frequency. The model predicted that if an activated network within the visual cortex increased in size, the resonance frequency of the network would decrease. We tested this prediction experimentally using the steady-state visual evoked potential where we stimulated the visual cortex with different size stimuli at a range of driving frequencies. We demonstrate that the frequency corresponding to peak steady-state response inversely correlated with the size of the network. We conclude that although individual neurons possess resonance properties, oscillatory activity at the macroscopic level is strongly influenced by network interactions, and that the steady-state response can be used to investigate functional networks

How Does a Divided Population Respond to Change?

<div><p>Most studies on the response of socioeconomic systems to a sudden shift focus on long-term equilibria or end points. Such narrow focus forgoes many valuable insights. Here we examine the transient dynamics of regime shift on a divided population, exemplified by societies divided ideologically, politically, economically, or technologically. Replicator dynamics is used to investigate the complex transient dynamics of the population response. Though simple, our modeling approach exhibits a surprisingly rich and diverse array of dynamics. Our results highlight the critical roles played by diversity in strategies and the magnitude of the shift. Importantly, it allows for a variety of strategies to arise organically as an integral part of the transient dynamics—as opposed to an independent process—of population response to a regime shift, providing a link between the population's past and future diversity patterns. Several combinations of different populations' strategy distributions and shifts were systematically investigated. Such rich dynamics highlight the challenges of anticipating the response of a divided population to a change. The findings in this paper can potentially improve our understanding of a wide range of socio-ecological and technological transitions.</p></div

Snapshots show different number of coexisting peaks when Δs1*>Δscrit*>Δs2* and <i>D</i>₁ > <i>D</i>₂.

<p>Top panels (A.1) show the coexistence of three peaks at <i>t</i> = 14 and (A.2) shows how the newly emerging peak near </p><p></p><p></p><p></p><p><mi>s</mi><mi>R</mi><mo>*</mo></p><p></p><p></p><p></p> dominates over the moving peak originated near <p></p><p></p><p></p><p><mi>s</mi><mn>2</mn><mo>*</mo></p><p></p><p></p><p></p> at <i>t</i> = 20, (where <p></p><p></p><p><mo>Δ</mo></p><p><mi>s</mi><mn>1</mn><mo>*</mo></p><mo>=</mo><mn>0</mn><mo>.</mo><mn>3</mn><p></p><p></p><p></p>, <p></p><p></p><p><mo>Δ</mo></p><p><mi>s</mi><mn>2</mn><mo>*</mo></p><mo>=</mo><mn>0</mn><mo>.</mo><mn>2</mn><p></p><p></p><p></p>, <p></p><p></p><p><mo>Δ</mo></p><p><mi>s</mi></p><p><mi>c</mi><mi>r</mi><mi>i</mi><mi>t</mi></p><mo>*</mo><p></p><mo>=</mo><mn>0</mn><mo>.</mo><mn>2589</mn><p></p><p></p><p></p>, with <p></p><p></p><p></p><p><mi>s</mi><mn>1</mn><mo>*</mo></p><mo>=</mo><mn>0</mn><mo>.</mo><mn>2</mn><p></p><p></p><p></p>, <p></p><p></p><p></p><p><mi>s</mi><mn>2</mn><mo>*</mo></p><mo>=</mo><mn>0</mn><mo>.</mo><mn>7</mn><p></p><p></p><p></p>, <p></p><p></p><p></p><p><mi>s</mi><mi>R</mi><mo>*</mo></p><mo>=</mo><mn>0</mn><mo>.</mo><mn>5</mn><p></p><p></p><p></p>, and <i>σ</i> = 0.1, with <i>D</i>₁ = 0.05 and <i>D</i>₂ = 0.02, see Video J in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0128121#pone.0128121.s001" target="_blank">S1 File</a>. B) When <p></p><p></p><p><mo>Δ</mo></p><p><mi>s</mi><mn>1</mn><mo>*</mo></p><p></p><p></p><p></p> is too large, the the moving peak originated near <p></p><p></p><p></p><p><mi>s</mi><mn>2</mn><mo>*</mo></p><p></p><p></p><p></p> will dominate and no emergence of a new peak near <p></p><p></p><p></p><p><mi>s</mi><mi>R</mi><mo>*</mo></p><p></p><p></p><p></p> (where <p></p><p></p><p><mo>Δ</mo></p><p><mi>s</mi><mn>1</mn><mo>*</mo></p><mo>=</mo><mn>0</mn><mo>.</mo><mn>45</mn><p></p><p></p><p></p>, <p></p><p></p><p><mo>Δ</mo></p><p><mi>s</mi><mn>2</mn><mo>*</mo></p><mo>=</mo><mn>0</mn><mo>.</mo><mn>2</mn><p></p><p></p><p></p>, <p></p><p></p><p><mo>Δ</mo></p><p><mi>s</mi></p><p><mi>c</mi><mi>r</mi><mi>i</mi><mi>t</mi></p><mo>*</mo><p></p><mo>=</mo><mn>0</mn><mo>.</mo><mn>2589</mn><p></p><p></p><p></p>, with <p></p><p></p><p></p><p><mi>s</mi><mn>1</mn><mo>*</mo></p><mo>=</mo><mn>0</mn><mo>.</mo><mn>05</mn><p></p><p></p><p></p>, <p></p><p></p><p></p><p><mi>s</mi><mn>2</mn><mo>*</mo></p><mo>=</mo><mn>0</mn><mo>.</mo><mn>7</mn><p></p><p></p><p></p>, <p></p><p></p><p></p><p><mi>s</mi><mi>R</mi><mo>*</mo></p><mo>=</mo><mn>0</mn><mo>.</mo><mn>5</mn><p></p><p></p><p></p>, and <i>σ</i> = 0.1, with <i>D</i>₁ = 0.08 and <i>D</i>₂ = 0.06. see Video K in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0128121#pone.0128121.s001" target="_blank">S1 File</a>). The dashed lines show the locations of <p></p><p></p><p></p><p><mi>s</mi><mn>1</mn><mo>*</mo></p><p></p><p></p><p></p>, <p></p><p></p><p></p><p><mi>s</mi><mn>2</mn><mo>*</mo></p><p></p><p></p><p></p>, and <p></p><p></p><p></p><p><mi>s</mi><mi>R</mi><mo>*</mo></p><p></p><p></p><p></p>, while the solid lines represent the the theoretically calculated threshold(s) for the single peak population distribution case, i.e., <p></p><p></p><p><mo>Δ</mo></p><p><mi>s</mi></p><p><mi>c</mi><mi>r</mi><mi>i</mi><mi>t</mi></p><mo>*</mo><p></p><mo>=</mo><mn>3</mn><p><mn>3</mn></p><mi>σ</mi><mo>/</mo><mn>2</mn><p></p><p></p><p></p>.<p></p

Different snapshots at different times for the case of Δs1*>Δscrit*>Δs2* and with asymmetric variations (where Δs1*=0.6, Δs2*=0.3, Δscrit*=0.5196, with s1*=0.2, s2*=0.5, sR*=0.8, <i>σ</i> = 0.2, with <i>D</i>₁ = 0.05 and <i>D</i>₂ = 0.02, see Video V in S1 File).

<p>Note that the peak initially around </p><p></p><p></p><p></p><p><mi>s</mi><mn>1</mn><mo>*</mo></p><p></p><p></p><p></p> disintegrates completely while the other peak dominates temporarily before a new peak emerges suddenly and dominates at the end. The dashed lines show the locations of <p></p><p></p><p></p><p><mi>s</mi><mn>1</mn><mo>*</mo></p><p></p><p></p><p></p>, <p></p><p></p><p></p><p><mi>s</mi><mn>2</mn><mo>*</mo></p><p></p><p></p><p></p>, and <p></p><p></p><p></p><p><mi>s</mi><mi>R</mi><mo>*</mo></p><p></p><p></p><p></p>, while the solid lines represent the the theoretically calculated threshold(s) for the single peak population distribution case, i.e., <p></p><p></p><p><mo>Δ</mo></p><p><mi>s</mi></p><p><mi>c</mi><mi>r</mi><mi>i</mi><mi>t</mi></p><mo>*</mo><p></p><mo>=</mo><mn>3</mn><p><mn>3</mn></p><mi>σ</mi><mo>/</mo><mn>2</mn><p></p><p></p><p></p>.<p></p

Snapshots of the coexisting peaks for the extreme case.

<p>A) The top panel shows the coexistence of three peaks when </p><p></p><p></p><p><mo>Δ</mo></p><p><mi>s</mi><mn>1</mn><mo>*</mo></p><mo>=</mo><mn>0</mn><mo>.</mo><mn>65</mn><mo>,</mo><mo>Δ</mo><p><mi>s</mi><mn>2</mn><mo>*</mo></p><mo>=</mo><mn>0</mn><mo>.</mo><mn>35</mn><mo>></mo><mo>Δ</mo><p><mi>s</mi></p><p><mi>c</mi><mi>r</mi><mi>i</mi><mi>t</mi></p><mo>*</mo><p></p><mo>=</mo><mn>0</mn><mo>.</mo><mn>2598</mn><mo>,</mo><p></p><p></p><p></p> and with <i>symmetric</i> variations, i.e., <i>D</i>₁ = <i>D</i>₂ = 0.2 (where <p></p><p></p><p></p><p><mi>s</mi><mn>1</mn><mo>*</mo></p><mo>=</mo><mn>0</mn><mo>.</mo><mn>15</mn><p></p><p></p><p></p>, <p></p><p></p><p></p><p><mi>s</mi><mn>2</mn><mo>*</mo></p><mo>=</mo><mn>0</mn><mo>.</mo><mn>45</mn><p></p><p></p><p></p>, <p></p><p></p><p></p><p><mi>s</mi><mi>R</mi><mo>*</mo></p><mo>=</mo><mn>0</mn><mo>.</mo><mn>8</mn><p></p><p></p><p></p>, <i>σ</i> = 0.1), see Video O in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0128121#pone.0128121.s001" target="_blank">S1 File</a>. B) and C) Three or four peaks may coexist when <p></p><p></p><p><mo>Δ</mo></p><p><mi>s</mi><mn>1</mn><mo>*</mo></p><mo>=</mo><mn>0</mn><mo>.</mo><mn>5</mn><mo>,</mo><mo>Δ</mo><p><mi>s</mi><mn>2</mn><mo>*</mo></p><mo>=</mo><mn>0</mn><mo>.</mo><mn>3</mn><mo>></mo><mo>Δ</mo><p><mi>s</mi></p><p><mi>c</mi><mi>r</mi><mi>i</mi><mi>t</mi></p><mo>*</mo><p></p><mo>=</mo><mn>0</mn><mo>.</mo><mn>2598</mn><p></p><p></p><p></p> but with <i>asymmetric</i> variations, i.e., <i>D</i>₁ > <i>D</i>₂ (where <p></p><p></p><p></p><p><mi>s</mi><mn>1</mn><mo>*</mo></p><mo>=</mo><mn>0</mn><mo>.</mo><mn>3</mn><p></p><p></p><p></p>, <p></p><p></p><p></p><p><mi>s</mi><mn>2</mn><mo>*</mo></p><mo>=</mo><mn>0</mn><mo>.</mo><mn>5</mn><p></p><p></p><p></p>, <p></p><p></p><p></p><p><mi>s</mi><mi>R</mi><mo>*</mo></p><mo>=</mo><mn>0</mn><mo>.</mo><mn>8</mn><p></p><p></p><p></p>, <i>σ</i> = 0.1, with <i>D</i>₁ = 0.05 and <i>D</i>₂ = 0.02 for (B), and <i>D</i>₁ = 0.0420 and <i>D</i>₂ = 0.0225 for (C)), see R and S Videos in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0128121#pone.0128121.s001" target="_blank">S1 File</a>, respectively. The bottom panels (D.1 and D.2) show the snapshots at different times when <p></p><p></p><p><mo>Δ</mo></p><p><mi>s</mi><mn>1</mn><mo>*</mo></p><mo>=</mo><mn>0</mn><mo>.</mo><mn>35</mn><mo>></mo><mo>Δ</mo><p><mi>s</mi></p><p><mi>c</mi><mi>r</mi><mi>i</mi><mi>t</mi></p><mo>*</mo><p></p><mo>=</mo><mn>0</mn><mo>.</mo><mn>2598</mn><mo>></mo><mo>Δ</mo><p><mi>s</mi><mn>2</mn><mo>*</mo></p><mo>=</mo><mn>0</mn><mo>.</mo><mn>2</mn><p></p><p></p><p></p>, and with <i>asymmetric</i> variations (where <p></p><p></p><p></p><p><mi>s</mi><mn>1</mn><mo>*</mo></p><mo>=</mo><mn>0</mn><mo>.</mo><mn>45</mn><p></p><p></p><p></p>, <p></p><p></p><p></p><p><mi>s</mi><mn>2</mn><mo>*</mo></p><mo>=</mo><mn>0</mn><mo>.</mo><mn>6</mn><p></p><p></p><p></p>, <p></p><p></p><p></p><p><mi>s</mi><mi>R</mi><mo>*</mo></p><mo>=</mo><mn>0</mn><mo>.</mo><mn>8</mn><p></p><p></p><p></p>, <i>σ</i> = 0.1, with <i>D</i>₁ = 0.05 and <i>D</i>₂ = 0.01), see Video U in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0128121#pone.0128121.s001" target="_blank">S1 File</a>. The dashed lines show the locations of <p></p><p></p><p></p><p><mi>s</mi><mn>1</mn><mo>*</mo></p><p></p><p></p><p></p>, <p></p><p></p><p></p><p><mi>s</mi><mn>2</mn><mo>*</mo></p><p></p><p></p><p></p>, and <p></p><p></p><p></p><p><mi>s</mi><mi>R</mi><mo>*</mo></p><p></p><p></p><p></p>, while the solid lines represent the the theoretically calculated threshold(s) for the single peak population distribution case, i.e., <p></p><p></p><p><mo>Δ</mo></p><p><mi>s</mi></p><p><mi>c</mi><mi>r</mi><mi>i</mi><mi>t</mi></p><mo>*</mo><p></p><mo>=</mo><mn>3</mn><p><mn>3</mn></p><mi>σ</mi><mo>/</mo><mn>2</mn><p></p><p></p><p></p>.<p></p