Allometric cascade: a model for resolving body mass effects on metabolism

Expanding upon a preliminary communication (Nature 417 (2002) 166), we here further develop a "multiple-causes model" of allometry, where the exponent b is the sum of the influences of multiple contributors to control. The relative strength of each contributor, with its own characteristic value of b(i), is determined by c(i), the control contribution or control coefficient. A more realistic equation for the scaling of metabolism with body size thus can be written as BMR=MR(0)Sigmac(i)(M/M(0))(bi), where MR(0) is the "characteristic metabolic rate" of an animal with a "characteristic body mass", M(0). With M(0) of 1 unit mass (usually kg), MR(0) takes the place of the value a, found in the standard scaling equation, b(i) is the scaling exponent of the process i, and c(i) is its control contribution to overall flux, or the control coefficient of the process i. One can think of this as an allometric cascade, with the b exponent for overall energy metabolism being determined by the b(i) and c(i) values for key steps in the complex pathways of energy demand and energy supply. Key intrinsic factors (such as neural and endocrine processes) or ecological extrinsic factors are considered to act through this system in affecting allometric scaling of energy turnover. Applying this model to maximum vs. BMR data for the first time explains the differing scaling behaviour of these two biological states in mammals, both in the absence and presence of intrinsic regulators such as thyroid hormones (for BMR) and catecholamines (for maximum metabolic rate).     

Avalanches in Self-Organized Critical Neural Networks: A Minimal Model for the Neural SOC Universality Class

The brain keeps its overall dynamics in a corridor of intermediate activity and it has been a long standing question what possible mechanism could achieve this task. Mechanisms from the field of statistical physics have long been suggesting that this homeostasis of brain activity could occur even without a central regulator, via self-organization on the level of neurons and their interactions, alone. Such physical mechanisms from the class of self-organized criticality exhibit characteristic dynamical signatures, similar to seismic activity related to earthquakes. Measurements of cortex rest activity showed first signs of dynamical signatures potentially pointing to self-organized critical dynamics in the brain. Indeed, recent more accurate measurements allowed for a detailed comparison with scaling theory of non-equilibrium critical phenomena, proving the existence of criticality in cortex dynamics. We here compare this new evaluation of cortex activity data to the predictions of the earliest physics spin model of self-organized critical neural networks. We find that the model matches with the recent experimental data and its interpretation in terms of dynamical signatures for criticality in the brain. The combination of signatures for criticality, power law distributions of avalanche sizes and durations, as well as a specific scaling relationship between anomalous exponents, defines a universality class characteristic of the particular critical phenomenon observed in the neural experiments. Thus the model is a candidate for a minimal model of a self-organized critical adaptive network for the universality class of neural criticality. As a prototype model, it provides the background for models that may include more biological details, yet share the same universality class characteristic of the homeostasis of activity in the brain.     

Feedforward Inhibition and Synaptic Scaling – Two Sides of the Same Coin?

Feedforward inhibition and synaptic scaling are important adaptive processes that control the total input a neuron can receive from its afferents. While often studied in isolation, the two have been reported to co-occur in various brain regions. The functional implications of their interactions remain unclear, however. Based on a probabilistic modeling approach, we show here that fast feedforward inhibition and synaptic scaling interact synergistically during unsupervised learning. In technical terms, we model the input to a neural circuit using a normalized mixture model with Poisson noise. We demonstrate analytically and numerically that, in the presence of lateral inhibition introducing competition between different neurons, Hebbian plasticity and synaptic scaling approximate the optimal maximum likelihood solutions for this model. Our results suggest that, beyond its conventional use as a mechanism to remove undesired pattern variations, input normalization can make typical neural interaction and learning rules optimal on the stimulus subspace defined through feedforward inhibition. Furthermore, learning within this subspace is more efficient in practice, as it helps avoid locally optimal solutions. Our results suggest a close connection between feedforward inhibition and synaptic scaling which may have important functional implications for general cortical processing.     

Synaptic Scaling Enables Dynamically Distinct Short- and Long-Term Memory Formation

Memory storage in the brain relies on mechanisms acting on time scales from minutes, for long-term synaptic potentiation, to days, for memory consolidation. During such processes, neural circuits distinguish synapses relevant for forming a long-term storage, which are consolidated, from synapses of short-term storage, which fade. How time scale integration and synaptic differentiation is simultaneously achieved remains unclear. Here we show that synaptic scaling – a slow process usually associated with the maintenance of activity homeostasis – combined with synaptic plasticity may simultaneously achieve both, thereby providing a natural separation of short- from long-term storage. The interaction between plasticity and scaling provides also an explanation for an established paradox where memory consolidation critically depends on the exact order of learning and recall. These results indicate that scaling may be fundamental for stabilizing memories, providing a dynamic link between early and late memory formation processes.     

Can Power-Law Scaling and Neuronal Avalanches Arise from Stochastic Dynamics?

The presence of self-organized criticality in biology is often evidenced by a power-law scaling of event size distributions, which can be measured by linear regression on logarithmic axes. We show here that such a procedure does not necessarily mean that the system exhibits self-organized criticality. We first provide an analysis of multisite local field potential (LFP) recordings of brain activity and show that event size distributions defined as negative LFP peaks can be close to power-law distributions. However, this result is not robust to change in detection threshold, or when tested using more rigorous statistical analyses such as the Kolmogorov–Smirnov test. Similar power-law scaling is observed for surrogate signals, suggesting that power-law scaling may be a generic property of thresholded stochastic processes. We next investigate this problem analytically, and show that, indeed, stochastic processes can produce spurious power-law scaling without the presence of underlying self-organized criticality. However, this power-law is only apparent in logarithmic representations, and does not survive more rigorous analysis such as the Kolmogorov–Smirnov test. The same analysis was also performed on an artificial network known to display self-organized criticality. In this case, both the graphical representations and the rigorous statistical analysis reveal with no ambiguity that the avalanche size is distributed as a power-law. We conclude that logarithmic representations can lead to spurious power-law scaling induced by the stochastic nature of the phenomenon. This apparent power-law scaling does not constitute a proof of self-organized criticality, which should be demonstrated by more stringent statistical tests.     

Dynamic Neural Network Models of the Premotoneuronal Circuitry Controlling Wrist Movements in Primates

Dynamic recurrent neural networks were derived to simulate neuronal populations generating bidirectional wrist movements in the monkey. The models incorporate anatomical connections of cortical and rubral neurons, muscle afferents, segmental interneurons and motoneurons; they also incorporate the response profiles of four populations of neurons observed in behaving monkeys. The networks were derived by gradient descent algorithms to generate the eight characteristic patterns of motor unit activations observed during alternating flexion-extension wrist movements. The resulting model generated the appropriate input-output transforms and developed connection strengths resembling those in physiological pathways. We found that this network could be further trained to simulate additional tasks, such as experimentally observed reflex responses to limb perturbations that stretched or shortened the active muscles, and scaling of response amplitudes in proportion to inputs. In the final comprehensive network, motor units are driven by the combined activity of cortical, rubral, spinal and afferent units during step tracking and perturbations.The model displayed many emergent properties corresponding to physiological characteristics. The resulting neural network provides a working model of premotoneuronal circuitry and elucidates the neural mechanisms controlling motoneuron activity. It also predicts several features to be experimentally tested, for example the consequences of eliminating inhibitory connections in cortex and red nucleus. It also reveals that co-contraction can be achieved by simultaneous activation of the flexor and extensor circuits without invoking features specific to co-contraction.     

Divisive Gain Modulation with Dynamic Stimuli in Integrate-and-Fire Neurons

The modulation of the sensitivity, or gain, of neural responses to input is an important component of neural computation. It has been shown that divisive gain modulation of neural responses can result from a stochastic shunting from balanced (mixed excitation and inhibition) background activity. This gain control scheme was developed and explored with static inputs, where the membrane and spike train statistics were stationary in time. However, input statistics, such as the firing rates of pre-synaptic neurons, are often dynamic, varying on timescales comparable to typical membrane time constants. Using a population density approach for integrate-and-fire neurons with dynamic and temporally rich inputs, we find that the same fluctuation-induced divisive gain modulation is operative for dynamic inputs driving nonequilibrium responses. Moreover, the degree of divisive scaling of the dynamic response is quantitatively the same as the steady-state responses—thus, gain modulation via balanced conductance fluctuations generalizes in a straight-forward way to a dynamic setting.     

The simultaneous recurrent neural network for addressing the scaling problem in static optimization.

A trainable recurrent neural network, Simultaneous Recurrent Neural network, is proposed to address the scaling problem faced by neural network algorithms in static optimization. The proposed algorithm derives its computational power to address the scaling problem through its ability to "learn" compared to existing recurrent neural algorithms, which are not trainable. Recurrent backpropagation algorithm is employed to train the recurrent, relaxation-based neural network in order to associate fixed points of the network dynamics with locally optimal solutions of the static optimization problems. Performance of the algorithm is tested on the NP-hard Traveling Salesman Problem in the range of 100 to 600 cities. Simulation results indicate that the proposed algorithm is able to consistently locate high-quality solutions for all problem sizes tested. In other words, the proposed algorithm scales demonstrably well with the problem size with respect to quality of solutions and at the expense of increased computational cost for large problem sizes.     

The dual role of the extracellular matrix in synaptic plasticity and homeostasis

Recent studies have deepened our understanding of multiple mechanisms by which extracellular matrix (ECM) molecules regulate various aspects of synaptic plasticity and have strengthened a link between the ECM and learning and memory. New findings also support the view that the ECM is important for homeostatic processes, such as scaling of synaptic responses, metaplasticity and stabilization of synaptic connectivity. Activity-dependent modification of the ECM affects the formation of dendritic filopodia and the growth of dendritic spines. Thus, the ECM has a dual role as a promoter of structural and functional plasticity and as a degradable stabilizer of neural microcircuits. Both of these aspects are likely to be important for mental health.     

An approach to improve Wang-Smith chaotic simulated annealing

Previous research shows that Wang-Smith chaotic simulated annealing, which employs a gradually decreasing time-step, has only a scaling effect to computational energy of the Hopfield model without changing its shape. This makes the net has sensitive dependence on the value of damping factor. Considering Chen-Aihara chaotic simulated annealing with decaying self-coupling has a shape effect to computational energy of the Hopfield model, a novel approach to improve Wang-Smith chaotic simulated annealing, which reaps the benefits of Wang-Smith model and Chen-Aihara model, is proposed in this paper. With the aid of this method the improved model can affect on computational energy of the Hopfield model from scaling and shape. By adjusting the time-step, the improved neural network can also pass from a chaotic to a non-chaotic state. From numerical simulation experiments, we know that the improved model can escape from local minima more efficiently than original Wang-Smith model.     

Arc/Arg3.1 mediates homeostatic synaptic scaling of AMPA receptors

Homeostatic plasticity may compensate for Hebbian forms of synaptic plasticity, such as long-term potentiation (LTP) and depression (LTD), by scaling neuronal output without changing the relative strength of individual synapses. This delicate balance between neuronal output and distributed synaptic weight may be necessary for maintaining efficient encoding of information across neuronal networks. Here, we demonstrate that Arc/Arg3.1, an immediate-early gene (IEG) that is rapidly induced by neuronal activity associated with information encoding in the brain, mediates homeostatic synaptic scaling of AMPA type glutamate receptors (AMPARs) via its ability to activate a novel and selective AMPAR endocytic pathway. High levels of Arc/Arg3.1 block the homeostatic increases in AMPAR function induced by chronic neuronal inactivity. Conversely, loss of Arc/Arg3.1 results in increased AMPAR function and abolishes homeostatic scaling of AMPARs. These observations, together with evidence that Arc/Arg3.1 is required for memory consolidation, reveal the importance of Arc/Arg3.1's dynamic expression as it exerts continuous and precise control over synaptic strength and cellular excitability.     

Adapting coincidence scalers and neural modelling studies of vision

Summary Some extensions of the theory of adapting coincidence scaling are presented in the context of neural theory and modelling.Previously the theory of adapting coincidence scaling has been successfully applied to quite a number of specific problems mainly drawn from psychophysical theories of vision: van de Grind et al. (1970a, b); Koenderink et al. (1970a, b). Here emphasis is on neurophysiological problems and after a brief discussion of the coding and component problems of neural network modelling and a survey of basic coincidence scaling mechanisms a paradigm for neural encoding is treated in some detail. This paradigm (Fig. 6A) is similar to the neuromimes developed and studied by Harmon (1959, 1961) and Küpfmüller and Jenik (1961) for deterministic input signals. On the basis of the introductory discussion of the coding problem it is assumed that the neural code in the peripheral part of the nervous system that we choose as our hunting ground, viz. the retina, is an average event rate code with a Poisson point process as a carrier. Thus the paradigm for neural encoding is studied for such a stochastic input point process. It is then among other things shown that such a simple encoder can generate a wide variety of multimodal interval distributions for certain choices of its parameters. Next we turn to a classic coincidence model of vision and give extremely accurate simulation results to substitute for the lacking analytic solution of the underlying K-fold coincidence problem.A shortcoming of this model is analysed in terms of elementary neural operations and it is shown that the problem of specifying a generalized version of the model ties in with the problem of developing models to explain the quantal signals (bumps) observed on the generator potential during intracellular recordings from the eccentric cell of Limulus. A cybernetic principle for bump size adaptation is formulated on the basis of the apparent and possibly significant similarity of this adaptation process with the event rate reduction principle embodied in the so called V R-machine (van de Grind et al., 1970a) which is one of our set of adapting coincidence scalers.     

Principles underlying mammalian neocortical scaling

 The neocortex undergoes a complex transformation from mouse to whale. Whereas synapse density remains the same, neuron density decreases as a function of gray matter volume to the power of around −1/3, total convoluted surface area increases as a function of gray matter volume to the power of around 8/9, and white matter volume disproportionately increases as a function of gray matter volume to the power of around 4/3. These phylogenetic scaling relationships (including others such as neuron number, neocortex thickness, soma radius, and number of cortical areas) are clues to understanding the principles driving neocortex organization, but there is currently no theory that can explain why these neocortical quantities scale as they do. Here I present a two-part model that explains these neocortical allometric scaling laws. The first part of the model is a special case of the physico-mathematical model recently put forward to explain the quarter power scaling laws in biology. It states that the neocortex is a space-filling neural network through which materials are efficiently transported, and that synapse sizes do not vary as a function of gray matter volume. The second part of the model states that the neocortex is economically organized into functionally specialized areas whose extent of area-interconnectedness does not vary as a function of gray matter volume. The model predicts, among other things, that the number of areas and the soma radius increase as a function of gray matter volume to the power of 1/3 and 1/9, respectively, and empirical support is demonstrated for each. Also, the scaling relationships imply that, although the percentage of the total number of neurons to which a neuron connects falls as a function of gray matter volume with exponent −1/3, the network diameter of the neocortex is invariant at around two. Finally, I discuss how a similar approach may have promise in explaining the scaling relationships for the brain and other organs as a function of body mass. Received: 23 December 1999 / Accepted in revised form: 2 August 2000     

Using two palpable measurements improves the subject-specific femoral modeling

Subject-specific musculoskeletal models are essential to biomedical research and clinical applications, such as customized joint replacement, computer-aided surgical planning, gait analysis and automated segmentation. Generating these models from CT or magnetic resonance imaging (MRI) is time and resource intensive, requiring special skills. Therefore, in many studies individual bone models are approximated by scaling a generic template. Thus, the primary goal of this study was to determine a set of clinically available parameters (palpable measures and demographic data) that could improve the prediction of femoral dimensions, as compared to predicting these variables using uniform scaling based on palpable length. Similar to previous non-homogenous anthropometric scaling methods, the non-homogenous scaling method proposed in this study improved the prediction over uniform scaling of five key femoral measures. Homogenous scaling forces all dimensions of an object to be scaled equally, whereas non-homogenous scaling allows the dimensions to be scaled independently. The largest improvement was in femoral depth, where the coefficient of determination (r²) improved from 0.22 (homogenous) to 0.60 (non-homogeneous). In general, the major advantage of this non-homogenous scaling method is its ability to support the accurate and rapid generation of subject-specific femoral models since all parameters can be collected clinically, without imaging or invasive methods.     

Pattern association and retrieval in a continuous neural system

This paper studies the behavior of a large body of neurons in the continuum limit. A mathematical characterization of such systems is obtained by approximating the inverse input-output nonlinearity of a cell (or an assembly of cells) by three adjustable linearized sections. The associative spatio-temporal patterns for storage in the neural system are obtained by using approaches analogous to solving space-time field equations in physics. A noise-reducing equation is also derived from this neural model. In addition, conditions that make a noisy pattern retrievable are identified. Based on these analyses, a visual cortex model is proposed and an exact characterization of the patterns that are storable in this cortex is obtained. Furthermore, we show that this model achieves pattern association that is invariant to scaling, translation, rotation and mirror-reflection.     

Development of Melanocyte Progenitors in Murine Steel Mutant Neural Crest Explants Cultured With Stem Cell Factor,Endothelin-3, or TPA

Stem cell factor (SCF) has been suggested to be indispensable for the development of neural crest cells into melanocytes because Steel mutant mice (i.e., Sl/Sf¹) have no pig-mented hairs. On the other hand, it has been demonstrated that the addition of endothelin 3 (ET-3) or TPA to neural crest cell cultures can induce melanocyte differentiation without addition of extrinsic SCF. In this study, we excluded the influence of intrinsic SCF by using SI/SI mouse embryos to study more precisely the effects of natural cytokines, such as extrinsic soluble SCF or ET-3, or chemical reagents, such as TPA or cholera toxin. We found that SCF is supplied within the wild-type neural crest explants and that ET-3 cannot induce melanocyte differentiation or proliferation without SCF. These results indicate that SCF plays a critical role in survival or G1/S entry of melanocyte progenitors and that SCF initially stimulates their proliferation and then ET-3 accelerates their proliferation and differentiation. TPA has the ability to elicit neural crest cell differentiation into melanocytes without exogenously added SCF but it is not as effective as SCF because many more melanocytes developed in the wild-type neural crest explants cultured with TPA.     

A Scaling Rule for Landscape Patches and How It Applies to Conserving Soil Resources in Savannas

Scaling issues are complex, yet understanding issues such as scale dependencies in ecological patterns and processes is usually critical if we are to make sense of ecological data and if we want to predict how land management options, for example, are constrained by scale. In this article, we develop the beginnings of a way to approach the complexity of scaling issues. Our approach is rooted in scaling functions, which integrate the scale dependency of patterns and processes in landscapes with the ways that organisms scale their responses to these patterns and processes. We propose that such functions may have sufficient generality that we can develop scaling rules—statements that link scale with consequences for certain phenomena in certain systems. As an example, we propose that in savanna ecosystems, there is a consistent relationship between the size of vegetation patches in the landscape and the degree to which critical resources, such as soil nutrients or water, become concentrated in these patches. In this case, the features of the scaling functions that underlie this rule have to do with physical processes, such as surface water flow and material redistribution, and the ways that patches of plants physically “capture” such runoff and convert it into plant biomass, thereby concentrating resources and increasing patch size. To be operationally useful, such scaling rules must be expressed in ways that can generate predictions. We developed a scaling equation that can be used to evaluate the potential impacts of different disturbances on vegetation patches and on how soils and their nutrients are conserved within Australian savanna landscapes. We illustrate that for a 10-km² paddock, given an equivalent area of impact, the thinning of large tree islands potentially can cause a far greater loss of soil nitrogen (21 metric tons) than grazing out small grass clumps (2 metric tons). Although our example is hypothetical, we believe that addressing scaling problems by first conceptualizing scaling functions, then proposing scaling rules, and then deriving scaling equations is a useful approach. Scaling equations can be used in simulation models, or (as we have done) in simple hypothetical scenarios, to collapse the complexity of scaling issues into a manageable framework. Received 8 December 1998; accepted 17 August 1999.     

A bayesian recurrent neural network for unsupervised pattern recognition in large incomplete data sets

A recurrent neural network, modified to handle highly incomplete training data is described. Unsupervised pattern recognition is demonstrated in the WHO database of adverse drug reactions. Comparison is made to a well established method, AutoClass, and the performances of both methods is investigated on simulated data. The neural network method performs comparably to AutoClass in simulated data, and better than AutoClass in real world data. With its better scaling properties, the neural network is a promising tool for unsupervised pattern recognition in huge databases of incomplete observations.