Adaptive feedback control models of the vestibulocerebellum and spinocerebellum

We extend the cerebellar learning model proposed by Kawato and Gomi (1992) to the case where a specific region of the cerebellum executes adaptive feed-back control as well as feedforward control. The model is still based on the feedback-error-learning scheme. The proposed adaptive feedback control model is developed in detail as a specific neural circuit model for three different regions of the cerebellum and the learning of the corresponding representative movements: (i) the flocculus and adaptive modification of the vestibulo-ocular reflex and optokinetic eye-movement responses, (ii) the vermis and adaptive posture control, and (iii) the intermediate zones of the hemisphere and adaptive control of locomotion. As a representative example, simultaneous adaptation of the vestibulo-ocular reflex and the optokinetic eye-movement response was successfully simulated while the Purkinje cells receive copies of motor commands through recurrent neural connections as well as vestibular and retinal-slip parallel-fiber inputs.     

Emergence of symmetric, modular, and reciprocal connections in recurrent networks with Hebbian learning

While learning and development are well characterized in feedforward networks, these features are more difficult to analyze in recurrent networks due to the increased complexity of dual dynamics – the rapid dynamics arising from activation states and the slow dynamics arising from learning or developmental plasticity. We present analytical and numerical results that consider dual dynamics in a recurrent network undergoing Hebbian learning with either constant weight decay or weight normalization. Starting from initially random connections, the recurrent network develops symmetric or near-symmetric connections through Hebbian learning. Reciprocity and modularity arise naturally through correlations in the activation states. Additionally, weight normalization may be better than constant weight decay for the development of multiple attractor states that allow a diverse representation of the inputs. These results suggest a natural mechanism by which synaptic plasticity in recurrent networks such as cortical and brainstem premotor circuits could enhance neural computation and the generation of motor programs. Received: 27 April 1998 / Accepted in revised form: 16 March 1999     

Cerebellar function: coordination, learning or timing?

Theories of cerebellar function have largely involved three ideas: movement coordination, motor learning or timing. New evidence indicates these distinctions are not particularly meaningful, as the cerebellum influences movement execution by feedforward use of sensory information via temporally specific learning.     

Recurrent cerebellar architecture solves the motor-error problem

Current views of cerebellar function have been heavily influenced by the models of Marr and Albus, who suggested that the climbing fibre input to the cerebellum acts as a teaching signal for motor learning. It is commonly assumed that this teaching signal must be motor error (the difference between actual and correct motor command), but this approach requires complex neural structures to estimate unobservable motor error from its observed sensory consequences. We have proposed elsewhere a recurrent decorrelation control architecture in which Marr-Albus models learn without requiring motor error. Here, we prove convergence for this architecture and demonstrate important advantages for the modular control of systems with multiple degrees of freedom. These results are illustrated by modelling adaptive plant compensation for the three-dimensional vestibular ocular reflex. This provides a functional role for recurrent cerebellar connectivity, which may be a generic anatomical feature of projections between regions of cerebral and cerebellar cortex.     

Comments on ‘Is Partial Coherence a Viable Technique for Identifying Generators of Neural Oscillations?’

To aid prospective neural connectivity inference analysts and hoping to preclude misconception spread, we exploit the didatic value of some of the issues raised by Albo et al. (Biol Cybern 90: 318–326, 2004) who claim that signal-to-noise ratio (SNR) values can lead to mistakes in structural inference when using partial coherence in connection to Gersch’s 1970 method for spotting signal sources (Gersch in Math Biosci 14: 177– 196, 1972). We show theoretically that Gersch’s method is able only to spot which measurement of some common underlying factor has the least amount of additive noise and that this has nothing to do with any reasonable notion of ‘causality’ as suggested by Albo et al. (Biol Cybern 90: 318–326, 2004). We also show that despite the inherent structural ambiguity of the model used by Albo et al. (Biol Cybern 90: 318–326, 2004) to back their claim, its data can nonetheless furnish the correct time precedence hierarchy between the activities in its measured structures, both when simple (correlation) and more sophisticated methods are used (partial directed coherence) (Baccala and Sameshima in Biol Cybern 84:463–474, 2001a) in a true depiction of time series causality.     

Twenty four new microsatellite markers in two invasive pavement ants, <Emphasis Type="Italic">Tetramorium</Emphasis> sp.E and <Emphasis Type="Italic">T. tsushimae</Emphasis> (Hymenoptera: Formicidae)

Invasive species trigger biodiversity losses and alter ecosystem functioning, with life history shaping invasiveness (Sakai et al., Annu Rev Ecol Syst 32:305–332, 2001). However, pinpointing the relation of a specific life history to invasion success is difficult. One approach may be comparing congeners. The two Palearctic pavement ants, Tetramorium sp.E (widely known as T. caespitum, Schlick-Steiner et al., Mol Phylogenet Evol 40:259–273, 2006) and T. tsushimae have invaded North America (Steiner et al., Biol Invasions 8:117–123, 2006). Their life histories differ in that T. sp.E has separate single-queened colonies but T. tsushimae multi-queened colonies scattered over large areas (Sanada-Morimura et al., Insect Soc 53:141–148, 2006; Schlick-Steiner et al., Mol Phylogenet Evol 40:259–273, 2006; Steiner et al., Biol Invasions 8:117–123, 2006). Comparison of the genetic diversity in the entire native and non-native ranges will elucidate the invasion histories. Here, we present 13 and 11 microsatellites, developed for T. sp.E and T. tsushimae, respectively, and characterize all for both species. Florian M. Steiner, Wolfgang Arthofer and Birgit C. Schlick-Steiner contributed equally to this work.     

A hexapedal jointed-leg model for insect locomotion in the horizontal plane

We develop a simple model for insect locomotion in the horizontal (ground) plane. As in earlier work by Seipel et al. (Biol Cybern 91(0):76–90, 2004) we employ six actuated legs that also contain passive springs, but the legs, with “hip” and ‘knee’ joints, better represent insect morphology. Actuation is provided via preferred angle inputs at each joint, corresponding to zero torques in the hip and knee springs. The inputs are determined from estimates of foot forces in the cockroach Blaberus discoidalis via an inverse problem. The head–thorax–body is modeled as a single rigid body, and leg masses, inertia and joint dissipation are ignored. The resulting three degree-of-freedom dynamical system, subject to feedforward joint inputs, exhibits stable periodic gaits that compare well with observations over the insect’s typical speed range. The model’s response to impulsive perturbations also matches that of freely-running cockroaches (Jindrich and Full, J Exp Biol 205:2803–2823, 2002), and stability is maintained in the face of random foot touchdowns representative of real insects. We believe that this model will allow incorporation of realistic muscle models driven by a central pattern generator in place of the joint actuators, and that it will ultimately permit the study of proprioceptive feedback pathways involving leg force and joint angle sensing.     

Behavioral motor dysfunction in Kv3-type potassium channel-deficient mice

The voltage-gated potassium channels Kv3.1 and Kv3.3 are expressed in several distinct neuronal subpopulations in brain areas known to be involved in motor control such as cortex, basal ganglia and cerebellum. Depending on the lack of Kv3.1 or Kv3.3 channel subunits, mutant mice show different Kv3-null allele-dependent behavioral alterations that include constitutive hyperactivity, sleep loss, impaired motor performance and, in the case of the Kv3.1/Kv3.3 double mutant, also severe ataxia, tremor and myoclonus (Espinosa et al. 2001, J Neurosci 21, 6657-6665, Genes, Brain Behav 3, 90-100). The lack of Kv3.1 channel subunits is mainly responsible for the constitutively increased locomotor activity and for sleep loss, whereas the absence of Kv3.3 subunits affects cerebellar function, in particular Purkinje cell discharges and olivocerebellar system properties (McMahon et al. 2004, Eur J Neurosci 19, 3317-3327). Here, we describe two sensitive and non-invasive tests to reliably quantify normal and abnormal motor functions, and we apply these tests to characterize motor dysfunction in Kv3-mutant mice. In contrast to wildtype and Kv3.1-single mutants, Kv3.3-single mutants and Kv3 mutants lacking three and four Kv3 alleles display Kv3-null allele-dependent gait alterations. Although the Kv3-null allele-dependent gait changes correlate with reduced motor performance, they appear to not affect the training-induced improvement of motor performance. These findings suggest that altered cerebellar physiology in the absence of Kv3.3 channels is responsible for impaired motor task execution but not motor task learning.     

Unique features of the structural model of 'hard' cuticle proteins: implications for chitin-protein interactions and cross-linking in cuticle

Cuticular proteins are one of the determinants of the physical properties of cuticle. A common consensus region (extended R&R Consensus) in these proteins binds to chitin, the other major component of cuticle. We previously predicted the preponderance of beta-pleated sheet in the consensus region and proposed its responsibility for the formation of helicoidal cuticle (Iconomidou et al., Insect Biochem. Mol. Biol. 29 (1999) 285). Subsequently, we verified experimentally the abundance of antiparallel beta-pleated sheet in the structure of cuticle proteins (Iconomidou et al., Insect Biochem. Mol. Biol. 31 (2001) 877). Homology modelling of soft (RR-1) cuticular proteins using bovine plasma retinol binding protein (RBP) as a template revealed an antiparallel beta-sheet half-barrel structure as the basic folding motif (Hamodrakas et al., Insect Biochem. Molec. Biol. 32 (2002) 1577). The RR-2 proteins characteristic of hard cuticle, have a far more conserved consensus and frequently more histidine residues. Extension of modelling to this class of consensus, in this work, reveals in detail several unique features of the proposed structural model to serve as a chitin binding structural motif, thus providing the basis for elucidating cuticle's overall architecture and chitin-protein interactions in cuticle.     

Central mechanisms of motor skill learning

Recent studies have shown that frontoparietal cortices and interconnecting regions in the basal ganglia and the cerebellum are related to motor skill learning. We propose that motor skill learning occurs independently and in different coordinates in two sets of loop circuits: cortex-basal ganglia and cortex-cerebellum. This architecture accounts for the seemingly diverse features of motor learning.     

Shotgun Crystallization Strategy for Structural Genomics II: Crystallization Conditions that Produce High Resolution Structures for T. maritima Proteins

Currently, 119 high resolution structures of Thermotoga maritima proteins have been determined by the Joint Center for Structural Genomics (JCSG, www.jcsg.org). Sixty-seven of these were solved using the first implementation of the multi-tiered crystallization strategy at the JCSG for the efficient crystallization of large numbers of protein targets. Previously, we reported the analysis of all proteins crystallized using this multi-tiered strategy [Lesley, S.A. et al. (2002) Proc. Natl. Acad. Sci. USA 99, 11664–11669; Page, R. et al. (2003) Acta Crystallogr. D Biol. Crystallogr. 59, 1028–1037]. Here, we extend the analysis and describe the crystallization characteristics of those proteins that produced diffraction quality crystals, ultimately resulting in high resolution structures. First, we found that over 77% (52) of the crystals used for structure determination were produced directly from high-throughput coarse screens, indicating that less than one quarter of the crystals (15) required fine screening. In addition, as observed for the proteome screen [Page, R. et al. (2003) Acta Crystallogr. D Biol. Crystallogr. 59, 1028–1037], the majority of conditions that produced crystals for natively expressed proteins, whose structures have been determined, were distinct from those of their more extensively purified and selenomethionine-labeled counterparts. Finally, 99% of the proteins whose structures were solved crystallized in conditions contained in the JCSG Minimal Core Screen [Page, R. et al. (2003) Acta Crystallogr. D Biol. Crystallogr. 59, 1028–1037; Page, R. and Stevens, R.C. (2004) Methods 34, 373–389], a set of 67 conditions previously identified as those most likely to produce crystals of a diverse set of proteins, confirming its success for rapid identification of proteins with a natural propensity to crystallize.     

Dynamic updating of distributed neural representations using forward models

In this paper, we present a continuous attractor network model that we hypothesize will give some suggestion of the mechanisms underlying several neural processes such as velocity tuning to visual stimulus, sensory discrimination, sensorimotor transformations, motor control, motor imagery, and imitation. All of these processes share the fundamental characteristic of having to deal with the dynamic integration of motor and sensory variables in order to achieve accurate sensory prediction and/or discrimination. Such principles have already been described in the literature by other high-level modeling studies (Decety and Sommerville in Trends Cogn Sci 7:527–533, 2003; Oztop et al. in Neural Netw 19(3):254–271, 2006; Wolpert et al. in Philos Trans R Soc 358:593–602, 2003). With respect to these studies, our work is more concerned with biologically plausible neural dynamics at a population level. Indeed, we show that a relatively simple extension of the classical neural field models can endow these networks with additional dynamic properties for updating their internal representation using external commands. Moreover, an analysis of the interactions between our model and external inputs also shows interesting properties, which we argue are relevant for a better understanding of the neural processes of the brain.     

Are we ready for a natural history of motor learning?

Here we argue that general principles with regard to the contributions of the cerebellum, basal ganglia, and primary motor cortex to motor learning can begin to be inferred from explicit comparison across model systems and consideration of phylogeny. Both the cerebellum and the basal ganglia have highly conserved circuit architecture in vertebrates. The cerebellum has consistently been shown to be necessary for adaptation of eye and limb movements. The precise contribution of the basal ganglia to motor learning remains unclear but one consistent finding is that they are necessary for early acquisition of novel sequential actions. The primary motor cortex allows independent control of joints and construction of new movement synergies. We suggest that this capacity of the motor cortex implies that it is a necessary locus for motor skill learning, which we argue is the ability to execute selected actions with increasing speed and precision.     

A Comparison of Continuous and Discrete-time West Nile Virus Models

The first recorded North American epidemic of West Nile virus was detected in New York state in 1999, and since then the virus has spread and become established in much of North America. Mathematical models for this vector-transmitted disease with cross-infection between mosquitoes and birds have recently been formulated with the aim of predicting disease dynamics and evaluating possible control methods. We consider discrete and continuous time versions of the West Nile virus models proposed by Wonham et al. [Proc. R. Soc. Lond. B 271:501–507, 2004] and by Thomas and Urena [Math. Comput. Modell. 34:771–781, 2001], and evaluate the basic reproduction number as the spectral radius of the next-generation matrix in each case. The assumptions on mosquito-feeding efficiency are crucial for the basic reproduction number calculation. Differing assumptions lead to the conclusion from one model [Wonham, M.J. et al., [Proc. R. Soc. Lond. B] 271:501–507, 2004] that a reduction in bird density would exacerbate the epidemic, while the other model [Thomas, D.M., Urena, B., Math. Comput. Modell. 34:771–781, 2001] predicts the opposite: a reduction in bird density would help control the epidemic.     

Genome-wide meta-analysis for rheumatoid arthritis

Meta-analysis is being increasingly used as a tool for integrating data from different studies of complex phenotypes, because the power of any one study to identify causal loci is limited. We applied a novel meta-analytical approach (Loesgen et al. in Genet Epidemiol 21(Suppl 1):S142–S147, 2001) in compiling results from four studies of rheumatoid arthritis in Caucasians including two studies from NARAC (Jawaheer et al. in Am J Hum Genet 68:927–936, 2001; Jawaheer et al. in Arthritis Rheum 48:906–916, 2003), one study from the UK (MacKay et al. in Arthritis Rheum 46:632–639, 2001) and one from France (Cornelis et al. in Proc Natl Acad Sci USA 95:10746–10750, 1998). For each study, we obtained NPL scores by performing interval mapping (2 cM intervals) using GeneHunter2 (Kruglyak et al. in Am J Hum Genet 58:1347–1363, 1996; Markianos et al. in Am J Hum Genet 68:963–977, 2001). The marker maps differed among the three consortium groups, therefore, the marker maps were aligned after the interval mapping was completed and the NPL scores that were within 1 cM of each other were combined using the method of Loesgen et al. (Genet Epidemiol 21(Suppl 1):S142–S147, 2001) by calculating the weighted average of the NPL score. This approach avoids some problems in analysis encountered by using GeneHunter2 when some markers in the sample are not genotyped. This procedure provided marginal evidence (P<0.05) of linkage on chromosome 1, 2, 5 and 18, strong evidence (P<0.01) on chromosomes 8 and 16, and overwhelming evidence in the HLA region of chromosome 6.     

The objects of face perception

In a comprehensive series of experiments that combine neural modeling, behavioral data, and fMRI, Jiang et al. (this issue of Neuron) advance a general object and face classification model, based on a feedforward shape-detector architecture. The model accounts for configural face processing as well as for shape-based fMRI activation in the fusiform face area (FFA).     

Information transmission in oscillatory neural activity

Periodic neural activity not locked to the stimulus or to motor responses is usually ignored. Here, we present new tools for modeling and quantifying the information transmission based on periodic neural activity that occurs with quasi-random phase relative to the stimulus. We propose a model to reproduce characteristic features of oscillatory spike trains, such as histograms of inter-spike intervals and phase locking of spikes to an oscillatory influence. The proposed model is based on an inhomogeneous Gamma process governed by a density function that is a product of the usual stimulus-dependent rate and a quasi-periodic function. Further, we present an analysis method generalizing the direct method (Rieke et al. in Spikes: exploring the neural code. MIT Press, Cambridge, 1999; Brenner et al. in Neural Comput 12(7):1531-1552, 2000) to assess the information content in such data. We demonstrate these tools on recordings from relay cells in the lateral geniculate nucleus of the cat.     

A Model for Multi-site Pacing of Fibrillation Using Nonlinear Dynamics Feedback

Traditionally, cardiac defibrillation requires a strong electric shock. Many unwanted side effects of this shock could be eliminated if defibrillation were performed using weak stimuli applied to several locations throughout the heart. Such multi-site pacing algorithms have been shown to defibrillate both experimentally (Pak et al., Am J Physiol 285:H2704–H2711, 2003) and theoretically (Puwal and Roth, J Biol Systems 14:101–112, 2006). Gauthier et al. (Chaos, 12:952–961, 2002) proposed a method to pace the heart using an algorithm based on nonlinear dynamics feedback applied through a single electrode. Our study applies a related but simpler algorithm, which essentially configures each electrode as a demand pacemaker, to simulate the multi-site pacing of fibrillating cardiac tissue. We use the numerical model developed by Fenton et al. (Chaos, 12:852–892, 2002) as the reaction term in a reaction–diffusion equation that we solve over a two-dimensional sheet of tissue. The defibrillation rate after pacing for 3 s is about 30%, which is significantly higher than the spontaneous defibrillation rate and is higher than observed in previous experimental and theoretical studies. Tuning the algorithm period can increase this rate to 45%. Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Emergence of protocellular growth laws

Template-directed replication is known to obey a parabolic growth law due to product inhibition (Sievers & Von Kiedrowski 1994 Nature 369, 221; Lee et al. 1996 Nature 382, 525; Varga & Szathmáry 1997 Bull. Math. Biol. 59, 1145). We investigate a template-directed replication with a coupled template catalysed lipid aggregate production as a model of a minimal protocell and show analytically that the autocatalytic template-container feedback ensures balanced exponential replication kinetics; both the genes and the container grow exponentially with the same exponent. The parabolic gene replication does not limit the protocellular growth, and a detailed stoichiometric control of the individual protocell components is not necessary to ensure a balanced gene-container growth as conjectured by various authors (Gánti 2004 Chemoton theory). Our analysis also suggests that the exponential growth of most modern biological systems emerges from the inherent spatial quality of the container replication process as we show analytically how the internal gene and metabolic kinetics determine the cell population's generation time and not the growth law (Burdett & Kirkwood 1983 J. Theor. Biol. 103, 11-20; Novak et al. 1998 Biophys. Chem. 72, 185-200; Tyson et al. 2003 Curr. Opin. Cell Biol. 15, 221-231). Previous extensive replication reaction kinetic studies have mainly focused on template replication and have not included a coupling to metabolic container dynamics (Stadler et al. 2000 Bull. Math. Biol. 62, 1061-1086; Stadler & Stadler 2003 Adv. Comp. Syst. 6, 47). The reported results extend these investigations. Finally, the coordinated exponential gene-container growth law stemming from catalysis is an encouraging circumstance for the many experimental groups currently engaged in assembling self-replicating minimal artificial cells (Szostak 2001 et al. Nature 409, 387-390; Pohorille & Deamer 2002 Trends Biotech. 20 123-128; Rasmussen et al. 2004 Science 303, 963-965; Szathma ry 2005 Nature 433, 469-470; Luisi et al. 2006 Naturwissenschaften 93, 1-13).