Analysis of impulse adaptation in motoneurons

Biological clockwork underlying adaptive rhythmic movements

Owing to the complexity of neuronal circuits, precise mathematical descriptions of brain functions remain an elusive ambition. A more modest focus of many neuroscientists, central pattern generators, are more tractable neuronal circuits specialized to generate rhythmic movements, including locomotion. The relative simplicity and well-defined motor functions of these circuits provide an opportunity for uncovering fundamental principles of neuronal information processing. Here we present the culmination of mathematical analysis that captures the adaptive behaviors emerging from interactions between a central pattern generator, the body, and the physical environment during locomotion. The biologically realistic model describes the undulatory motions of swimming leeches with quantitative accuracy and, without further parameter tuning, predicts the sweeping changes in oscillation patterns of leeches undulating in air or swimming in high-viscosity fluid. The study demonstrates that central pattern generators are capable of adapting oscillations to the environment through sensory feedback, but without guidance from the brain.

Positive feedback loops sustain repeating bursts in neuronal circuits

Voluntary movements in animals are often episodic, with abrupt onset and termination. Elevated neuronal excitation is required to drive the neuronal circuits underlying such movements; however, the mechanisms that sustain this increased excitation are largely unknown. In the medicinal leech, an identified cascade of excitation has been traced from mechanosensory neurons to the swim oscillator circuit. Although this cascade explains the initiation of excitatory drive (and hence swim initiation), it cannot account for the prolonged excitation (10-100 s) that underlies swim episodes. We present results of physiological and theoretical investigations into the mechanisms that maintain swimming activity in the leech. Although intrasegmental mechanisms can prolong stimulus-evoked excitation for more than one second, maintained excitation and sustained swimming activity requires chains of several ganglia. Experimental and modeling studies suggest that mutually excitatory intersegmental interactions can drive bouts of swimming activity in leeches. Our model neuronal circuits, which incorporated mutually excitatory neurons whose activity was limited by impulse adaptation, also replicated the following major experimental findings: (1) swimming can be initiated and terminated by a single neuron, (2) swim duration decreases with experimental reduction in nerve cord length, and (3) swim duration decreases as the interval between swim episodes is reduced.

Mechanisms underlying rhythmic locomotion: interactions between activation, tension and body curvature waves

Undulatory animal locomotion arises from three closely related propagating waves that sweep rostrocaudally along the body: activation of segmental muscles by motoneurons (MNs), strain of the body wall, and muscle tension induced by activation and strain. Neuromechanical models that predict the relative propagation speeds of neural/muscle activation, muscle tension and body curvature can reveal crucial underlying control features of the central nervous system and the power-generating mechanisms of the muscle. We provide an analytical explanation of the relative speeds of these three waves based on a model of neuromuscular activation and a model of the body-fluid interactions for leech anguilliform-like swimming. First, we deduced the motoneuron spike frequencies that activate the muscle and the resulting muscle tension during swimming in intact leeches from muscle bending moments. Muscle bending moments were derived from our video-recorded kinematic motion data by our body-fluid interaction model. The phase relationships of neural activation and muscle tension in the strain cycle were then calculated. Our study predicts that the MN activation and body curvature waves have roughly the same speed (the ratio of curvature to MN activation speed ≈0.84), whereas the tension wave travels about twice as fast. The high speed of the tension wave resulting from slow MN activation is explained by the multiplicative effects of MN activation and muscle strain on tension development. That is, the product of two slower waves (activation and strain) with appropriate amplitude, bias and phase can generate a tension wave with twice the propagation speed of the factors. Our study predicts that (1) the bending moment required for swimming is achieved by minimal MN spike frequency, rather than by minimal muscle tension; (2) MN activity is greater in the mid-body than in the head and tail regions; (3) inhibitory MNs not only accelerate the muscle relaxation but also reduce the intrinsic tonus tension during one sector of the swim cycle; and (4) movements of the caudal end are passive during swimming. These predictions await verification or rejection through further experiments on swimming animals.

Potencial de ação: do estímulo à adaptação neural

INTRODUÇÃO: O potencial de ação (PA) origina-se graças a uma perturbação do estado de repouso da membrana celular, com consequente fluxo de íons, por meio da membrana e alteração da concentração iônica nos meios intra e extracelular. OBJETIVOS: Sintetizar o conhecimento científico acumulado até o presente sobre o potencial de ação neural e o seu processo de adaptação sob aplicação de um estímulo constante. MATERIAIS E MÉTODOS: Busca realizada nas bases Springer, ScienceDirect, PubMed, IEEE Xplore, Google Acadêmico, Portal de Periódicos da Capes, além de livros referentes ao assunto. O idioma de preferência selecionado foi o inglês, com as keywords: action potential; adaptation; accommodation; rheobase; chronaxy; nerve impulse. Efetuou-se a procura de artigos com uma janela de tempo de 1931 a 2010 e livros de 1791 a 2007. RESULTADOS: Dos trabalhos selecionados, foram extraídas informações a respeito dos seguintes tópicos: potencial de ação e suas fases; condução nervosa; reobase; cronaxia; acomodação; e adaptação neuronal. CONCLUSÃO: Um estímulo que crie PA, se aplicado de maneira constante, pode reduzir a frequência de despolarizações em função do tempo e, consequentemente, adaptar a célula. O tempo que a célula demora, na ausência de estímulos, para recuperar sua frequência original é definido como desadaptação.

Mechanisms underlying rhythmic locomotion: dynamics of muscle activation

We have studied the dynamical properties of tension development in leech longitudinal muscle during swimming. A new method is proposed for modeling muscle properties under functionally relevant conditions where the muscle is subjected to both periodic activation and rhythmic length changes. The 'dual-sinusoid' experiments were conducted on preparations of leech nerve cord and body wall. The longitudinal muscle was activated periodically by injection of sinusoidal currents into an identified motoneuron. Simultaneously, sinusoidal length changes were imposed on the body wall with prescribed phase differences (12 values equally spaced over 2π radians) with respect to the current injection. Through the singular value decomposition of appropriately constructed tension data matrices, the leech muscle was found to have a multiplicative structure in which the tension was expressed as the product of activation and length factors. The time courses of activation and length factors were determined from the tension data and were used to develop component models. The proposed modeling method is a general one and is applicable to contractile elements for which the effects of series elasticity are negligible.

Mechanisms underlying rhythmic locomotion: body-fluid interaction in undulatory swimming

Swimming of fish and other animals results from interactions of rhythmic body movements with the surrounding fluid. This paper develops a model for the body-fluid interaction in undulatory swimming of leeches, where the body is represented by a chain of rigid links and the hydrodynamic force model is based on resistive and reactive force theories. The drag and added-mass coefficients for the fluid force model were determined from experimental data of kinematic variables during intact swimming, measured through video recording and image processing. Parameter optimizations to minimize errors in simulated model behaviors revealed that the resistive force is dominant, and a simple static function of relative velocity captures the essence of hydrodynamic forces acting on the body. The model thus developed, together with the experimental kinematic data, allows us to investigate temporal and spatial (along the body) distributions of muscle actuation, body curvature, hydrodynamic thrust and drag, muscle power supply and energy dissipation into the fluid. We have found that: (1) thrust is generated continuously along the body with increasing magnitude toward the tail, (2) drag is nearly constant along the body, (3) muscle actuation waves travel two or three times faster than the body curvature waves and (4) energy for swimming is supplied primarily by the mid-body muscles, transmitted through the body in the form of elastic energy, and dissipated into the water near the tail.