Visuomotor Control: Drosophila Bridges the Gap

SummaryFruit flies with genetic lesions disrupting the structure of a brain region known as the protocerebral bridge fail to aim their movements correctly when crossing gaps, implicating this central brain neuropile in the visual control of goal-directed behaviour

Brain Evolution: Getting Better All the Time?

Recent studies on bats, goats and hominids suggest that some mammalian brains may have undergone dramatic evolutionary reductions in size. These studies emphasise the importance of selective pressures upon mammalian brain evolution and the need to integrate studies of neuroanatomy, neurophysiology and behaviour

Action potential energy efficiency varies among neuron types in vertebrates and invertebrates.

The initiation and propagation of action potentials (APs) places high demands on the energetic resources of neural tissue. Each AP forces ATP-driven ion pumps to work harder to restore the ionic concentration gradients, thus consuming more energy. Here, we ask whether the ionic currents underlying the AP can be predicted theoretically from the principle of minimum energy consumption. A long-held supposition that APs are energetically wasteful, based on theoretical analysis of the squid giant axon AP, has recently been overturned by studies that measured the currents contributing to the AP in several mammalian neurons. In the single compartment models studied here, AP energy consumption varies greatly among vertebrate and invertebrate neurons, with several mammalian neuron models using close to the capacitive minimum of energy needed. Strikingly, energy consumption can increase by more than ten-fold simply by changing the overlap of the Na+ and K+ currents during the AP without changing the APs shape. As a consequence, the height and width of the AP are poor predictors of energy consumption. In the Hodgkin–Huxley model of the squid axon, optimizing the kinetics or number of Na+ and K+ channels can whittle down the number of ATP molecules needed for each AP by a factor of four. In contrast to the squid AP, the temporal profile of the currents underlying APs of some mammalian neurons are nearly perfectly matched to the optimized properties of ionic conductances so as to minimize the ATP cost

Channelling Evolution: Canalization and the nervous system

A recent paper suggests that genes can interact in networks to limit variation of phenotype. Similar principles might apply to the regulation of ion channels in nerve cell

Prey speed influences the speed and structure of the raptorial strike of a ‘sit-and-wait’ predator

Predators must often employ flexible strategies to capture prey. Particular attention has been given to the strategies of visual predators that actively pursue their prey, but sit-and-wait predators have been largely overlooked, their strategies often characterized as stereotyped. Praying mantids are primarily sit-and-wait predators that often employ crypsis to catch their prey using a raptorial strike produced by their highly modified forelimbs. Here, we show that the raptorial strike of the Madagascan marbled mantis (Polyspilota aeruginosa) varies in duration from 60 to 290 ms due to the tibial extension alone; slower strikes involve slower tibial extensions that may also be interrupted by a pause. The success of a strike is independent of its duration or the presence of these pauses. However, prey speed affects the duration of tibial extension and the probability of a pause occurring, both increasing at slower prey speeds. Adjusting the duration of the tibial extension according to prey speed allows mantids to time the final downward sweep of the tibia to their prey’s approach. The use of visual inputs to adjust the motor pattern controlling forelimb movements shows that not all aspects of the strike are stereotyped and that sit-and-wait predators can produce behavioural flexibility

Recurrent proofs of the irrationality of certain trigonometric values

We use recurrences of integrals to give new and elementary proofs of the irrationality of pi, tan(r) for all nonzero rational r, and cos(r) for all nonzero rational r^2. Immediate consequences to other values of the elementary transcendental functions are also discussed

On the frequency of permutations containing a long cycle

A general explicit upper bound is obtained for the proportion $P(n,m)$ of elements of order dividing $m$, where $n-1 \le m \le cn$ for some constant $c$, in the finite symmetric group $S_n$. This is used to find lower bounds for the conditional probabilities that an element of $S_n$ or $A_n$ contains an $r$-cycle, given that it satisfies an equation of the form $x^{rs}=1$ where $s\leq3$. For example, the conditional probability that an element $x$ is an $n$-cycle, given that $x^n=1$, is always greater than 2/7, and is greater than 1/2 if $n$ does not divide 24. Our results improve estimates of these conditional probabilities in earlier work of the authors with Beals, Leedham-Green and Seress, and have applications for analysing black-box recognition algorithms for the finite symmetric and alternating groups

Matched short-term depression and recovery encodes interspike interval at a central synapse

Reversible decreases in synaptic strength, known as short-term depression (STD), are widespread in neural circuits. Various computational roles have been attributed to STD but these tend to focus upon the initial depression rather than the subsequent recovery. We studied the role of STD and recovery at an excitatory synapse between the fast extensor tibiae (FETi) and flexor tibiae (flexor) motor neurons in the desert locust (Schistocerca gregaria) by making paired intracellular recordings in vivo. Over behaviorally relevant pre-synaptic spike frequencies, we found that this synapse undergoes matched frequency-dependent STD and recovery; higher frequency spikes that evoke stronger, faster STD also produce stronger, faster recovery. The precise matching of depression and recovery time constants at this synapse ensures that flexor excitatory post-synaptic potential (EPSP) amplitude encodes the presynaptic FETi interspike interval (ISI). Computational modelling shows that this precise matching enables the FETi-flexor synapse to linearly encode the ISI in the EPSP amplitude, a coding strategy that may be widespread in neural circuits

Balanced excitatory and inhibitory synaptic currents promote efficient coding and metabolic efficiency

A balance between excitatory and inhibitory synaptic currents is thought to be important for several aspects of information processing in cortical neurons in vivo, including gain control, bandwidth and receptive field structure. These factors will affect the firing rate of cortical neurons and their reliability, with consequences for their information coding and energy consumption. Yet how balanced synaptic currents contribute to the coding efficiency and energy efficiency of cortical neurons remains unclear. We used single compartment computational models with stochastic voltage-gated ion channels to determine whether synaptic regimes that produce balanced excitatory and inhibitory currents have specific advantages over other input regimes. Specifically, we compared models with only excitatory synaptic inputs to those with equal excitatory and inhibitory conductances, and stronger inhibitory than excitatory conductances (i.e. approximately balanced synaptic currents). Using these models, we show that balanced synaptic currents evoke fewer spikes per second than excitatory inputs alone or equal excitatory and inhibitory conductances. However, spikes evoked by balanced synaptic inputs are more informative (bits/spike), so that spike trains evoked by all three regimes have similar information rates (bits/s). Consequently, because spikes dominate the energy consumption of our computational models, approximately balanced synaptic currents are also more energy efficient than other synaptic regimes. Thus, by producing fewer, more informative spikes approximately balanced synaptic currents in cortical neurons can promote both coding efficiency and energy efficiency