Can you snatch the grasshopper? The Mathematics behind escape reflexes in a Locust.
Ever try to catch a grasshopper? He always notices you approaching, looming over him, trying to catch him before he leaps out of the way. Whenever you get too close, or move too fast, he escapes your grasp, jumping away in the blink of an eye. This is known as the looming response, and the neuron responsible for this reflex is called the Lobule Giant Movement Detector (LGMD). Dr. Simon Peron, Dr. Peter Jones, and Dr. Fabrzio Gabbianni use an extremely well designed biological experiment, and develop a mathematical model to understand exactly how the LGMD neuron in a Locust functions. The LGMD neuron receives retinotopic input from the eye, and responds to fast-moving visual stimulus. When the neuron fires, it stimulates the motor region and the grasshopper the hops away. Here Peron et al. Use a mixture of current clamp and calcium imaging to figure out the pre-synaptic organization onto the LGMD. They then create a model to show that the retinotopic synaptic organization alone does not explain the data, and propose that synaptic weight must matter as well. In order to obtain these results not only do they need to have good data and scientific controls, but a solid understanding of the mathematics behind dendritic filtering.
How do they determine the synaptic organization? In previous work, they noticed that dendrites do not have any voltage gated calcium channels (VGCC), and therefore there is no calcium increase when the voltage increases in the dendrite. Furthermore, they noticed the synapses are nicotinic acetylcholine receptors. Meaning they allow calcium ions into the cell only when an excitatory synapse from the retina is active. This is amazing stroke of luck! Because the calcium enters the cell only when a synapse is active, they are able to use calcium imaging to determine the location of the synapse! Normally VGCC will make this method fail, because the calcium signal is too spread out. Thus, when they stimulate the eye with light (ON) or a shadow (OFF) stimuli, they are able to observe approximately where the synapse is located on the dendritic tree!
Using a mathematical model, they show that the particular synaptic layout is necessary for the LGMD to perform the computation but not sufficient. Here we need to look at figure 1B and Figure 5 to understand the layout they found. Click the link to open the figures in a separate window.* Notice that Dorsal(top) and Ventral(bottom) go across the dendrites, and that posterior(back) to anterior(front) goes along the dendrites. This set up allows the cell to determine which way the looming shadow comes from, and if the signal is fast enough and in the right direction, the locust will jump away. By recording the electrical signal in the axon of LGMD they show in Fig 5 that the maximum firing rate is the lowest when the shadow moves from Posterior-to-Anterior (Back-to-front). This means that when the looming response comes from the back the response isn’t as strong. However, very interestingly, the sustained firing rate of the LGMD is also lower in Ventral-to-Dorsal (bottom-to-top) is lower. Meaning that Ventral-to-Dorsal isn’t as strong of a stimulus for the LGMD as well. This means that the LGMD is directionally prefers Anterior-to-Posterior (Front-to-back) and Dorsal-to-Ventral (top-to-bottom) motion. These are the motions most often associated with looming stimulus in the wild and thus makes sense. Shadows moving in the non-preferred directions, are often not associated with getting caught. However, if the stimulus is fast enough the grasshopper will still jump away.
But here is the math comes in, and makes this an interesting paper from a computational perspective. Let’s examine the Posterior-to-Anterior (back-to-front) motion in more detail. If all the synaptic weights are the same we would not expect these results. Notice in the model that the posterior input is near the Axon. It is a well-known result that when synapses fire along a dendritic branch of constant radius towards the axon that the signal is stronger than if the synaptic motion was the opposite direction away from the axon (Koch 1999). Thus, one would expect that moving posterior-to-anterior (back-to-front) would result in a lower firing rate. That’s exactly what the experiment shows! However, Peron et al say the Model disagrees, why is that? Notice figure 1B again. Notice the radius of the dendrites the get thinner at the edges. At the edge the radius is thin about 2 microns, but at the base of the dendrites, where they meet the axon the radius is 5 microns. That’s a 150% increase in radius! That effect will counteract filtering effect from moving towards the axon. As a result, a model with equal synaptic weights fails to capture the behavior. Thus, the synaptic weight must be higher in the preferred directions. This is even more likely the case in the Ventral-to-Dorsal (bottom-to-top), as there is no reason in the neurons morphological structure that Ventral to Dorsal motion shouldn’t be preferred, implying synaptic input strength does indeed matter. When the model is updated to include stronger synaptic weights in the preferred directions, the model agrees very closely with the data.
Still this isn’t conclusive evidence for the Dorsal-to-Ventral mechanism, nor does it explain why the synapses would be stronger in the Dorsal-to-Ventral direction. Any science paper leaves us with new questions to ask, and for Peron et al. To me it makes sense why the synapse is stronger the thicker the dendritic radius and thus (Anterior to Posterior motion), yet I find myself wondering what presynaptic mechanism cause the difference between Ventral-to-Dorsal and Dorsal-to-Ventral firing. However, answering this question is out of the scope of Peron et al’s study. In the discussion they propose several potential causes of Dorsal-to-Ventral (top-to-bottom) synaptic weights, including inhibition to other areas of the neuron, and or some kind of feed-forward inhibition, but ultimately, like all science, further study is needed. Nonetheless, the paper makes a solid contribution to understanding how a single neuron can compute spatial information.
Author: Alex White
Source: Peron et al. (2009) "Precise Subcellular Input Retinotopy and Its Computational Consequences in an Identified Visual Interneuron" Neuron https://www.sciencedirect.com/science/article/pii/S0896627309006928
How do they determine the synaptic organization? In previous work, they noticed that dendrites do not have any voltage gated calcium channels (VGCC), and therefore there is no calcium increase when the voltage increases in the dendrite. Furthermore, they noticed the synapses are nicotinic acetylcholine receptors. Meaning they allow calcium ions into the cell only when an excitatory synapse from the retina is active. This is amazing stroke of luck! Because the calcium enters the cell only when a synapse is active, they are able to use calcium imaging to determine the location of the synapse! Normally VGCC will make this method fail, because the calcium signal is too spread out. Thus, when they stimulate the eye with light (ON) or a shadow (OFF) stimuli, they are able to observe approximately where the synapse is located on the dendritic tree!
Using a mathematical model, they show that the particular synaptic layout is necessary for the LGMD to perform the computation but not sufficient. Here we need to look at figure 1B and Figure 5 to understand the layout they found. Click the link to open the figures in a separate window.* Notice that Dorsal(top) and Ventral(bottom) go across the dendrites, and that posterior(back) to anterior(front) goes along the dendrites. This set up allows the cell to determine which way the looming shadow comes from, and if the signal is fast enough and in the right direction, the locust will jump away. By recording the electrical signal in the axon of LGMD they show in Fig 5 that the maximum firing rate is the lowest when the shadow moves from Posterior-to-Anterior (Back-to-front). This means that when the looming response comes from the back the response isn’t as strong. However, very interestingly, the sustained firing rate of the LGMD is also lower in Ventral-to-Dorsal (bottom-to-top) is lower. Meaning that Ventral-to-Dorsal isn’t as strong of a stimulus for the LGMD as well. This means that the LGMD is directionally prefers Anterior-to-Posterior (Front-to-back) and Dorsal-to-Ventral (top-to-bottom) motion. These are the motions most often associated with looming stimulus in the wild and thus makes sense. Shadows moving in the non-preferred directions, are often not associated with getting caught. However, if the stimulus is fast enough the grasshopper will still jump away.
But here is the math comes in, and makes this an interesting paper from a computational perspective. Let’s examine the Posterior-to-Anterior (back-to-front) motion in more detail. If all the synaptic weights are the same we would not expect these results. Notice in the model that the posterior input is near the Axon. It is a well-known result that when synapses fire along a dendritic branch of constant radius towards the axon that the signal is stronger than if the synaptic motion was the opposite direction away from the axon (Koch 1999). Thus, one would expect that moving posterior-to-anterior (back-to-front) would result in a lower firing rate. That’s exactly what the experiment shows! However, Peron et al say the Model disagrees, why is that? Notice figure 1B again. Notice the radius of the dendrites the get thinner at the edges. At the edge the radius is thin about 2 microns, but at the base of the dendrites, where they meet the axon the radius is 5 microns. That’s a 150% increase in radius! That effect will counteract filtering effect from moving towards the axon. As a result, a model with equal synaptic weights fails to capture the behavior. Thus, the synaptic weight must be higher in the preferred directions. This is even more likely the case in the Ventral-to-Dorsal (bottom-to-top), as there is no reason in the neurons morphological structure that Ventral to Dorsal motion shouldn’t be preferred, implying synaptic input strength does indeed matter. When the model is updated to include stronger synaptic weights in the preferred directions, the model agrees very closely with the data.
Still this isn’t conclusive evidence for the Dorsal-to-Ventral mechanism, nor does it explain why the synapses would be stronger in the Dorsal-to-Ventral direction. Any science paper leaves us with new questions to ask, and for Peron et al. To me it makes sense why the synapse is stronger the thicker the dendritic radius and thus (Anterior to Posterior motion), yet I find myself wondering what presynaptic mechanism cause the difference between Ventral-to-Dorsal and Dorsal-to-Ventral firing. However, answering this question is out of the scope of Peron et al’s study. In the discussion they propose several potential causes of Dorsal-to-Ventral (top-to-bottom) synaptic weights, including inhibition to other areas of the neuron, and or some kind of feed-forward inhibition, but ultimately, like all science, further study is needed. Nonetheless, the paper makes a solid contribution to understanding how a single neuron can compute spatial information.
Author: Alex White
Source: Peron et al. (2009) "Precise Subcellular Input Retinotopy and Its Computational Consequences in an Identified Visual Interneuron" Neuron https://www.sciencedirect.com/science/article/pii/S0896627309006928
留言
張貼留言