Simplicity, Flexibility, and Interpretability in a Model of Dendritic Protein Distributions

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Previews Health Organization (Courtine and Sofroniew, 2019), and neurological recovery remains very limited. Indeed, no clinical trial so far has proven efficacy of a therapeutic repair strategy to improve functional recovery after spinal cord injury (Courtine and Sofroniew, 2019). Interventions modulating the cell biology of neurons and glial cells provide great hope toward developing novel therapy concepts. Transiently targeting proteins that modulate actin dynamics, e.g., by small-molecule drugs, RNA interference, or viral expression, may emerge as a promising strategy to induce actin-driven regrowth of axons after injury. REFERENCES Courtine, G., and Sofroniew, M.V. (2019). Spinal cord repair: advances in biology and technology. Nat. Med. 25, 898–908.

Flynn, K.C., Hellal, F., Neukirchen, D., Jacob, S., Tahirovic, S., Dupraz, S., Stern, S., Garvalov, B.K., Gurniak, C., Shaw, A.E., et al. (2012). ADF/cofilin-mediated actin retrograde flow directs neurite formation in the developing brain. Neuron 76, 1091–1107. Hellal, F., Hurtado, A., Ruschel, J., Flynn, K.C., Laskowski, C.J., Umlauf, M., Kapitein, L.C., Strikis, D., Lemmon, V., Bixby, J., et al. (2011). Microtubule stabilization reduces scarring and causes axon regeneration after spinal cord injury. Science 331, 928–931. Lowery, L.A., and Van Vactor, D. (2009). The trip of the tip: understanding the growth cone machinery. Nat. Rev. Mol. Cell Biol. 10, 332–343. Richardson, P.M., and Issa, V.M.K. (1984). Peripheral injury enhances central regeneration of primary sensory neurones. Nature 309, 791–793. Ruschel, J., Hellal, F., Flynn, K.C., Dupraz, S., Elliott, D.A., Tedeschi, A., Bates, M., Sliwinski, C., Brook, G., Dobrindt, K., et al. (2015). Axonal regeneration. Systemic administration of epothilone B

promotes axon regeneration after spinal cord injury. Science 348, 347–352. Sengottuvel, V., Leibinger, M., Pfreimer, M., Andreadaki, A., and Fischer, D. (2011). Taxol facilitates axon regeneration in the mature CNS. J. Neurosci. 31, 2688–2699. Tedeschi, A., Dupraz, S., Curcio, M., Laskowski, C.J., Schaffran, B., Flynn, K.C., Santos, T.E., Stern, S., Hilton, B.J., Larson, M.J.E., et al. (2019). ADF/Cofilin-mediated actin turnover promotes axon regeneration in the adult CNS. Neuron 103, this issue, 1073–1085. Yang, P., and Yang, Z. (2012). Enhancing intrinsic growth capacity promotes adult CNS regeneration. J. Neurol. Sci. 312, 1–6. Zhang, Y., Chen, K., Sloan, S.A., Bennett, M.L., Scholze, A.R., O’Keeffe, S., Phatnani, H.P., Guarnieri, P., Caneda, C., Ruderisch, N., et al. (2014). An RNA-sequencing transcriptome and splicing database of glia, neurons, and vascular cells of the cerebral cortex. J. Neurosci. 34, 11929–11947.

Simplicity, Flexibility, and Interpretability in a Model of Dendritic Protein Distributions Cian O’Donnell1,* 1Bristol Computational Neuroscience Unit, School of Computer Science, Electrical and Electronic Engineering, and Engineering Mathematics, University of Bristol, Bristol, UK *Correspondence: [email protected] https://doi.org/10.1016/j.neuron.2019.09.010

In this issue of Neuron, Fonkeu et al. (2019) present a mathematical model of mRNA and protein synthesis, degradation, diffusion, and trafficking in neuronal dendrites. The model can predict the spatial distribution and temporal dynamics of proteins along dendrites. The authors use the model to account for in situ imaging data of CaMKII⍺ mRNA and protein in hippocampal neurons.

The goal of computational modeling in biology is not to capture every last detail in whatever system we are studying, but to help us understand how the system works. As a result, a model should be judged by its practical usefulness toward answering a particular set of questions, not by whether it includes this or that protein or mechanism. Three desirable properties of models that affect their practical usefulness are simplicity, flexibility, and interpretability. Simplicity enables mathematical analysis and quick simulation on a

computer. Flexibility allows the model to capture a wide range of phenomena. Interpretability allows us to relate model parameters and variables to things measurable in the lab. Frustratingly, however, these properties often seem to trade off against each other; it is usually difficult to meet all three demands in one model. In this issue of Neuron, Fonkeu et al. (2019) present that rare thing: a mathematical model of mRNA and protein synthesis, diffusion, and trafficking in neuronal dendrites that is simple, flexible, and interpretable.

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Why was the model by Fonkeu et al. (2019) needed? Learning and memory in the brain is largely due to modifications of synapses distributed across each neuron’s dendritic tree, hundreds of microns from the cell’s nucleus in the soma. Because these dendritic and synaptic structures need proteins to operate and their makeup changes during synaptic plasticity, to understand learning and memory, we need to understand how protein distribution is controlled across the dendritic tree.

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Previews To elaborate on the problem: mRNAs can only be transcribed from DNA in the nucleus, after which two things can happen. Either proteins can immediately be translated from the mRNA and shipped wherever they need to go in the cell or the mRNAs can be translocated out of the nucleus, transported around the cell, and then proteins can be translated locally where needed. The latter scenario arguably makes more sense from an energetic point of view: why actively transport proteins en masse along the dendrites when, instead, a small number of mRNA molecules could be transported out to the dendrites to manufacture the proteins on demand where needed? Empirically, however, neurons appear to use a mix of both strategies, actively transporting both mRNA and proteins along dendrites. The question therefore shifts to: what are the respective effects of mRNA and protein synthesis, degradation, diffusion, and trafficking on the resulting distribution of proteins in dendrites? Existing mathematical models of dendritic protein expression captured only somatic protein translation (Bressloff and Earnshaw, 2007; Williams et al., 2016) and did not account for the joint effects of mRNA and protein transport in dendrites. The Fonkeu et al. (2019) study presents an elegant, minimal model capturing all these mechanisms. The model sits at an intersection of several historical lines of research. The basic partial differential equations are widely used in physics and chemistry, commonly known as the ‘‘drift-diffusion model’’ (Crank, 1979). The study also brings ideas from the field of systems biology, where mathematical models have been heavily employed to study the dynamics of gene expression in cells (Alon, 2006), albeit mostly without including the dramatic spatial properties of elongated cells like neurons. Perhaps most relevant for a neuroscience audience though is the link to the classic dendritic cable theory of Rall (Segev et al., 1995). In the 1950s–1960s, Rall advanced the use of cable theory to model the spread of electrical charge in dendrites. The mathematical form of the models used by Rall is notably similar to that used by Fonkeu et al. (2019) to describe

the dynamics of mRNA and proteins. A key concept emerging from both types of models is the idea of a space constant l, which represents the typical length scale over which the respective voltage, mRNA, or protein varies along the dendrite. If the space constant for a given protein was calculated at, say, a few microns, then we might expect the spatial profile of this protein’s expression to look lumpy, varying substantially along the dendrite. In contrast, if a protein had a space constant of a thousand microns or more, then we should expect that protein’s concentration to vary only slightly across the dendritic tree. As a test case for the model, Fonkeu et al. (2019) used parameter estimates from the literature to attempt to replicate their in situ imaging data of CaMKII⍺ protein and mRNA molecules from the dendrites of cultured rodent hippocampal neurons. In addition to accounting for the data, Fonkeu et al. (2019) took advantage of the interpretability of the model’s parameters to dissociate relative effects of diffusion versus active trafficking. Interestingly they found that mRNA active trafficking rates and degradation rates had large effects on mRNA distribution while varying the mRNA diffusion rate had only negligible effects. CaMKII⍺ protein tended to have a more uniform steadystate distribution than its mRNA due to a higher diffusion coefficient. Fonkeu et al. (2019) went on to simulate what happens when new CaMKII⍺ mRNA and protein are synthesized, finding that somatic transcription has only very slow and spatially uniform effects on dendritic protein levels. In contrast, when Fonkeu et al. (2019) simulated a spatially and temporally localized protein translation event in a dendrite, they found a wave of protein expression that lasts only a few hours and spreads only 100–200 mm from the site of translation. So far, so good. But what are the model’s limitations? What can it not do? First, Fonkeu et al. (2019) assumed only a single one-dimensional dendrite. The model would need to be modified to capture the effects of dendritic spines, which can slow diffusion by trapping molecules (Santamaria et al., 2006), or to capture the elaborate branching morphologies of real dendrites. As with elec-

trophysiology models, clever innovations may allow a branched version of this model to retain analytical tractability (Abbott et al., 1991). Alternatively, the partial differential equations could be approximated by a set of ordinary differential equations, one for each neighboring spatial compartment on a dendrite. This would mean losing analytical tractability, but the model could still be numerically simulated on a computer. Second, the model is formulated in terms of concentrations of molecules, not single discrete molecule counts. This approximation is reasonable when large number of molecules are present because the inherent stochasticity of molecular diffusion and reactions gets averaged out. Indeed, CaMKII⍺ was an ideal test case in this regard as it is one of the most abundantly expressed proteins in dendrites. But CaMKII⍺ may be atypical. Dendritic compartments may contain single-digit copy numbers of some molecular species (Kosik, 2016). In this regime, the effects of inherently stochastic processes, such as molecular binding and unbinding to motor proteins, may be substantial. In many cases, this noise cannot be averaged away; there may be no ‘‘deterministic version’’ of such models (Mahmutovic et al., 2012). Third, the model terms are all linear. In reality, there are likely to be nonlinearities that affect protein expression. For example, protein translation requires the presence of ribosome machinery, which may be locally limited in number (Kosik, 2016). This means that protein translation rates may temporarily saturate in certain regions of the cell, and multiple protein types may compete for the same limited ribosome resource. Although the model could readily be expanded to capture these phenomena, the resulting nonlinear ‘‘reaction-driftdiffusion’’ models can soon produce complicated dynamics that limit analytical tractability. In such case, the field may need to switch to numerical simulations, as the electrophysiological modeling field has done to elaborate Rall’s models with nonlinear voltagedependent ion channels. The above caveats should not be taken as disadvantages of the model by Fonkeu et al. (2019). On the contrary, Neuron 103, September 25, 2019 951

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Previews the authors have presented us with a powerful new framework capturing the dominant factors controlling dendritic protein distributions, which will serve as a foundation upon which future models must be built. Its impact will likely be amplified by the development of the smart webtool (http://www. tchumatchenko.de/Visualisation.html) to allow experimentalists to plug in parameter values for their protein of choice. In summary, like all good models, the Fonkeu et al. (2019) framework gives us both an insight into the mechanisms underlying a complicated system and a useful machine for making quantitative, testable predictions for future experiments.

REFERENCES Abbott, L.F., Farhi, E., and Gutmann, S. (1991). The path integral for dendritic trees. Biol. Cybern. 66, 49–60. Alon, U. (2006). An Introduction to Systems Biology: Design Principles of Biological Circuits (Chapman and Hall/CRC). Bressloff, P.C., and Earnshaw, B.A. (2007). Diffusion-trapping model of receptor trafficking in dendrites. Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 75, 041915. Crank, J. (1979). The Mathematics of Diffusion (Oxford University Press). Fonkeu, Y., Kraynyukova, N., Hafner, A.-S., Kochen, L., Sartori, F., Schuman, E.M., and Tchumatchenko, T. (2019). How mRNA localization and protein synthesis sites influence dendritic protein distribution and dynamics. Neuron 103, this issue, 1109–1122.

Kosik, K.S. (2016). Life at low copy number: how dendrites manage with so few mRNAs. Neuron 92, 1168–1180. Mahmutovic, A., Fange, D., Berg, O.G., and Elf, J. (2012). Lost in presumption: stochastic reactions in spatial models. Nat. Methods 9, 1163–1166. Santamaria, F., Wils, S., De Schutter, E., and Augustine, G.J. (2006). Anomalous diffusion in Purkinje cell dendrites caused by spines. Neuron 52, 635–648. Segev, I., Rinzel, J., and Shepherd, G.M. (1995). The Theoretical Foundation of Dendritic Function: Selected Papers of Wilfrid Rall with Commentaries (MIT Press). Williams, A.H., O’Donnell, C., Sejnowski, T.J., and O’Leary, T. (2016). Dendritic trafficking faces physiologically critical speed-precision tradeoffs. eLife 5, e20556.

Scratching after Stroking and Poking: A Spinal Circuit Underlying Mechanical Itch Zilong Wang,1 Christopher R. Donnelly,1 and Ru-Rong Ji1,2,3,* 1Center

for Translational Pain Medicine, Department of Anesthesiology, Duke University Medical Center, Durham, NC 27710, USA of Neurobiology, Duke University Medical Center, Durham, NC 27710, USA 3Department of Cell Biology, Duke University Medical Center, Durham, NC 27710, USA *Correspondence: [email protected] https://doi.org/10.1016/j.neuron.2019.09.009 2Department

Mechanical itch is a desire to scratch due to light mechanical stimuli. In this issue of Neuron, Pan et al. (2019) identify a feedforward inhibition circuit in the spinal cord dorsal horn that processes mechanical itch as well as spontaneous itch. How do you feel when your skin is gently grazed by a hair or when an insect is climbing on your skin? Most people will have an instinctual urge to scratch their skin in response to such stimuli. This sensation is defined as mechanical itch, a distinct sensory entity from chemical itch elicited by chemical pruritogens. Under physiological conditions, mechanical itch is a warning sign, serving a protective role to alert an organism to possible environmental hazards. Unfortunately, hypersensitivity of mechanical itch is also a symptom in chronic itch (Ikoma et al., 2006). Distinct cellular mechanisms may underlie mechanical and chemical itch (Bourane et al., 2015;

Feng et al., 2018). It remains unknown which population(s) of peripheral (primary) sensory neurons mediates mechanical itch, nor do we understand which population of neurons in the spinal cord transmits mechanical itch. In this issue of Neuron, Pan et al. (2019) identified a unique subpopulation of spinal cord excitatory interneurons (INs) that are required for mechanical itch. These spinal INs express the neuropeptide Ucn3 in inner lamina II and lamina III. Strikingly, using an intersectional genetic strategy to ablate >97% of Ucn3+ INs, Pan et al. (2019) demonstrate that mechanical itch elicited by gentle touch is completely abolished without affecting

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chemical pruritogen-induced itch. Further experiments using DREADD-based chemogenetic approaches demonstrate that silencing spinal Ucn3+ INs attenuates mechanical itch, while acute activation of Ucn3+ neurons is sufficient to evoke spontaneous scratching. Which neurons provide afferent synaptic inputs onto Ucn3+ INs? Further analysis reveals that Ucn3+ INs receive inputs from Ab low-threshold mechanoreceptors (Ab-LTMRs). Interestingly, monosynaptic tracing discovered that 89% of Ucn3-innervating DRG sensory neurons co-express Toll-like receptor 5 (TLR5). Thus, TLR5+ LTMRs make synaptic connections to spinal Ucn3+