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2. Volonte, D., Peoples, A.J., and Galbiati, F.(2003). Modulation of myoblast fusion bycaveolin-3 in dystrophic skeletal muscle cells:implications for Duchenne muscular dystrophyand limb-girdle muscular dystrophy-1C. Mol.Biol. Cell 14, 4075–4088.

3. Sens, K.L., Zhang, S., Jin, P., Duan, R.,Zhang, G., Luo, F., Parachini, L., and Chen, E.H.(2010). An invasive podosome-like structurepromotes fusion pore formation duringmyoblast fusion. J. Cell Biol. 191, 1013–1027.

4. Kesper, D.A., Stute, C., Buttgereit, D.,Kreiskother, N., Vishnu, S., Fischbach, K.F.,and Renkawitz-Pohl, R. (2007). Myoblast fusionin Drosophila melanogaster is mediatedthrough a fusion-restricted myogenic-adhesivestructure (FuRMAS). Dev. Dyn. 236, 404–415.

5. Kim, S., Shilagardi, K., Zhang, S., Hong, S.N.,Sens, K.L., Bo, J., Gonzalez, G.A., andChen, E.H. (2007). A critical function for theactin cytoskeleton in targeted exocytosis ofprefusion vesicles during myoblast fusion. Dev.Cell 12, 571–586.

6. Richardson, B.E., Beckett, K., Nowak, S.J., andBaylies, M.K. (2007). SCAR/WAVE and Arp2/3are crucial for cytoskeletal remodeling at thesite of myoblast fusion. Development 134,4357–4367.

7. Rochlin, K., Yu, S., Roy, S., and Baylies, M.K.(2010). Myoblast fusion: when it takes more tomake one. Dev. Biol. 341, 66–83.

8. Berger, S., Schafer, G., Kesper, D.A., Holz, A.,Eriksson, T., Palmer, R.H., Beck, L., Klambt, C.,Renkawitz-Pohl, R., and Onel, S.F. (2008).

WASP and SCAR have distinct roles inactivating the Arp2/3 complex during myoblastfusion. J. Cell Sci. 121, 1303–1313.

9. Massarwa, R., Carmon, S., Shilo, B.Z., andSchejter, E.D. (2007). WIP/WASp-basedactin-polymerization machinery is essentialfor myoblast fusion in Drosophila. Dev. Cell 12,557–569.

10. Schafer, G., Weber, S., Holz, A., Bogdan, S.,Schumacher, S., Muller, A., Renkawitz-Pohl, R.,and Onel, S.F. (2007). The Wiskott-Aldrichsyndrome protein (WASP) is essential formyoblast fusion in Drosophila. Dev. Biol. 304,664–674.

11. Gimona, M., Buccione, R., Courtneidge, S.A.,and Linder, S. (2008). Assembly and biologicalrole of podosomes and invadopodia. Curr.Opin. Cell Biol. 20, 235–241.

12. Weaver, A.M. (2006). Invadopodia: specializedcell structures for cancer invasion. Clin. Exp.Metastasis 23, 97–105.

13. Martens, S., and McMahon, H.T. (2008).Mechanisms of membrane fusion: disparateplayers and common principles. Nat. Rev. Mol.Cell Biol. 9, 543–556.

14. Mukai, A., Kurisaki, T., Sato, S.B.,Kobayashi, T., Kondoh, G., and Hashimoto, N.(2009). Dynamic clustering and dispersion oflipid rafts contribute to fusion competence ofmyogenic cells. Exp. Cell Res. 315, 3052–3063.

15. Yamaguchi, H., Takeo, Y., Yoshida, S.,Kouchi, Z., Nakamura, Y., and Fukami, K.(2009). Lipid rafts and caveolin-1 are requiredfor invadopodia formation and extracellular

matrix degradation by human breast cancercells. Cancer Res. 69, 8594–8602.

16. Carman, C.V., Sage, P.T., Sciuto, T.E., de laFuente, M.A., Geha, R.S., Ochs, H.D.,Dvorak, H.F., Dvorak, A.M., and Springer, T.A.(2007). Transcellular diapedesis is initiated byinvasive podosomes. Immunity 26, 784–797.

17. Quintavalle, M., Elia, L., Condorelli, G., andCourtneidge, S.A. (2010). MicroRNA controlof podosome formation in vascular smoothmuscle cells in vivo and in vitro. J. Cell Biol.189, 13–22.

18. Rottiers, P., Saltel, F., Daubon, T., Chaigne-Delalande, B., Tridon, V., Billottet, C.,Reuzeau, E., and Genot, E. (2009). TGFbeta-induced endothelial podosomes mediatebasement membrane collagen degradation inarterial vessels. J. Cell Sci. 122, 4311–4318.

19. Destaing, O., Saltel, F., Geminard, J.C.,Jurdic, P., and Bard, F. (2003). Podosomesdisplay actin turnover and dynamicself-organization in osteoclasts expressingactin-green fluorescent protein. Mol. Biol. Cell14, 407–416.

Department of Cancer Biology, VanderbiltUniversity Medical Center, Nashville,TN 37232, USA.*E-mail: alissa.weaver@vanderbilt.edu

DOI: 10.1016/j.cub.2010.12.024

Neuroscience: What We CannotModel, We Do Not Understand

To understand computations in neuronal circuits, a model of a small patchof cortex has been developed that can describe the firing regime in thevisual system remarkably well.

William S. Anderson1

and Gabriel Kreiman2,3,4,*

Circuits of neurons in the brain arevery complicated: because of themultiple non-linearities, differenttypes of neurons, complex dendriticgeometries, diverse connectivitypatterns and dependencies on learningand development, the cerebral cortexand other neuronal circuits constitutethe most complex systems everstudied by science. Perhaps notsurprisingly, the computationalpower that emerges from suchcircuits is astounding; neuronalnetworks are responsible fordiverse cognitive phenomenasuch as seeing, smelling,remembering, planning and so on.

To understand how functionemerges from ensembles of neuronsand their interactions, we needa rigorous interplay of theoreticalwork and experimental approachescapable of listening to the activity

of neurons. This synergy of theoryand neurophysiology is beautifullyillustrated in recent work byRasch et al.[1]. These authors took a courageousapproach using computational modelsto describe the activity in a local 5 x5 mm patch of neocortex with animpressive set of 35,000 neuronsandw4million synapses. They focusedon primary visual cortex, one of themost studied parts of cortex and thefirst stage in the hierarchical cascadeof processes that convert the retinalinput into our visual perceptions. TheLogothetis lab used multiple microwireelectrodes to measure the activity ofneurons in primary visual cortex ofanesthetized monkeys while themonkeys watched a natural scenemovie. The authors then ‘presented’the same movie to their model toexplore its fidelity and quantitativelycompare the computational outputand the neurophysiological one.

To compare the circuit in silicoand in vivo, one must consider what

aspects of the complex neuronalensemble responses one aims toexplain. Instead of trying to predict thedetailed spiking activity of every singleneuron as done in many other studies(for example [2,3]), Rasch et al. [1]defined a ‘firing regime’ that ischaracterized by several propertiesof the neuronal responses. Theseproperties included the firing rate,distribution of interspike intervals,variability in spike counts over time,degree of burst firing and degreeof synchronization in the network.The authors use these inter-relatedproperties to define the state of thenetwork.Another important aspect that the

theorist must consider when thinkingabout such network models is thelarge number of parameters that ariseas a consequence of the complexity inthe circuitry. The modeler needs tomake decisions about the number andtype of neurons, their distribution andconnectivity, the type of ionicchannels they are embedded with andtheir corresponding characteristics.Some of these decisions may beconstrained by experimental data;others may require more guesswork.Parameters are our enemies. It isextremely difficult froma computational viewpoint tosystematically characterize the

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whole parameter space. For convexoptimization problems, one cantune and optimize each parameterseparately, but it is often difficult toassess whether the problem at handis convex or not. In high-dimensionalspaces, the curse of dimensionalitymakes itself evident. Rasch et al. [1]start by approximating parametersby intelligent estimation based onexisting data taken from the literature.Remarkably, without tuningparameters, the model doesnot perform too badly and thecomputational circuit is a reasonableapproximation to the empiricallydefined firing regime.

Rasch et al. [1] went on to turnknobs here and there to examine thesensitivity and robustness of themodel to different variables andassumptions. By tuning parameters,the authors were able significantly toimprove the fit to the experimentaldata and, more importantly, along theway, they discovered specific knobsthat are more relevant to influence themodel output. Specifically, keyparameters included the relativesynaptic weights of excitatory toinhibitory neurons [4] and the relativeweighting of the patchy long-rangeconnections (which were reduced toavoid pathologic oscillatory behavior).The model was also quite sensitive tocertain channel conductanceparameters, specifically NMDA, andsurprisingly GABAB with its relativelyslow dynamics. Many modelers haveactually ignored this conductance inmore complex and detailed simulationstudies [5], and Rasch et al. [1] contendthat it might improve the fit to obtainrealistic firing rates by providing longerlasting and non-linear qualities to thefiring rates of the inhibitory cellcomponent.

In the same way that all roadslead to Rome, there may be multipledifferent ways to build a network withsimilar output properties. In a landmarkstudy, Prinz and colleagues [6], andsubsequently several other groups,showed that different combinationsof intrinsic neuronal properties aswell as connectivity patterns can leadto the same properties at the networklevel. In a similar vein, Rasch et al. [1]discovered robustness in the outputto a large number of knobs andparameters in their model. In otherwords, quite distinct combinationsof parameters can lead to the samefiring regime.

How well does the modelapproximate the statistical fingerprintor firing regime of primary visualcortex? Rasch et al. [1] elegantlyevaluated the answer to this questionby comparing the differences betweenthe model results and theexperimental data to the variabilityacross recordings from the sameelectrodes, across different repetitionsof the movie stimulus or acrossrecordings from different individualmonkeys. Neurophysiologicalrecordings in cortex typically showa significant degree of variabilityacross repetitions, neurons andmonkeys; much has been written anddiscussed about this variability (forexample [7,8]). The difference betweenthe best model and theneurophysiological responses wasabout as large as the differencebetween different physiologicalrecordings in response to the samemovie (in terms of the firing regime).In other words, given two sets of datadescribing the ten statisticalproperties that defined the firingregime, it would be difficult todiscriminate which one came from themodel and which one came from themonkey.

In addition to the importanceof this work to characterizingand understanding the principlesunderlying the behavior of complexneuronal circuits, computationalmodels of this sort can also helpunderstand abnormal patterns ofactivity in cortex. One example ofthis type of effort is the ongoingeffort to understand epilepsy throughcomputational models. Neuronalsynchrony occurs readily in denselyinterconnected model networks[5,9,10]. Because synchronousneuronal firing is so easily produced,many authors have examined thisas evidence of pathology or evenrepresentations of seizures incomputational models [5,11,12].Likely to avoid this pathologicbehavior, Rasch et al. [1] imposeda strong constraint on the modeledsystem: it must reproduce the sparseand at times irregular firing behavior ofthe experimental (albeit anesthetized)animal preparation. Rasch et al. [1]allude in their comments to animportant limitation to this approach:given this form of optimization into the‘computational advantageous regime’,it is not clear that the model couldsubsequently reproduce long range

oscillatory behavior similar to thealpha rhythm in the resting awakestate. Thus, in addition to helpingus characterize the firing regimes ofcortex and the mechanisms by whichneuronal circuits lead to these regimes,the type of computational modelingused by Rasch et al. [1] can help ustranslate this understanding toinvestigate conditions of clinicalrelevance.The instructive work of Rasch et al.

[1] highlights many of the keychallenges ahead. What is the‘appropriate’ level of abstraction tobuild models in neuroscience?Should we build models with manyparameters to take into account evermore realistic aspects of the biology[13] or should we consider ‘toy models’that aim to extract the key principlesof neuronal networks [14]? Should weaim to predict the spike timing ofevery neuron with millisecondprecision or rather to characterizemore global aspects of the networkbehavior? To take a simple analogy,the accuracy in predicting how anobject moves may benefitfrom considering a model that includesfriction, object shape, object materialand how/when/where forcesare applied among other variables.However, a single parametermodel that ignores many ofthese variables and assumes pointmasses (force = mass x acceleration)may take us a long way towardsgeneralization and understanding.The theoretical physicist RichardFeynman famously wrote: ‘‘What Icannot create, I do not understand.’’Similarly, theoretical efforts andcomputational models constituteessential requirements tounderstand the function of complexcircuits of neurons. Stay tuned,plenty of exciting theoreticaland computational work ahead.

References1. Rasch, M., Schuch, K., Logothetis, N., and

Maass, W. (2010). Statistical comparison ofspike responses to natural stimuli in monkeyarea V1 with simulated responses ofa detailed laminar network model for a patchof V1. J Neurophysiol., epub ahead of print.

2. Keat, J., Reinagel, P., Reid, R.C., andMeister, M. (2001). Predicting every spike:a model for the responses of visual neurons.Neuron 30, 803–817.

3. David, S.V., and Gallant, J.L. (2005). Predictingneuronal responses during natural vision.Network 16, 239–260.

4. Mazzoni, A., Panzeri, S., Logothetis, N.K., andBrunel, N. (2008). Encoding of naturalisticstimuli by local field potential spectra innetworks of excitatory and inhibitory neurons.PLoS Comput. Biol. 4, 1–20.

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6. Prinz, A.A., B.D., and Marder, E. (2004).Similar network activity from disparate circuitparameters. Nat. Neurosci. 7, 1345–1352.

7. Koch, C. (1999). Biophysics of Computation(New York: Oxford University Press).

8. Kreiman, G. (2004). Neural coding:computational and biophysical perspectives.Physics Life Rev. 1, 71–102.

9. Suffczynski, P., Lopes da Silva, F., Parra, J.,Velis, D., and Kalitzin, S. (2005). Epileptictransitions: model predictions andexperimental validation. J. Clin. Neurophysiol.22, 288–299.

10. Borgers, C., and Kopell, N. (2003).Synchronization in networks of excitatoryand inhibitory neurons with sparse,random connectivity. Neural Comput. 15,509–538.

11. Anderson, W.S., Kudela, P., Cho, J.,Bergey, G.K., and Franaszczuk, P.J. (2007).Studies of stimulus parameters for seizuredisruption using neural network simulations.Biol. Cybern. 97, 173–194.

12. Santhakumar, V., Aradi, I., and Soltesz, I. (2005).Role of mossy fiber sprouting and mossy cellloss in hyperexcitability: a network model of thedentate gyrus incorporating cell types andaxonal topography. J. Neurophysiol 93,437–453.

13. Markram, H. (2006). The blue brain project.Nat. Rev. Neurosci. 7, 153–160.

14. Serre, T., Kreiman, G., Kouh, M., Cadieu, C.,Knoblich, U., and Poggio, T. (2007). A

quantitative theory of immediate visualrecognition. Prog. Brain Res. 165C, 33–56.

1Department of Neurosurgery, Brigham andWomen’s Hospital, Boston, MA, USA.2Children’s Hospital, Harvard MedicalSchool, Boston, MA, USA. 3Center for BrainScience, Harvard University, Cambridge, MA,USA. 4Swartz Center for TheoreticalNeuroscience, Harvard University,Cambridge, MA, USA.*E-mail: Gabriel.Kreiman@childrens.harvard.edu

DOI: 10.1016/j.cub.2010.12.049