Encyclopedia of Computational Neuroscience

Living Edition
| Editors: Dieter Jaeger, Ranu Jung

Dendritic Spines

  • William R. HolmesEmail author
Living reference work entry
DOI: https://doi.org/10.1007/978-1-4614-7320-6_132-1


Dendritic Spine Synaptic Input Membrane Area Spine Head Calcium Conductance 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Many types of neurons receive synaptic inputs on dendritic spines which are short protrusions of membrane composed of a bulbous “head” connected to the dendrite by a thin “stem” or “neck” (Yuste 2010). Although spines are typically small in size, they occur in high densities along dendrites and may compose 40–60 % of the total dendritic surface area. There are two straightforward methods for including spines in computational models of neurons without representing every spine explicitly.

Detailed Description

Spines are widely regarded to serve a biochemical function by providing an isolated compartment where highly localized calcium signals and subsequent reactions can occur. An electrical function was initially proposed by Rall who showed that the steady-state attenuation of a signal from the spine head to the dendrite could be expressed as VSH/VBI = 1 + RSS/RBI, where VSH and VBI are the voltages at the spine head and dendrite, respectively; RSS is the spine stem resistance; and RBI is the input resistance at the dendrite. Rall suggested that changes in spine stem diameter might be important for plasticity because of its effect on RSS, but studies searching for such changes produced mixed results. Others have suggested that if voltage-dependent conductances are present on spines, then spines might amplify inputs and could otherwise increase the computational possibilities of the cell. Many of the more interesting possibilities suggested by theoretical studies require a large RSS, but whether or not RSS is sufficiently large has been controversial.

Because the proportion of membrane area occupied by spines can be large, single-neuron models that ignore spines are bound to produce erroneous results. There are two straightforward methods for including spines in models without coding each and every spine, as long as these implicitly included spines do not receive synaptic input. First, if dendritic and spine membranes are assumed to have the same specific membrane resistance and capacitance, Rm and Cm, spines can be implicitly included in a model by increasing Cm and reducing Rm according to the proportion of total membrane area contributed by spines. We call this the Rm–Cm method. For example, if spines increase the membrane area of a dendrite by 33 %, then spines can be implicitly modeled by multiplying the dendrite Cm by 1.33 and dividing dendritic Rm by 1.33. Alternatively, one can keep Rm and Cm constant but increase length and diameter in such a way as to keep intracellular resistance constant (i.e., keep length/diameter2 constant). We call this the l-d method. For example, if spines increase membrane area by 33 %, let F = 1.33 and multiply length by F2/3 and diameter by F1/3.

These two methods for including spines in models implicitly provide identical results with passive models, but they make very different assumptions when voltage-dependent conductances are present. The first method, where Rm and Cm are changed, assumes that spines have passive membrane, while the second method, where length and diameter are changed, assumes that the spines have the same densities of voltage-dependent conductances as the dendrite. The cell should have a lower input resistance with the second method but should also respond more nonlinearly with voltage perturbations. Needless to say, results may be very different.

Nevertheless, it is straightforward to modify either method to include spines possessing different densities of voltage-dependent conductances than present on the dendrite. With the first method, one should change dendritic Rm and Cm as described above but also modify the maximum conductance density (g-bar) for each conductance by \( {\overline{\mathrm{g}}}_{\mathrm{d}-\mathrm{new}}=\left({\overline{\mathrm{g}}}_{\mathrm{d}-\mathrm{old}}{\mathrm{A}}_{\mathrm{d}}+{\overline{\mathrm{g}}}_{\mathrm{s}\mathrm{pine}}{\mathrm{A}}_{\mathrm{s}}\right)/{\mathrm{A}}_{\mathrm{d}} \) where Ad is the membrane area of the dendritic segment and As is the membrane area of all spines on that segment. With the second method, one should modify the maximum conductance density for every conductance on each dendrite by \( {\overline{\mathrm{g}}}_{\mathrm{d}-\mathrm{new}}=\left({\overline{\mathrm{g}}}_{\mathrm{d}-\mathrm{old}}{\mathrm{A}}_{\mathrm{d}}+{\overline{\mathrm{g}}}_{\mathrm{s}\mathrm{pine}}{\mathrm{A}}_{\mathrm{s}}\right)/\left({\mathrm{A}}_{\mathrm{d}}+{\mathrm{A}}_{\mathrm{s}}\right) \) and then change length and diameter of the dendrite as described above. These expressions assume spine head and neck have the same channel densities. If this is not true, one could calculate an equivalent \( {\overline{\mathrm{g}}}_{\mathrm{spine}} \) to use.

These methods are easily incorporated into single-neuron simulators such as NEURON or GENESIS and work well for voltage-dependent conductances with fixed reversal potentials. However, these methods are subject to error when calcium and calcium-dependent conductances are present and particularly so if these conductances have different densities in spines and dendrites. Calcium accumulation and removal can be different in spines and dendrites, and different intracellular calcium concentrations will affect the calcium Nernst potential and activation of calcium-dependent conductances differently. The Rm–Cm method is preferred if dendrites have calcium conductances and spines do not. The l-d method is preferred if calcium conductances are on both dendrites and spines, but activation of calcium-dependent potassium conductances in spines remains problematic. It is possible to compensate for these types of errors by adjusting calcium pool parameters or by considering spine calcium and calcium-dependent conductances as separate conductances with their own parameters when conductances are merged into dendrites. These errors are not likely to be significant in short-time simulations but can be seen to accumulate over longer time periods.


  1. Yuste R (2010) Dendritic spines. MIT Press, Cambridge, MAGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Department of Biological SciencesOhio UniversityAthensUSA