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# NMODL

This document describes how to use the NBSR model description language to add membrane mechanisms to NEURON.

NEURON's extensions to the NBSR language are described in:

- NEURON Extension to NMODL

## Model Description Language

### Introduction

The kinds of mechanisms that can be added are:

- Channels in which the model consists of current-voltage relationships.
- Calculation of internal and external ionic concentration changes due to currents carried by specific ions.

Many user defined mechanisms can be simultaneously "insert"ed into sections in NEURON; NEURON will keep track of the total current for each ionic species used and the effect of that current on the membrane potential. For example, suppose a calcium pump, sodium-calcium exchanger, calcium channel, radial calcium diffusion, and calcium activated potassium mechanisms are inserted into a cable section. Then the total calcium current is calculated as the sum of the individual currents from the calcium pump, exchanger, and channel. The internal calcium concentration just under the membrane is calculated from the total calcium current and diffusion away from the surface. The potassium current through the cagk channel is calculated from the internal calcium concentration next to the membrane and the membrane potential. And the membrane potential is calculated from the total current. (The above is only a partial list of the interactions among these channels. The point is that the ionic current, membrane voltage, and concentration computations are consistent regardless of the channels inserted into the cable section.)

Mechanisms are normally local. That is they do not depend on what is happening at other places on the neuron. However, a method exists for writing mechanisms that depend on variables of mechanisms at other locations. For example the calcium concentration at a presynaptic mechanism can be used to calculate the conductance change at a postsynaptic mechanism. (See, Importing variables from other mechanisms.) Also, FUNCTION's written in a model are global and may be used in other models if they do not involve range variables.

#### History

MODL (model description language) was originally developed at the NBSR (National Biomedical Simulation Resource) to specify models for simulation with SCoP (Simulation Control Program). With MODL one specifies a physical model in terms of simultaneous nonlinear algebraic equations, differential equations, or kinetic schemes. MODL translates the specification into the C language which is then compiled and linked with the SCoP program. It turned out that only modest extensions to the MODL syntax were necessary to allow it to translate model descriptions into a form suitable for compiling and linking with NEURON V2. The extended version was called NMODL. In NEURON V3 the advent of the object oriented interpreter, OC, allowed Point Processes to be treated as objects instead of parallel arrays of variables. The model description translator that emits code suitable for NEURON V3 is called NOCMODL. NMODL and NOCMODL handle identical input model descriptions, they differ merely in the output interface code. A prototype model description translator has been written to generate code suitable for linking with GENESIS.

This document discusses only the differences between NMODL and MODL. A complete user manual for the standard model description language is available from NBSR. A brief description of MODL is in the document entitled, "SCoP Language Summary".

#### Usage

The easiest way to write membrane mechanisms is by analogy with the examples. The example files come in pairs with a .mod and .hoc extension. Models (membrane mechanisms) are linked into neuron with the command:

        nrnivmodl  file1 file2 file3 ...

In the list of `.mod` files you do not type the extension, only the prefix. If there are no files specified then nrnivmodl will use all the mod files in the current working directory. When nrnivmodl is finished, there will exist a version of NEURON called special which contains those membrane mechanisms described in the files. `special` should be renamed to something more suitable. The associated `.hoc` files can be executed by special to test various aspects of the models.

It is extremely important that mechanisms have consistent units. To ensure this use the command:

        modlunit file

leaving off the file extension. For more information about units click here.

#### Rationale

Our first nerve simulation program, CABLE, contained several built-in membrane mechanisms, including radial calcium diffusion, calcium channel, calcium activated potassium channel, calcium pump, etc. However, in practice, only the Hodgkin-Huxley squid channels were enough of a standard to be used "as is" across more than one series of simulations. The other channels all required some type of modification to be useful as new situations arose. Sometimes the modifications were minor, such as changing the coordinate system for radial calcium diffusion so that there were more compartments near the membrane, but often we were forced to add an entirely new mechanism from scratch such as Frankenhaeuser-Huxley channels for Xenopus node. The problem was greatly compounded for other users of CABLE who needed to add new channels but were not familiar with the numerical issues or the detailed interface requirements. NMODL with NEURON is a significant improvement over CABLE with regard to adding new membrane mechanisms:

- Interface details are handled automatically.
- Consistency of units is ensured. (By checking with modlunit.)
- Mechanisms described by a kinetic scheme are written with a syntax in which the reactions are clearly apparent.
- There is often a great increase in clarity since statements are directly related to discourse at the model level instead of the C programming level.
- The high level description language often provides a great deal of leverage in that one model statement can get translated into very many C statements. For example, kinetic reaction statements get translated into statements which explicitly calculate sparse jacobian matrix coefficients.

At the same time, since the model description is translated into C, the computation speed remains the same or better than a hand coded mechanism in CABLE.

### General Paradigm

Membrane mechanisms deal with currents, concentrations, potentials, and state variables and it is helpful to know how NEURON treats these variables in order to correctly write a new membrane mechanism.

NEURON integrates its equations using the function `fadvance()`. During a call to this function the value of the global time variable, `t`, is increased by the value of `dt` `(t = t + dt)`, and all the voltages, currents, concentrations, etc. are changed to new values appropriate to the new value of time. The default numerical method used by NEURON produces values which have an error proportional to `dt`. That is, it makes no sense to ask at what time in the interval are the values most accurate. However, by setting the global variable `secondorder` equal to 2, the values produced by `fadvance` have errors proportional to `dt^2` and it is important to realize that

- membrane potential is second order correct at time, `t`.
- currents are second order correct at time, `t - dt/2`.
- channel states are second order correct at time, `t + dt/2`;.
- concentrations are second order correct at time, `t`.

`fadvance()` goes about its business by first setting up the current conservation matrix equation to be used in the calculation of membrane potential. To do this it calls the current functions for each mechanism in each segment which compute conductance using the old values of states and current using the old values of states and membrane potential. The value of time when the BREAKPOINT block is called is t+dt/2 so models which depend explicitly on time will be second order correct if they use the value of `t`. `fadvance()` then solves the matrix equation for the new value of the membrane potential. Depending on the value of `secondorder` it then may re-call these current functions with the average of the new and old membrane potentials to get an accurate final value of the current. It then calls the state integrator functions using the new value of the membrane potential and the second order correct currents to calculate the new values of the states. The details of this method can be gleaned from the file `nrn/src/nrnoc/fadvance.c`.

It is therefore necessary for NMODL to divide up the statements properly into a current function and a state function. It also has to create the interface between model variables and NEURON and create a memory allocation function so that segments have separate copies of each variable. Finally, it has to make sure that local model currents get added to the correct global ionic currents.

Note: This simulation method is very effective and highly efficient when currents depend on membrane potential and ionic concentrations do not change on the same time scale as the membrane potential. When these conditions are not met, however, such as in a calcium pump mechanism in which the current depends on the concentrations of calcium next to the membrane, one must be careful to use a `dt` small enough to prevent the occurrence of numerical instabilities. (Or else using a single model to describe both the pump current and that current's effect on concentration so that the concentrations and pump states may be computed simultaneously. An example of such a model is in nrn/demo/release/cabpump.mod) A future version of NEURON will have the option (slightly less efficient) of calculating all state variables simultaneously so that numerical stability is guaranteed.

Further discussion of the numerical methods used by NEURON are found here.

### Basic NMODL Statements

Only a small part of the full model description language is relevant to neuron mechanisms. The important concepts held in common are the declaration of all variables as

#### Parameter

Description:
  These are variables which are set by the user and not changed by the model itself. In a NEURON context some of these parameters need to be range variables which can vary with position and some are more useful as global variables. Special variables to NEURON such as `celsius`, `area`, `v`, etc. if used in a model should be declared as parameters. (and you should not assign values to them in the model). Ionic concentrations, currents, and potentials that are used but not set in this particular model should be declared as parameters. NMODL does not enforce the "constantness" of parameters but stylistically it is a good rule to follow since there is a special field editor widget in NEURON's graphical user interface which makes it easier to modify a PARAMETER's value. There is an unfortunate restriction on PARAMETER's in that they cannot declare arrays. Even if an array is conceptually a PARAMETER, it must be declared as an ASSIGNED variable. In NMODL, PARAMETERS and ASSIGNED variables are practically synonyms. They substantively differ only in that when a panel of variables is automatically created, PARAMETERS are displayed in augmented field editors which make it easier to change values whereas ASSIGNED variables are displayed in field editors in which the only way to change the value is to type it from the keyboard. (see `xvalue()`).

#### State

Description:
  These are variables which are the unknowns in differential and algebraic equations. They are normally the variables to be "SOLVE"ed for within the BREAKPOINT block. For example, in HH channels the states are m, h, and n. In a NEURON context they are always range variables. Ionic concentration is a state only if the concentration is being calculated within that specific model (mechanism). ERRORS in the simulation would occur if concentrations were computed in more than one mechanism inserted at the same location. Membrane potential, `v`, is never a state since only NEURON itself is allowed to calculate that value.

#### Assigned

Description:
  These are variables which can be computed directly by assignment statements and are important enough that you may wish to know their value during a simulation. In a NEURON context you will wish to divide them between range variables and global variables.

#### Constant

Description:
  These are variables that cannot be changed during the simulation.

#### Local

Description:
  These are equivalent to C static variables ie shared between all instances of a given mechanism.

#### Independent

Description:
  This specifies the mathematical independent variable. For NMODL this statement is unnecessary since the independent variable is always time, `t`.

#### Pointer

Basically what is needed is a way to implement the hoc statement

    section1.var1_mech1(x1) =  section2.var2_mech2(x2)

efficiently from within a mechanism without having to explicitly connect them through assignment at the HOC level everytime the `var2` might change.

First of all, the variables which point to the values in some other mechanism are declared within the NEURON block via

    NEURON {
       POINTER var1, var2, ...
    }

These variables are used exactly like normal variables in the sense that they can be used on the left or right hand side of assignment statements and used as arguments in function calls. They can also be accessed from HOC just like normal variables. It is essential that the user set up the pointers to point to the correct variables. This is done by first making sure that the proper mechanisms are inserted into the sections and the proper point processes are actually "located" in a section. Then, at the hoc level each POINTER variable that exists should be set up via the command:

        setpointer pointer, variable

where pointer and variable have enough implicit/explicit information to determine their exact segment and mechanism location. For a continuous mechanism, this means the section and location information. For a point process it means the object. The variable may also be any hoc variable or voltage, v.

For example, consider a synapse which requires a presynaptic potential in order to calculate the amount of transmitter release. Assume the declaration in the presynaptic model

    NEURON { POINTPROCESS Syn   POINTER vpre }

Then

    objref syn
    somedendrite {syn = new Syn(.8)}
    setpointer syn.vpre, axon.v(1)

will allow the syn object to know the voltage at the distal end of the axon section. As a variation on that example, if one supposed that the synapse needed the presynaptic transmitter concentration (call it tpre) calculated from a point process model called "release" (with object reference rel, say) then the statement would be

    setpointer syn.tpre, rel.AcH_release

The caveat is that tight coupling between states in different models may cause numerical instability. When this happens, merging models into one larger model may eliminate the instability, unless the model is so simple that time does not appear, such as a passive channel. In that case, `v` is normally chosen as the independent variable. MODL required this statement but NMODL will implicitly generate one for you. When currents and ionic potentials are calculated in a particular model they are declared either as STATE, or ASSIGNED depending on the nature of the calculation or whether they are important enough to save. If a variable value needs to persist only between entry and exit of an instance one may declare it as LOCAL, but in that case the model cannot be vectorized and different instances cannot be called in parallel.

#### Include

Description:

  The INCLUDE statement replaces itself with the contents of the indicated file. eg.

      INCLUDE "units.inc"

  If the full path to the file is not given, the file is first looked for in the current working directory, then in the directory where the original .mod file was located, and then in the directories specified by the colon separated list in the environment variable MODL_INCLUDES. Notice that the INCLUDE filename explicitly requires a complete file name --- don't leave off the suffix, if any.

  Other blocks which play similar roles in NMODL and MODL are

#### Breakpoint

Description:
  This is the main computation block of the model. Any states are integrated by a SOLVE statement. Currents are set with assignment statements at the end of this block. Think of this block as making sure that on exit, all variables are consistent at time, `t`. The reason this block is named BREAKPOINT is because in SCoP it was called for each value of the INDEPENDENT variable at which the user desired to plot something. It was responsible for making all variables consistent at that value of the INDEPENDENT variable (which usually required integrating states from their values at the previous call using SOLVE statements). In NMODL, this block is usually called twice every time step (with voltage equal to v+.001 and voltage equal to v) in order to calculate the conductance from the currents. Often, errors result if one computes values for states in this block. All states depending explicitly or implicitly on time should only be changed in a block called by a SOLVE statement.

#### Derivative

Description:

  If the states are governed by differential equations, this block is used to assign values to the derivatives of the states. Such statements are of the form `y' = expr`. These equations are normally integrated from the old values of the states to their new values at time, `t`, via a SOLVE statement in the BREAKPOINT block. The expression may explicitly involve time. The SOLVE statement for a DERIVATIVE block should explicitly invoke either

              SOLVE deriv METHOD euler
      or
              SOLVE deriv METHOD runge
      or
              SOLVE deriv METHOD derivimplicit

  because the default integration method is a variable time step runge-kutta method which cannot work in a NEURON context. The first two methods above are computationally cheap but are numerically unstable when equations are stiff (states vary a lot within a `dt` step).

  HH type mechanisms have state equations which are particularly simple and extra efficiency and accuracy is easily obtained by integrating the states analytically. The `hh2.mod` example shows how to do this.

#### Nonlinear

Description:

  This block solves simultaneous equations in the form of a list of statements with the syntax,

              ~ expr = expr

  When this block is called by the SOLVE statement, the values of the states are computed so that the equations are true. The default method used is Newton's method. These kinds of equations can also appear within a DERIVATIVE block.

#### Kinetic

Description:
  This block specifies a sequence of chemical reactions. The default method used is backwards euler which is very stable but only first order correct. If the SOLVE statement specifies a "METHOD sparse" the method is still backwards euler but the computation may be much faster.

#### Procedure

Description:

  Procedures normally do not return a value but are called for their side effects, eg, the setting of variables. Procedures are callable from NEURON by the user.

  However if a procedure is called by the user, and it makes use of any range variables, then the user is responsible for telling the mechanism from what location it should get its range variable data. This is done with the hoc function:

              setdata_mechname(x)

  where mechname is the mechanism name. For range variables there must of course be a currently accessed section. In the case of Point processes, one calls procedures using the object notation

              pp_objref.procname()

  In this case procname uses the instance data of the point process referenced by pp_objref.

  Sometimes, state equations are so simple, e.g. HH states, that significant efficiency gains and extra accuracy are obtainable by a special integration procedure. In this case the procedure can be called by a SOLVE statement and actually integrates the states (but don't call it directly at the user level!). If a PROCEDURE is solved by a SOLVE statement it may return an error code (By default it returns an error code of 0 which denotes success.) To return a non-zero error code use the idiom

      VERBATIM
      return ...;
      ENDVERBATIM

#### Function

Description:
  This block can be called at either the user level or from within the model description. Functions return a double precision value. Functions can also be called from other models. When the calling model is translated a warning will be generated. Just be sure to load all needed models. Use the suffix of the model where the function is declared. The user level caveats stated for procedures apply.

#### Table

Description:

  The TABLE statement is very useful in a NEURON context because of the potentially great increase in speed of simulation. Often rate functions are complicated functions of the voltage and it is very expensive to calculate their values over and over at every segment. By using tables of rate coefficients, it is not uncommon to improve simulation speed by a factor of 5.

  In the context of a procedure taking one argument, TABLE has the syntax

      TABLE variables DEPEND dependencies FROM lowest TO highest WITH tablesize

  where: variables is a list of variable names each of which will have its own table, dependencies is a list of parameters that, when any of them changes their value, cause the tables to be recalculated, lowest is the least arg value for the first table entry, highest is the greatest arg value for the last table entry, and table size is the number of elements in each table.

  Each model that has a table also has a flag associated with it that can be changed by the user called usetable_suffix which specifies that the tables are to be used (1, default) or not used (0).

  With usetable_suffix = 0, when the procedure is called it ignores the tables and just computes the values using the assignment statements as any normal procedure.

  With usetable_suffix = 1, when the procedure is called, the arg value is used to assign values to the "variables" by looking them up in the tables; the time normally spent executing the assignment statements is saved. If the tables are out of date (a "dependency" has a different value from its value the last time the tables were constructed) or have never been created, the tables are created.

  Note that updating tables with `tablesize=200` is equivalent to calling the procedure 200 times with different values of the argument. This investment is only repaid if the tables remain valid for many more than 200 subsequent calls to the procedure and if the calculation takes more time than an interpolated table lookup.

#### Initial

Description:

  The INITIAL block is called when the user executes the finitialize() function from hoc. Just prior to executing the user code in the INITIAL block (and if an INITIAL block does not exist) all states are set to the values in the state0 variables (default 0). It may be useful to declare some state0 variables as GLOBAL or RANGE in the NEURON block in order to give some user control over the default initialization of states. In the INITIAL block these or any other variables may be set to calculated values. Note that states can also be initialized explicitly by the user at the hoc level.

  The case where an ionic variable is also a STATE requires some care to deal properly with it in the INITIALIZE block. The problem is that the ionic variable, eg. cai, is actually the value of a local copy of the ionic variable which is located in the variable named _ion_cai. Because of the order of copying and default initialization, cai is always initialized to 0 regardless of the global value of cai and on exit the global value of cai is then set to 0 as well. The way to avoid this is either to make sure the state0 variable, cai0, is set properly or (I believe more preferably), set the local cai variable explicitly using the global cai variable with a VERBATIM statement within the INITIAL block. The idiom is:

      VERBATIM
      cai = _ion_cai;
      ENDVERBATIM

  Many other features of the model description language, such as DISCRETE blocks, and sensitivity analysis, optimization are not relevant in the NEURON context and may or may not produce meaningful translations. Since NMODL produces a c file, it is possible for the highly motivated to modify that file in order to do something implementation dependent. In this regard, the VERBATIM block can be used to place c code within the model description file.

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