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## 18. The GENESIS Parameter Search Library

## 18.1 What is automated parameter searching?

Most GENESIS simulations, especially highly realistic simulations of single neurons, have large numbers of parameters which are not strongly constrained by existing experimental data. In such cases, the modeler has to choose the parameters that cause the model to produce outputs which are as close as possible to the outputs of the real system. Doing this manually is a very tedious process: typically one parameter at a time is adjusted and the modeler sees if the simulation outputs are any closer to the desired behavior than before. Although a lot of insight can be obtained this way, the nonlinear behavior of neurons and the strong interactions between many parameters in creating neural behaviors make this unnecessarily difficult. In order to make parameter searching easier, we have developed a library of parameter search objects and functions which automate the search process. Manual parameter searches that might take months of boring work can often be done in a few days of automated searches with no user intervention whatsoever, and the results will typically be better as well.

## 18.2 The parameter searching process

First, the simulation whose parameters will be varied must be created and debugged. The modeler must then determine a way to compare the output of the simulation with a desired output so that a numerical match value is computed after each simulation. Typically, the smaller the match value the closer the simulation matches the data, with zero representing a perfect match. The modeler can create his or her own match function (in GENESIS script language or in C code) or use one of the predefined match functions. Typical match functions for neuron outputs compare the times of spikes, the shape of interspike interval waveforms, or both.

Then the modeler must create and initialize a ``paramtableXX'' object (see below for what XX means). This object contains tables of parameters and can update these to give the next parameter set to try. The initial parameter values are set using the ``initparamXX'' functions. Then the modeler writes a function in the GENESIS script language to run the search. This process is as follows:

1. Run a new simulation.
2. Calculate a match value.
3. Notify the paramtableXX object of the match value.
4. Tell the paramtableXX object to calculate the next set of parameters.
5. Adjust the parameters of your model based on the new set of parameters.

Once this is done, the function is called and the search begins. Full examples of this process for all the parameter search objects are included in the parameter search demos in the Scripts/param directory. We strongly advise you to use these scripts as prototypes for your own parameter searches, as this will make the process much simpler.

## 18.3 The GENESIS parameter search library

All of the GENESIS functions and objects pertaining to parameter searching are in the ``param'' library. There are two broad classes of entities in this library:

1. Objects that hold information about parameter searches and select new parameter sets based on the results of previous simulations. These objects are all called ``paramtableXX'' where XX is an abbreviation for the parameter search method.
2. Functions that are used to calculate how close a simulation is to some desired behavior.
3. Various helper functions.

The paramtable objects currently include:

paramtableBF | Implements brute-force parametersearch
paramtableCG | Implements conjugate-gradient descent parameter search
paramtableGA | Implements genetic algorithm parameter search
paramtableSA | Implements simulated annealing parameter search
paramtableSS | Implements stochastic parameter search

The matching functions include:

shapematch | Returns goodness of match between two waveform files
spkcmp | Returns goodness of match between two spike time files

The helper functions include:

gen2spk | Creates file with spike times from file of Vm vs. time
getparamGA | Gets parameters from the paramtableGA object
initparamBF | Initializes parameters for the paramtableBF object
initparamCG | Initializes parameters for the paramtableCG object
initparamGA | Initializes parameters for the paramtableGA object
initparamSA | Initializes parameters for the paramtableSA object
initparamSS | Initializes parameters for the paramtableSS object
setparamGA | Sets parameters for the paramtableGA object
setsearch | Specifies which parameters will be varied in a search

## 18.4 Recommendations

We recommend the SA method for simulations with small numbers of parameters (less than 10), and either the SA or the GA method for larger numbers of parameters. The CG method can be used for very simple or highly linear models, but experience shows that the SA method can be as good or better than the CG method even in these cases. The SS method is mostly a historical artifact and is usually not the best method to use. The BF method is useful for an initial mapping of parameter space, but not for the searching process per se. See the documentation for the individual paramtable objects for more detailed recommendations.

Your searches will be much more likely to succeed if the starting model at least qualitatively matches the main features of the real system's behavior. To give an extreme example, you wouldn't use a one-compartment model with simple Na and K Hodgkin-Huxley channels and try to match the outputs of a Purkinje cell in a bursting mode. The model should at least be able to show some kind of bursting behavior in this case before you began the search. Similarly, if the cell shows strong spike frequency adaptation the model must have channels that can do this too (e.g. M-current or AHP potassium channels). Automated searching can't make a bad model good.

If possible, the matching function should be tailored to the data to be matched. For instance, in a rapidly adapting cell, matching the first few spikes may be more critical than matching the last spike, which may have a wide variation in timings in the real system. Ideally a new matching function should be written in C for each cell type, although this is not always practical. This can reduce the length of the search by heavily penalizing models which are obviously incorrect and thus removing them from consideration.

Note that the paramtable objects have many parameters of their own that can affect the success or failure of a search. Advice on these can be found in the documentation for the individual objects.

It is very important to save the state of the search regularly, in case of a computer crash. All the routines have SAVE actions that should be invoked regularly.

Searches that involve a lot of deleting of old elements will usually cause some memory leaks, since GENESIS is not completely free of such leaks yet. It is vital to call ``reclaim'' after deleting a lot of elements or the memory allocated to such elements will not be freed. If this happens you may run out of memory on your computer very fast! Even with this precaution, long searches can cause appreciable memory leaks, so that a simulation which starts off at (say) five megabytes may grow to 10 or 15 megabytes or more. This is especially true for large searches which take days to run. The best solution is to periodically save the state of the paramtable object to disk, get out of GENESIS, and restore the state of the object. This can all be done from a shell script; examples are shown in the demo directories.

Parallel GENESIS (PGENESIS) is very useful for parameter searching if you have access to a parallel supercomputer (don't we all? I have three in my bedroom right now...).

## 18.5 Bug reports.

Send all bug reports to Mike Vanier at mvanier@cs.caltech.edu. Before you report a bug, read the bug reporting procedure, Reporting Bugs.

## 18.6 Caveats

Wonderful though parameter searching is, modelers must always remember that a parameter search can't find a good model if none exists in the parameter space. However, the failure of a parameter search to find a good match often can be a clue that some important component is missing from the model, which can be very useful information.

Becoming adept at parameter searching takes intelligence, practice and experience. In particular, understanding the different options in the parameter search objects and knowing which methods work best under which circumstance is non-trivial. This is an ongoing area of research, and no doubt more and spiffier methods will be developed in the future (maybe even by you, the disgruntled GENESIS programmer!).

## 18.7 Information about the Parameter-search (paramtable) Objects

Parameter searching in the GENESIS `param' library is controlled by one of the `paramtable' objects. Each object implements a different search algorithm. The list of paramtable objects currently includes:

paramtableBF | Implements brute-force parametersearch
paramtableCG | Implements conjugate-gradient descent parameter search
paramtableGA | Implements genetic algorithm parameter search
paramtableSA | Implements simulated annealing parameter search
paramtableSS | Implements stochastic parameter search

We cannot describe each of these methods in detail here; for more general information about the methods (and comparisons between them) using a variety of single neuron models, see the paper:

``A comparative survey of automated parameter-search methods for compartmental neural models'' by Michael C. Vanier and James M. Bower, Journal of Computational Neuroscience 7: 149-171 (1999).

The paramtable objects have two functions:

1. To store parameter tables.
2. To calculate the next parameter set to simulate, given the results of previous simulations.

The first function is quite similar for most of the methods, while the second is completely different. Here we will give general information about the paramtable objects and briefly describe some of the common fields and actions for these objects; for a full description of the individual paramtable objects see the documentation for those objects.

### Actions

Actions in paramtable objects are somewhat different from actions elsewhere in GENESIS. (See the documentation on Actions for more information about GENESIS actions.} Typically, GENESIS actions are called every time step under control of the schedule (e.g. INIT and PROCESS actions), or are called by special functions (e.g. the RESET and CHECK actions, called for all elements by the "reset" and "check" functions, respectively). In contrast, many of the actions in paramtable objects are meant to be called explicitly e.g.

        call my_paramtable_object INITSEARCH

Thus, they are more like member functions in C++ i.e. functions that ``belong'' to a particular object. These actions are often very different from object to object, and most paramtable objects also have several actions that are specific to that object. Using actions in this way is arguably an abuse of the GENESIS action mechanism, but since it works well and there is currently no decent alternative, that's what was done.

Here are some actions that you should know about, which are in many of the paramtable objects:

TABCREATE | Allocates memory for the paramtable object.
TABDELETE | Frees previously-allocated memory.
INITSEARCH | Initializes the parameter search process.
RANDOMIZE | Performs some object-specific randomization process.
EVALUATE | Evaluates a previously-simulated parameter set
| given a numeric match value.
UPDATE_PARAMS | Calculates the next parameter set to simulate.
SAVE | Saves a binary image of the paramtable object.
SAVEBEST | Saves a text file containing the best parameter set
| obtained so far.
RESTORE | Restores a binary image of the paramtable object.
RESTOREBEST | Restores a text file containing the best parameter set
| obtained so far (not functional for all objects).
DISPLAY | Prints a representation of a parameter set to stdout.
RESTART | Restarts the parameter search process, preserving the
| best parameter set obtained so far.
ACCEPT | Copies the current parameter set to the locations for
| the best parameter set.

Some of these actions (e.g. TABCREATE) are used in other parts of GENESIS for different purposes, and some (e.g. EVALUATE, RESTOREBEST) are not currently used in all paramtable objects. Most of these actions also require arguments; for the specific syntax of the argument lists for each action see the documentation for the individual objects. Note that the same action may require different arguments in two different objects, or may have different optional arguments.

### Fields

Here we briefly describe several fields that are present in most or all of the paramtable objects, and that are involved in the actual storage of parameter data. Fields that are specific to particular methods will not be mentioned; for them please see the documentation for the specific paramtable objects.

Field | Description
iteration_number | Number of simulation iterations so far
num_params | Total number of parameters in each parameter set
num_params_to_search | Number of parameters that are actually being
| searched over
search | 1-D array of binary flags representing which
| parameters are to be searched over
type | 1-D array of parameter types (see below)
center | 1-D array of centers of parameter ranges
range | 1-DD array of range values of parameter table
min | 1-D array of minimum values of parameter table
max | 1-D array of maximum values of parameter table
label | 1-D array of parameter labels
current | 1-D array of parameter values to be simulated next
current_match | Match value of last parameter set simulated
best | 1-D array of the best parameter values obtained so
| far in the search
best_match | Best match value obtained so far
done | Flag: if 1, the search is finished
filename | Name of the binary file to store paramtable state
alloced | Flag: 0 if the parameter tables have not been
| allocated; 1 if they have

Many of the above fields are for bookkeeping only (e.g. the label field), and some are set by the method and are readonly (e.g. the iteration_number field). The `search' flags are usually set by the `setsearch' function (see setsearch). The type, center, range, min, max, and label fields are normally set by the `initparamXX' functions, where XX = {BF, CG, GA, SA, SS}. See the documentation for those functions for more details.

### Parameter types and parameter ranges

Parameters come in two basic types: additive and multiplicative. An additive parameter is one whose value will be added to a starting value as an offset. An example of this might be an offset of the steady-state activation curve of an ionic channel (m_inf(V)), or a membrane potential offset. For instance, an additive parameter value of 0.002 volts might be added to the midpoint of the activation curve of a sodium channel (which might be, say, -55 mV to start with) to get a new midpoint of -53 mV. This would make the cell somewhat less excitable, since at a particular membrane potential fewer Na channels would be open (ignoring inactivation).

A multiplicative parameter (the more common type) is a scaling value that is multiplied by a starting value of a parameter to get the actual value. An example of this would be the maximal conductance of an ionic channel type in a particular compartment. In this case, a multiplicative parameter value of 2.0 might mean to multiply the starting value of a given ionic channel by 2 to get the new value.

The reason for distinguishing between the two types of parameters is that ranges are set differently for the two types. A range of, say, 10.0 for a multiplicative parameter with a center point of 1.0 means that the parameter can vary from between 0.1 and 10.0. Furthermore, a random value in this parameter range is as likely to be below 1.0 as it is to be above 1.0. This is accomplished by internally storing the parameter values as the log of the true value. Thus, a random value in this range is calculated by choosing a value from the uniform distribution in (-log(10), log(10)), and then taking the antilog of the resulting value. Multiplicative parameters are natural for scaling factors from a starting point, such as scaling factors for ionic conductances. Additive parameters are simpler: a center point of 0.0 and a range of 1.0 for an additive parameter means the parameter is located in the range (-1.0, 1.0), as you would expect. Furthermore, a random value in this range is calculated by choosing a value from the uniform distribution in (-1.0, 1.0), also as expected. Additive parameters are often used for offsets that can be either positive or negative from a starting value, such as offsets in activation curves or membrane potential offsets to compensate for an unknown electrode junction potential.

At this point, you might be wondering what the big deal is. If you want to have a parameter representing a maximal conductance which is some value between 100 and 200 Siemens per square meter, why not just set the minimum value to 100 and the maximum value to 200 and be done with it? In fact, although it's not obvious, this is equivalent to defining an additive parameter with a starting value of 150 and a range of 50. If this is what you want, fine. However, sometimes you might want to start at 100 and be able to select values from one-half to twice that value; that's a multiplicative parameter. Sometimes it doesn't even matter which type of parameter you use.

### Writing parameter search scripts

At the risk of sounding redundant, we strongly advise that you use the sample scripts in the Scripts/param directory as prototypes for your parameter searching scripts. This is by far the easiest way to learn how to use the parameter search objects, and can save you an enormous amount of frustration. It is also recommended that serious students read the source code in the param subdirectory of genesis; the code is heavily commented and reading it will clarify a lot of obscure issues. If you're not used to reading C code, this would be a good place to start :-)

### Modifying channel kinetics

One common application of parameter searching is to modify the kinetics of voltage- or calcium-dependent ionic channels. This is especially important when you use channels taken from one brain region for a cell in another brain region for which the kinetic data for the channel in question has not been established. It is also useful when the kinetic data used to build the channel is of questionable quality. There are a number of ways you can modify channel kinetics in a parameter search:

1. You can scale the time constants of the activation/inactivation curves uniformly, making the channel faster or slower. This can be used to compensate for unknown temperature corrections among other things. In this case, one usually uses a multiplicative parameter centered on 1.0 as a scaling factor for the channel time constants. The ``scaletabchan'' function in GENESIS is then used to actually modify the kinetics of the channel (see the demos for examples).
2. You can shift an activation curve to the left or right with respect to the X axis (usually voltage or calcium concentration). Here one usually uses an additive parameter centered on 0.0 as an offset factor for the activation curve. Again, the "scaletabchan" function can be used to modify the kinetics.
3. You can change the shape of the activation curve. This is more complicated, since in principle an arbitrary curve may need a large number of parameters to describe it, but if the curve has some standard shape (e.g. a sigmoid or a sum of sigmoids), the parameters describing the curve can be used in a parameter search.

Note that if you use ``scaletabchan'' to shift an activation curve to the left or right ((2) above), you must realize that GENESIS will get rid of all values that are shifted beyond the range of the x-axis. Thus, if you shift to the left and then later shift to the right you will not necessarily end up with the same activation curve you started with. For this reason, we recommend recreating channels from scratch for each iteration of a parameter search, and using parameters which represent offsets from the starting activation curve in this case. See the demonstration scripts in Scripts/param for examples of this. This does not usually cause a serious slowdown. However, it does lead us nicely into our final topic.

### Memory leaks

When running a parameter search that creates and deletes channels (or an entire cell) at each iteration of a parameter search, care must be taken to avoid memory leaks, which can accumulate and eventually cause your computer to run out of memory. If this happens, your search will terminate abnormally. The most important things to remember are as follows. If you re-create a cell for each iteration of a search (which is often the best way to go), you MUST delete the previously-created cell before creating a new one. You must also call TABDELETE on all tabchannels that were part of the cell BEFORE you delete the channels themselves; it is NOT done automatically for you. Finally, you have to call ``reclaim'' for the memory to actually be freed. This is very lame, and we intend to do a much better job in future versions of GENESIS, but for now, you have to live with it.

Even despite these precautions, there are some memory leaks which will inevitably accumulate in parameter searches when you delete/restore cells on each iteration. Many of these have to do with string handling and there is currently no way to avoid them. We recommend that you run a parameter search for a fixed number of iterations (say 1000), save the parameter table, exit GENESIS, restart GENESIS and restore the parameter table and keep going. This can all be done from within a shell script; again, see the demos for examples.

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