A stochastic simulation of the G-protein cascade of phototransduction.

A stochastic simulation of the G-protein cascade of phototransduction.

‘Walk’ is a program that simulates activation and inactivation in the G-protein cascade of reactions that underlie phototransduction (and a variety of other biological signalling cascades). It was written specifically for Windows 95/98/NT/2000 by Lucian Wischik. There is no Mac version.

 Download Walk v2.00 for Windows 95/98/NT/2000 (ZIP 708KB)

On some machines the display must be set to 256 colours for Walk to work correctly.  If you find you cannot see any molecules when you set up a simulation, then go to Windows ‘Display Properties’, then ‘Settings’, and under ‘Color palette’ select ‘256 color’.  At this stage you might also want to change ‘Font size’ to ‘Small fonts’, to ensure that the lettering all fits into the boxes correctly. To use Help, you will need to change the Help pointer to the new location of Walk's web page.  After you have started Walk, click ‘Help’, then click ‘Configure Help’, and under ‘Prefix’ enter the new web location. Note that if you still have problems, then you may need to prefix this by ‘netscape’, or the name of your browser.

Walk v2.00 has a number of advanced features that are only available by password. If you are interested in using any of the following, please contact Trevor Lamb

  • Dimeric effector protein, PDE
  • Inactivation reactions (stochastic or deterministic)
  • Stochastic number and position of initial R*s
  • Evaluation of the electrical response

Using Walk


‘Walk’ is a Windows program for simulating the G-protein cascade of reactions underlying not only phototransduction, but also many other biological signalling processes. It was written by Lucian Wischik, and is based on an earlier DOS version written by Trevor Lamb. For instructions on downloading and installation, see Walk's home page.

Minimum requirements are a 486 processor with 8MB of RAM, running Windows 3.1, but greatly preferable is a Pentium processor with at least 16MB of RAM, running Windows 95 or NT. The latest version, Walk v2.00, will only run under Windows 95 or NT.

While Walk is provided as freeware, we would be very grateful if you would acknowledge its use, in published papers and/or in teaching documentation. Scientific references to the methodology are given on the page Science underlying Walk.

Password priveleges  

Walk v2.00 has a number of advanced features that are only available by password. If you are interested in using any of the following, please contact Trevor Lamb.

  • Dimeric effector protein, E (e.g. PDE** = G*-PDE-G*)
  • Inactivation reactions (stochastic or deterministic)
  • Stochastic number and position of initial R*s
  • Evaluation of the electrical response

Getting Help

There are two ways of obtaining help within Walk.

  1. Walk's built-in Help is obtained by hitting F1 (or Help, Contents). Although this is incomplete, a highly recommended feature for new-comers is the ‘Guided Walk-through’ that you can take: After F1, choose Quick Start.
  2. Help from Walk's home can be invoked by choosing Help followed by one of: Using Walk | Simulation | Science. This should fire up your default web-browser, and go the Walk's help directory and open the appropriate topic. If there is any difficulty, you can select your preferred browser, using Help | Configure help.  

Overview of using Walk

Here's a brief overview of the kind of way that you might use Walk:

  1. Start a new simulation:
    File, New, and go to Settings
    Mess with the settings, and perhaps choose an output file-name
    Click Apply, and Close, to accept the settings
    Click Go, to start the simulation running
    Have fun watching it go: zoom, pan and scroll the display
    Bring up the Key window and/or the Graphs window to watch progress
    Maximize the speed (click Lightning)
    Leave it running
    Look at the behaviour of multiple runs (mean, variance, etc.)
    Close the file.
  2. Choose a new set of parameters to investigate
  3. Start a simulation going, as in 1 above
  4. Save these parameters as a template, so you can quickly re-start
  5. When a decent number of runs has been done, go to 2 again
  6. Open any of the log files you have created, or the sample log file (Example.wlk) and look at the graphs
  7. Output the graphical results in ascii form, or as an image.


Starting a new simulation

Click the ‘New’ button (or choose File | New from the pull-down menus). Then select one of the existing Templates (you can customise your own later). Next click either OK, to get started immediately, or else Settings, to allow you to alter parameters. After you hit OK, a display of molecules will appear in the main window. To start the simulation, click the ‘Go’ button (green arrow), or hit F2.

Zoom, pan, scroll

To look more closely at the reacting molecules, you can:

  • Zoom in and out -- using the Zoom slider, or the F5 and F7 keys
  • Reset to unity zoom -- F6 (or View | Normal)
  • Pan and scroll -- by either dragging the molecular display (using the left button), or using the sliders/arrows at the sides
  • Re-position the centre of the display -- by clicking the right button at the desired location
  • Find R* -- F8 (or View | Find R*)

Monitoring the progress of simulations

To monitor progress of the simulations, you can look at either (or both) of the ‘Key’ window and the ‘Graphs’ window.

Key window

By clicking the ‘Key’ button (which looks like a traffic light), hitting F9, or selecting View | Key, you will open the Key window. This contains a legend to the molecular species, as well as a simulation clock, and counters for the numbers of molecules (which can be either ‘Total produced’ or ‘Remaining active’). You can drag this window to a convenient place.

For Key and Graphs, you can select either of two ways of counting: ‘Produced’ plots the total number of each species (e.g. G*s) that have been produced up to that time, whereas ‘Active’ plots only the number remaining in the active form (e.g. G*s that have not yet bound to E).

Graphs window

You can open the Graphs window by clicking the ‘Graphs’ button, by hitting F11, or by selecting Simulation | Graphs. Again, you can drag this window anywhere convenient. By default, the graph auto-scales, and will periodically update itself as the simulation progresses. Alternatively, you can enter explicit scales in the ‘ms’ and ‘mols’ boxes. Until you have completed at least one run, you can only look at the current simulation, but subsequently you can look at previous ones by checking the ‘History’ box, and then choosing the appropriate traces.


You can plot the theoretical curve for G* activation, predicted by Lamb & Pugh (1992). After you check the ‘G* Theory’ box, you can select one or more of:

  • ‘Diffusion limit’ - the continuous case in the diffusion limit
  • ‘Full analytical’ - the continuous case, but with the reaction rate constants as chosen in the Settings
  • ‘Full discrete’ - the discrete case, using the actual grid dimensions chosen

See Lamb (1994) p.1443 for details. Note that, as yet, no suitable theory is available for E* activation.


You can output the graphical traces in comma-delimited ascii form (for input to a plotting package) by clicking Export. Or you can copy the image to the clipboard by hitting Copy, so that you can embed the graph into a Word document or other application.

Electrical response

If you have password privelege, you will find that Graphs has two tabs: ‘Elec’ for the Electrical response, in addition to ‘Mols’ for the standard graphs of counts of molecules.

Simulation speed: Lightning versus Demonstration

You can make the simulations run faster (at the expense of updating the display only occasionally) by clicking the ‘Lightning’ button, equivalent to selecting Speed | Max. In normal (non-lightning) display mode, the computation speed will depend on the Zoom setting (on most display hardware). You can fine-tune the display-versus-speed trade-off by hitting a number key from 1 to 0(=10); this sets the number of dt's between display updates.


If you want to see how fast the calculations are running (and how much longer the present run should take to complete), select Simulation | Performance, or hit F4. The Performance window will show the proportions of cpu time spent on graphics and on calculations, and will give an overall speed indication: ‘Cycle rate’ is the number of dt's being simulated per sec of real time. [With a 133 MHz Pentium, the standard parameters should lead to a Cycle rate of about 150 steps per sec in lightning mode; i.e. about 1 time step/sec, per MHz of cpu speed. This gives a total computation time of about 5 mins for a standard run of 100 ms].

If you minimize Walk while a simulation is running, the calculations will continue to run in the background -- this is indicated by an asterisk (*) before the title on the minimized icon. Thus, you can leave Walk running minimized while you are using other applications, or overnight.

Short-cut (function) keys

The following short-cut keys are available during a simulation:

  • F1 - Internal Help
  • F2 - Go / Pause
  • F3 - Lightning: Toggle maximum speed on/off
  • F4 - Performance
  • F5 - Zoom Out
  • F6 - Zoom Unity
  • F7 - Zoom In
  • F8 - Find R*
  • F9 - Key
  • F10 - Settings
  • F11 - Graphs
  • 1-0(=10) - Simulation dt's per display update

Settings: Changing the parameters of a simulation

To change any of the simulation parameters, you need to open the Settings dialog window. This can be done at the stage of File, New, or at any subsequent time, e.g. after you have set some initial parameters. Although it is possible to change parameters while a simulation is running, this is not very meaningful, and so output is then prohibited.
The various settings are grouped under different ‘Tabs’, as follows:


You can specify the general reaction scheme, and set the rate constant of reaction for each species of active molecule. If you have password priveleges you can choose whether the effector is dimeric (e.g. PDE**, as in the photoreceptor).


Here, you can set the lateral diffusion coefficient for each species of molecule. The values cannot exceed a limit of Dmax = dx^2 / 4 dt. (The ‘Diffusion scaling’ check-box is used to artificially increase all diffusion coefficients by a small amount, to allow for a shortcoming in the diffusion algorithm. At finite concentrations, molecules are not always free to move in an arbitrary direction, and this restriction on direction causes a slight reduction in effective diffusion coefficient. See Lamb, 1994, p.1445 for details.)


You can set the initial concentration, or density, (in molecules/um^2) of G and E in the membrane. Note that (unless you have password priveleges) there will always be just a single R* present, and that it will start from the centre of the simulation region.


You can set the diameters of the reacting molecules (in nm), as well as the pixel size (dx) and the size of the overall array. As you change diameter or pixel size, the shape of the resulting molecule is shown. Note that G* is deemed to have the same diameter as G, and E* the same diameter as E (although each species has its own diffusion coefficient).

For rapid calculations, the pixel size (dx) should be set to a value close to the size of the molecules, so that molecules are represented as single pixels. For the standard molecular diameters, a pixel size of dx = 5 nm is convenient. Multi-pixel simulations are used mainly for demonstration purposes.

This is also where you set the simulation time step (dt). By default, the values of dx and dt are inter-linked, so that the maximum possible diffusion coefficient (Dmax = dx^2 / 4 dt) remains fixed. Thus, if you alter one of them, the other will change too. This is done to help inexperienced users avoid problems. However, you can un-link the two parameters by removing the check-mark to the right of them.

The value of dt must be sufficiently small that the probability of each molecule moving during a given time step is reasonably small. The standard value of dt = 2.5 us gives probabilities that are rather large, and if you have a fast processor it is a good idea to reduce this, to (say) 0.5 us. It is worthwhile having a look at the resulting probabilities of molecular movement in Settings, Diffusion; these are given as ‘fraction of max’ in the row below ‘Diffusion coefficients’.


This is where you specify the maximum simulation time, as well as the number of simulations to be done and the name of the output file, etc. Note that, in order to do multiple runs, you must specify a file for output of the results, in the box below ‘Keep a log’. The extension .wlk will be appended, and we refer to this file as a Walk Log file.



It is here, in Settings, Misc, where you can enable or disable sound effects. If you'd like to play round, then go to Control Panel | Sounds, and scroll down to Walk. You will then be able to assign whatever sounds you like to the various molecular interactions. This is also where it is possible to set the seed of the random number generator, for special purposes.


This feature is available by password only. It permits stochastic or deterministic inactivation of each of the molecular species R*, G*, R* and E**.

Input / Output

Output: creating a log file

The parameters for saving output (e.g. log file name, number of runs, etc) are set up using Settings, Batch; see above.

Altering the number of runs, and doing more runs

You may, at any time during a simulation, alter the number of runs to be done, by selecting Settings, Batch. After the chosen number of runs has been completed, or when you open an existing log file, you can perform additional simulations by clicking the ‘More runs’ button (‘+’, which replaces the ‘Go/Pause’ button at this stage), or by selecting Simulation, More runs. Next, hit ‘Go’ or ‘Lightning’ to start. The additional runs will be appended to the existing log file.

Interrupting computations

You can stop the computations at any time (e.g. by exiting Walk), but you will be prompted to save the current state. If you do so, then you can subsequently pick up again from exactly where you left off. But even if you don't save the current state, you can subsequently start the calculations again from the last completed run.

Customising your own templates

When you have set up parameters that suit you, you can save them in a Walk Template file (which will have the extension .wlt). You need to: File, Save as ... Save this template ..., then enter a file name, and click Save. You will next be prompted to enter a title and some comments, both of which will appear when you subsequently do File, New.

Input: Reading in a previous simulation (i.e. a Walk Log file, *.wlk)

You can open the sample log file, Example.wlk, or any other simulation file that you produce, by clicking the ‘Open’ button (or choosing File, Open). In the window that appears, select the file you want, and click Open. Once the file has been read in, the Graphs window will appear. Initially, just the mean traces for G* and E* are selected, but you can turn on/off any traces you wish.


Updated:  15 August 2018/Responsible Officer:  Director, JCSMR/Page Contact:  Web Manager