Update chosen-select knockout binding whenever changes are made to another knockout binding

Question

I have the following scenario:

I have a table with to multiple select input boxes (chosen.jquery).

<select multiple data-bind="
    chosen: $parent.SelectableOptions, 
    optionsText: 'Title', 
    optionsValue: 'InternalName', 
    chosenSelectedOptions: SelectedFields, 
    chosenEnable: Enabled" class="chzn-select"></select>

<select multiple data-bind="
    chosen: SelectedFields, 
    optionsText: 'Title', 
    optionsValue: 'InternalName', 
    chosenSelectedOptions: SelectedReadOnlyFields, 
    chosenEnable: Enabled" class="chzn-select"></select>    

Notice the chosenSelectedOptions binding in the first select input. This is bound to SelectedFields. This is an array, and this is the exact array that I wish to ad as possible options for the second select input. This can be seen by noticing the chosen binding for the second select input: SelectedFields.

The fields selected in the second select input, should be added to a new array called SelectedReadOnlyFields and stated in the chosenSelectedOptions binding.

Problem

As I'm fairly new to KnockoutJS, I'm not sure where to go from here, or how to set this up correctly. Whenever the SelectedFields array changes, I wish to update the possible options in the second select input, but I can't get this to work. I've read posts that mentions the following way to trigger an update on the chosen select input ($(element).trigger('chosen:updated')), but as I do not have an id on the second select input, I cannot locate that element.

EXTRA

Bindings in topic:

ko.bindingHandlers.chosen = {
    init: function (element) {
        ko.bindingHandlers.options.init(element);
        $(element).chosen({ disable_search_threshold: 1000, allow_single_deselect: true, width: "100%" });
    },
    update: function (element, valueAccessor, allBindings, viewModel) {
        ko.bindingHandlers.options.update(element, valueAccessor, allBindings);
        $(element).trigger('chosen:updated');
    }
};

ko.bindingHandlers.chosenSelectedOptions = {
    init: function (element, valueAccessor) {
        ko.bindingHandlers.selectedOptions.init(element, valueAccessor);
    },
    update: function (element, valueAccessor, allBindings, viewModel) {
        ko.bindingHandlers.selectedOptions.update(element, valueAccessor, allBindings);
        $(element).trigger('chosen:updated');
    }
};