As @SamRoberts explained, the Model–view–controller (MVC) pattern is well-suited as an architecture to design GUIs. I agree that there are not a lot of MATLAB examples out there to show such design...
Below is a complete yet simple example I wrote to demonstrate an MVC-based GUI in MATLAB.
- The model represents a 1D function of some signal - y(t) = sin(..t..). It is a handle-class object, that way we can pass the data around without creating unnecessary copies. It exposes observable properties, which allows other components to listen for change notifications.
 
- The view presents the model as a line graphics object. The view also contains a slider to control one of the signal properties, and listens to model change notifications. I also included an interactive property which is specific to the view (not the model), where the line color can be controlled using the right-click context menu. 
- The controller is responsible of initializing everything and responding to events from the view and correctly updating the model accordingly. 
Note that the view and controller are written as regular functions, but you could write classes if you prefer fully object-oriented code.
It is a little extra work compared to the usual way of designing GUIs, but one of the advantages of such architecture is the separation of the data from presentation layer. This makes for a cleaner and more readable code especially when working with complex GUIs, where code maintenance becomes more difficult.
This design is very flexible as it allows you to build multiple views of the same data. Even more you can have multiple simultaneous views, just instantiate more views instances in the controller and see how changes in one view are propagated to the other! This is especially interesting if your model can be visually presented in different ways.
In addition, if you prefer you can use the GUIDE editor to build interfaces instead of programmatically adding controls. In such a design we would only use GUIDE to build the GUI components using drag-and-drop, but we would not write any callback functions. So we'll only be interested in the .fig file produced, and just ignore the accompanying .m file. We would setup the callbacks in the view function/class. This is basically what I did in the View_FrequencyDomain view component, which loads the existing FIG-file built using GUIDE.

Model.m
classdef Model < handle
    %MODEL  represents a signal composed of two components + white noise
    % with sampling frequency FS defined over t=[0,1] as:
    %   y(t) = a * sin(2pi * f*t) + sin(2pi * 2*f*t) + white_noise
    % observable properties, listeners are notified on change
    properties (SetObservable = true)
        f       % frequency components in Hz
        a       % amplitude
    end
    % read-only properties
    properties (SetAccess = private)
        fs      % sampling frequency (Hz)
        t       % time vector (seconds)
        noise   % noise component
    end
    % computable dependent property
    properties (Dependent = true, SetAccess = private)
        data    % signal values
    end
    methods
        function obj = Model(fs, f, a)
            % constructor
            if nargin < 3, a = 1.2; end
            if nargin < 2, f = 5; end
            if nargin < 1, fs = 100; end
            obj.fs = fs;
            obj.f = f;
            obj.a = a;
            % 1 time unit with 'fs' samples
            obj.t = 0 : 1/obj.fs : 1-(1/obj.fs);
            obj.noise = 0.2 * obj.a * rand(size(obj.t));
        end
        function y = get.data(obj)
            % signal data
            y = obj.a * sin(2*pi * obj.f*obj.t) + ...
                sin(2*pi * 2*obj.f*obj.t) + obj.noise;
        end
    end
    % business logic
    methods
        function [mx,freq] = computePowerSpectrum(obj)
            num = numel(obj.t);
            nfft = 2^(nextpow2(num));
            % frequencies vector (symmetric one-sided)
            numUniquePts = ceil((nfft+1)/2);
            freq = (0:numUniquePts-1)*obj.fs/nfft;
            % compute FFT
            fftx = fft(obj.data, nfft);
            % calculate magnitude
            mx = abs(fftx(1:numUniquePts)).^2 / num;
            if rem(nfft, 2)
                mx(2:end) = mx(2:end)*2;
            else
                mx(2:end -1) = mx(2:end -1)*2;
            end
        end
    end
end
View_TimeDomain.m
function handles = View_TimeDomain(m)
    %VIEW  a GUI representation of the signal model
    % build the GUI
    handles = initGUI();
    onChangedF(handles, m);    % populate with initial values
    % observe on model changes and update view accordingly
    % (tie listener to model object lifecycle)
    addlistener(m, 'f', 'PostSet', ...
        @(o,e) onChangedF(handles,e.AffectedObject));
end
function handles = initGUI()
    % initialize GUI controls
    hFig = figure('Menubar','none');
    hAx = axes('Parent',hFig, 'XLim',[0 1], 'YLim',[-2.5 2.5]);
    hSlid = uicontrol('Parent',hFig, 'Style','slider', ...
        'Min',1, 'Max',10, 'Value',5, 'Position',[20 20 200 20]);
    hLine = line('XData',NaN, 'YData',NaN, 'Parent',hAx, ...
        'Color','r', 'LineWidth',2);
    % define a color property specific to the view
    hMenu = uicontextmenu;
    hMenuItem = zeros(3,1);
    hMenuItem(1) = uimenu(hMenu, 'Label','r', 'Checked','on');
    hMenuItem(2) = uimenu(hMenu, 'Label','g');
    hMenuItem(3) = uimenu(hMenu, 'Label','b');
    set(hLine, 'uicontextmenu',hMenu);
    % customize
    xlabel(hAx, 'Time (sec)')
    ylabel(hAx, 'Amplitude')
    title(hAx, 'Signal in time-domain')
    % return a structure of GUI handles
    handles = struct('fig',hFig, 'ax',hAx, 'line',hLine, ...
        'slider',hSlid, 'menu',hMenuItem);
end
function onChangedF(handles,model)
    % respond to model changes by updating view
    if ~ishghandle(handles.fig), return, end
    set(handles.line, 'XData',model.t, 'YData',model.data)
    set(handles.slider, 'Value',model.f);
end
View_FrequencyDomain.m
function handles = View_FrequencyDomain(m)    
    handles = initGUI();
    onChangedF(handles, m);
    hl = event.proplistener(m, findprop(m,'f'), 'PostSet', ...
        @(o,e) onChangedF(handles,e.AffectedObject));
    setappdata(handles.fig, 'proplistener',hl);
end
function handles = initGUI()
    % load FIG file (its really a MAT-file)
    hFig = hgload('ViewGUIDE.fig');
    %S = load('ViewGUIDE.fig', '-mat');
    % extract handles to GUI components
    hAx = findobj(hFig, 'tag','axes1');
    hSlid = findobj(hFig, 'tag','slider1');
    hTxt = findobj(hFig, 'tag','fLabel');
    hMenu = findobj(hFig, 'tag','cmenu1');
    hMenuItem = findobj(hFig, 'type','uimenu');
    % initialize line and hook up context menu
    hLine = line('XData',NaN, 'YData',NaN, 'Parent',hAx, ...
        'Color','r', 'LineWidth',2);
    set(hLine, 'uicontextmenu',hMenu);
    % customize
    xlabel(hAx, 'Frequency (Hz)')
    ylabel(hAx, 'Power')
    title(hAx, 'Power spectrum in frequency-domain')
    % return a structure of GUI handles
    handles = struct('fig',hFig, 'ax',hAx, 'line',hLine, ...
        'slider',hSlid, 'menu',hMenuItem, 'txt',hTxt);
end
function onChangedF(handles,model)
    [mx,freq] = model.computePowerSpectrum();
    set(handles.line, 'XData',freq, 'YData',mx)
    set(handles.slider, 'Value',model.f)
    set(handles.txt, 'String',sprintf('%.1f Hz',model.f))
end
Controller.m
function [m,v1,v2] = Controller
    %CONTROLLER  main program
    % controller knows about model and view
    m = Model(100);           % model is independent
    v1 = View_TimeDomain(m);  % view has a reference of model
    % we can have multiple simultaneous views of the same data
    v2 = View_FrequencyDomain(m);
    % hook up and respond to views events
    set(v1.slider, 'Callback',{@onSlide,m})
    set(v2.slider, 'Callback',{@onSlide,m})
    set(v1.menu, 'Callback',{@onChangeColor,v1})
    set(v2.menu, 'Callback',{@onChangeColor,v2})
    % simulate some change
    pause(3)
    m.f = 10;
end
function onSlide(o,~,model)
    % update model (which in turn trigger event that updates view)
    model.f = get(o,'Value');
end
function onChangeColor(o,~,handles)
    % update view
    clr = get(o,'Label');
    set(handles.line, 'Color',clr)
    set(handles.menu, 'Checked','off')
    set(o, 'Checked','on')
end
 

In the controller above, I instantiate two separate but synchronized views, both representing and responding to changes in the same underlying model. One view shows the time-domain of the signal, and another shows the frequency-domain representation using FFT.