ZoneLayoutTrigger.xaml

<zones:Zone.Style>
  <Style>
    <Style.Triggers>
      <DataTrigger Binding="{Binding IsChecked, ElementName=StackLeftSide}" Value="True">
        <Setter Property="zones:Zone.Layout">
          <Setter.Value>
            <ItemsPanelTemplate>
              <UniformGrid Columns="1" />
            </ItemsPanelTemplate>
          </Setter.Value>
        </Setter>
      </DataTrigger>
    </Style.Triggers>
  </Style>
</zones:Zone.Style>

...

<CheckBox x:Name="StackLeftSide" />