How to set custom Web Part values through powershell?

I am using a powershell script to initialize several values of a custom webpart and then insert that webpart onto a page. I have been partially successful using the method below:

$multiPartLeftWebPart = New-Object MultiPart.MultiPart.MultiPart
$multiPartLeftWebPart.CurveEquation = "{""x0"":5,""y0"":-11,""x1"":107,""y1"":-44,""x2"":257,""y2"":-56,""x3"":403,""y3"":-55}"
$multiPartLeftWebPart.SelectedTabs.Add("News")
$multiPartLeftWebPart.SelectedTabs.Add("FAQ")
$multiPartLeftWebPart.SelectedTabs.Add("Events")

In this webpart CurveEquation and SelectedTabs are custom values used by my webpart that are typically set through the editor pane.

My Issue is that when I go into my editor pane after I have run my script only the CurveEquation value is set. CurveEquation is a string and SelectedTabs is a List<string> object.

I have stepped through my code when the editor part is loading and confirmed that CurveEquation has the expected value and that there are 0 items in Selected tabs.

Do I need to do something special to set values of a List<string> object using powershell in this way?

Code for the property:

    [Personalizable(PersonalizationScope.Shared), WebBrowsable(false)]
    public List<String> SelectedTabs
    {
        get;
        set;
    }