My Trautwein relatives emigrated to the US in the early 1840s from Knittlingen, Wurttemberg.The Trautweins had been in Knittlingen for at least 2 generations before that. George Friedrich Trautwein was born in 1764. His father was Christopher Trautwein.The family were grape-growers. They may be Mathias' relatives.
My great uncle Moses Trautwein received this information from correspondence with relatives and officials in Germany in 1927. I hope this helps with you search.