In what ways did the Know Nothing Party and the Free Soil Party contribute to the breakup of the Union in 1860?

For much of the history of the United States there have been two major political parties, and at the start of the 1850s those two parties were the Democratic Party (1828-Present) and the Whig Party (1834-1854). The Democratic Party had established itself as the major party after the death of the Federalist Party (1791-1824) and under the leadership of Andrew Jackson after his election as president in 1828. The Whig Party emerged in the 1830s as an opposition party, essentially for those that despised Andrew Jackson. During the 1840s and 1850s the Whig Party fragmented over the tensions surrounding the issue of slavery and its expansion into the western United States; in particular the passage of the Kansas-Nebraska Act of 1854.
In the turbulent period of the 1850s both the Know Nothing Party (1844-1860) and the Free Soil Party (1848-1854) emerged as single issue parties as the Whig Party began to decline and die. The Know Nothing Party, or as they were officially known the American Party, was a nativist party or group focused on anti-immigrant policy. The target of their anti-foreignism was primarily Irish Catholics whose numbers had increased due to the famine in Ireland which reached its peak in 1848. The Free Soil Party grew out of the short-lived Liberty Party (1840-1848), which was also a single-issue party; their issue was the abolition of slavery. A more palatable form of political anti-slavery was limiting the expansion of slavery through a free-soil ideology. For the supporters of the Free Soil Party, free men owning and cultivating free soil represented a more ethical and financially sound system to slavery.
As the political tensions surrounding the issue of slavery in the 1850s increased a new party emerged, the Republican Party (1854-Present). The 1856 slogan of the party was “free soil, free labor, free men.” The Republican Party platform in 1860 supported the ideology of free soil. Supporters of the Republican Party came from both the Free Soil Party and many of the northern members of the American (Know Nothing) Party who increasingly saw slavery as a cancer on American society. So, the Know Nothings and Free Soilers contributed to the breakup of the Union in 1860 by providing members of the Republican Party who elected Abraham Lincoln, which precipitated the call for secession by South Carolina about a month after the election.

The Know Nothing Party had essentially dissipated by 1860. It emerged in the 1850s after the Whig party collapsed in the wake of Bleeding Kansas, and its main cause was espousing anti-immigrant and anti-Catholic sentiments. There was a large influx of immigrants to the US at this time, especially due to the Irish Potato Famine. After the Dred Scott decision in 1857, the party largely merged with the Republican Party due to increasing opposition to slavery.
The Free Soil Party, like the Know Nothing Party, was a single-issue party that had mostly died out by 1860. Free Soilers opposed the expansion of slavery into new territories in the west. They arose mainly in the aftermath of the Mexican-American War, when the US added new territories that could potentially become states. With each new addition, the question of whether or not to allow slavery brought up fierce debates. In order to avoid the divisive nature of abolition, many Free Soilers instead argued that slavery should be banned from the west because it would mean fewer opportunities for freemen and was therefore economically detrimental. This party largely died out after the Compromise of 1850 temporarily eased tension over the extension of slavery. Many Free Soilers instead joined the Republican Party.