The question of how to make painting relevant in today's contemporary art world is one which raises its head often in cultural circles.

It's water-cooler chat for the art anoraks among us, and it's not a new dilemma.

Many confusing treatises have been penned on this subject. Looking back through the annals of art history, when the Russian painter and pioneer of abstract art, Kasimir Malevich, produced his Black Square painting in 1915 (two years before Duchamp showed Fountain – the urinal that shocked the world), the peg holding painting's coat was already starting to feel shoogly.

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Fast forward to 1951, and post-modernism was pulling on that coat with all its might as Robert Rauschenberg launched White Painting on the world. This work, which consists of four stretched canvases covered with house paint, further stoked the debate about painting being just one of the tools in an artist's armoury.

Almost a century after Malevich's controversial work, a new exhibition – titled Seasons And Sacraments – opens today at Dundee Contemporary Arts (DCA) which attempts to bridge the gap between the classic approach to painting of 17th-century French artist Nicolas Poussin and the cutting edge of contemporary art practice.

Berlin and New York-based painter, performance artist, musician, critic and theoretician Jutta Koether first came to Dundee in the summer of 2008 to take part in Altered States of Paint at DCA. While she was in Scotland, she paid a visit to the Scottish National Gallery in Edinburgh with DCA curator, Graham Domke.

According to Koether, participating in Altered States of Paint and looking around the collection on The Mound convinced her that painting "could have a renewed life". The works which particularly caught her attention in the Scottish National Gallery were Poussin's Seven Sacraments, which depict the sacraments of the Catholic Church: baptism, eucharist, confirmation, marriage, penance, ordination and extreme unction.

Poussin painted two versions of the work, and it's the second and only complete set, created between 1644 and 1648, that is displayed in Edinburgh in an octagonal room. "Seeing the work coincided with a growing interest of mine of looking at classic paintings and giving them a contemporary relevance," explains Koether, who used to edit German culture and music publication Spex.

The teacher in Koether – she is currently a professor at the Hochschule für bildende Künste in Hamburg – set off on a quest to discover more about the work of Poussin. This led her to pick up TJ Clark's Sight Of Death: An Experiment In Art Writing, in which the art historian uses two paintings by Poussin – Landscape With A Man Killed By A Snake and Landscape With A Calm – as a starting point for an examination of art criticism and how modern human beings look at art and imagery.

In the book, Clark suggests that the reader thinks "about why some visual configurations are harder to put into words than others. And about whether there is an ethical, or even political, point to that elusiveness."

According to Koether, Clark's writings made her return to Poussin's work and to try to remake it in a 21st-century context. Last year, she exhibited four paintings in New York, referencing Poussin's famous painting cycle The Four Seasons (1660–64) during the 2012 Whitney Biennial. Mounted on transparent glass panels and installed in front of one of the museum's windows, Koether's images interacted with the building's architecture to become, in her words, a site-specific "window onto a window".

In Dundee, her re-imagining of The Four Seasons is presented on freestanding sheets of glass in Gallery 1. Poussin's work is a series of four paintings and depicts Old Testament scenes representing spring, summer, autumn and winter. This is the first time these large-scale paintings have been shown in Europe, following their premiere in New York last year.

Koether's response to Poussin's Seven Sacraments is a newly commissioned series made specifically for DCA. In this work, she reinterprets these seven paintings as a series of seven different approaches to contemporary painting. Confirmation presents everyday objects encased in clear liquid acrylic, attached to vast sheets of glass. Penance is symbolised by a contemporary Danish-designed perspex table that resembles Poussin's depiction of drapery, while Baptism is represented by a painted canvas featuring racing driver Sebastian Vettel rather than a scene from classical antiquity.

Seasons And Sacraments is Koether's largest exhibition in the UK to date, and coincides with the artist's inclusion in the current Tate Modern exhibition, A Bigger Splash: Painting After Performance.

Jutta Koether: Seasons And Sacraments, Dundee Contemporary Arts, 152 Nethergate, Dundee (01382 909900, until April 21