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Identifying different protein compositions and conformations from microscopic images of protein mixtures is a challenging open problem. We address this through disentangled representation learning, where separating protein compositions and conformations in an intermediate latent space enables accurate identification. By modeling compositions and conformations as content and transformation, the task can be reduced to disentangling content and transformation. The existing disentangling methods require an explicit parametric form for the transformation, which is unavailable for conformation, making these methods unsuitable. To overcome this limitation, we propose DualContrast, a novel contrastive learning-based method that implicitly parameterizes and disentangles both transformation and content. DualContrast achieves this by generating positive and negative pairs for content and transformation in both data and latent spaces. We demonstrate that existing self-supervised approaches fail under similar implicit parameterization, underscoring the necessity of our method. Through extensive experiments on 3D microscopic images of protein mixtures and additional shape-focused datasets beyond microscopy, we validate our claims and demonstrate the first in-principle fully unsupervised identification of different protein compositions and conformations in 3D microscopic images.