Many-body problem of celestial mechanics revolutionized applied mathematics and continues to provide inspiration. Math/physical communities are much less aware that there are numerous example of fascinating many-body problems of classical mechanics arising in live cells at drastically different scales: instead of years and millions of kilometers, in the cell we deal with minutes and microns. Another big difference is: rather than Newtonian mechanics in empty space, when acceleration is proportional to force, in the cells filled with viscous cytoplasm, we deal with Aristotelian mechanics, in which velocity is proportional to force. Yet another difference is a great diversity of complex inter-body forces in the cell, compared to pleasingly simple gravitational force of celestial mechanics. Because of this diversity, in cell biology we often need to solve the ill-posed inverse problem – reverse-engineering forces from the observed patterns and movements – contrasted with the well-posed direct problem of predicting patterns and movements from known forces.
I will discuss two many-body problems of cell biology – assembly of mitotic spindle from two centrosomes and tens of chromosomes, and nuclei positioning in multi-nucleated muscle cells. Three approaches – solutions of ODEs of ‘particle’ models, solutions of PDEs of continuous approximation, and energy minimization, complemented by computer screening – shed light on the molecular origins of the intracellular forces that ensure proper and robust cellular architecture.