An in vitro method for investigating mtDNA replication dysfunction in a biological sample removed from a subject susceptible of suffering from Cockayne syndrome, said method comprising the steps of: a. contacting said biological sample with a marker specific for a species selected in the group of: POLG1 protein, POLG2 protein, HTRA3 protein, and any combination of these species, in conditions enabling said marker(s) to react with their respective targets, and b. determining the level of one or more species selected in step a) from the group of: POLG1 protein, POLG2 protein, HTRA3 protein, and any combination of these species in said biological sample through measurement of the marker(s) that has(have) reacted with its(their) respective species in step a), or through measurement of the reaction product(s) obtained after reacting the marker(s) with its(their) respective species in step a), and c. comparing the level(s) determined in step b) with respective normal threshold value(s) determined for healthy subject(s) for each species selected in the group set forth in steps a) and b) to carry out said steps, and d. from the comparison made in step c), concluding about the existence of a dysfunction in mtDNA replication, wherein conclusion is made of the existence of a mtDNA replication dysfunction if the level of each species selected to carry out the above disclosed steps is as follows: - the level of POLG1 protein determined in step b) is decreased with respect to the normal threshold value introduced in step c) by at least 10%, and/or - the level of POLG2 protein determined in step b) is increased with respect to the normal threshold value introduced in step c) by at least 15%, and/or - the level of HTRA3 protein, in particular the long isoform of HTRA3 protein, determined in step b) is increased with respect to the normal threshold value introduced in step c) by at least 2-folds, or when at least two of the above measurements meet the above thresholds. a. contacting said biological sample with a marker specific for a species selected in the group of: POLG1 protein, POLG2 protein, HTRA3 protein, and any combination of these species, in conditions enabling said marker(s) to react with their respective targets, and b. determining the level of one or more species selected in step a) from the group of: POLG1 protein, POLG2 protein, HTRA3 protein, and any combination of these species in said biological sample through measurement of the marker(s) that has(have) reacted with its(their) respective species in step a), or through measurement of the reaction product(s) obtained after reacting the marker(s) with its(their) respective species in step a), and c. comparing the level(s) determined in step b) with respective normal threshold value(s) determined for healthy subject(s) for each species selected in the group set forth in steps a) and b) to carry out said steps, and d. from the comparison made in step c), concluding about the existence of a dysfunction in mtDNA replication, wherein conclusion is made of the existence of a mtDNA replication dysfunction if the level of each species selected to carry out the above disclosed steps is as follows: - the level of POLG1 protein determined in step b) is decreased with respect to the normal threshold value introduced in step c) by at least 10%, and/or - the level of POLG2 protein determined in step b) is increased with respect to the normal threshold value introduced in step c) by at least 15%, and/or - the level of HTRA3 protein, in particular the long isoform of HTRA3 protein, determined in step b) is increased with respect to the normal threshold value introduced in step c) by at least 2-folds, or when at least two of the above measurements meet the above thresholds. - the level of POLG1 protein determined in step b) is decreased with respect to the normal threshold value introduced in step c) by at least 10%, and/or - the level of POLG2 protein determined in step b) is increased with respect to the normal threshold value introduced in step c) by at least 15%, and/or - the level of HTRA3 protein, in particular the long isoform of HTRA3 protein, determined in step b) is increased with respect to the normal threshold value introduced in step c) by at least 2-folds,