Murthy is INSA senior professor in the Molecular Biophysics Unit, Indian Institute of Science (IISc), Bangalore. He obtained his bachelor's from Bangalore University (1970), master's from the Indian Institute of Technology, Madras (1972) and PhD from the IISc, Bangalore (1977). His research interests are X-ray crystallography, protein and virus structure. He has been awarded the Shantiswaroop Bhatnagar Prize, Rustum Choksi award, GN Ramachandran commemoration award, Hari Om Ashram Trust Award, Jagdish Chandra Bose Award for Life Sciences and G.N. Ramachandram gold medal for excellence in biological sciences. He has been elected to the Indian Academy of Sciences, Indian National Science Academy, and the National Academy of Sciences, India.

Krishnaswamy is EX- director, Natl. Inst. of Nutrition, Hyderabad, and past president, Nutrition Society of India (NSI). Her work on the prevention of cancer by turmeric highlights the role of malnutrition in cancer and on antimutagens and anticarcinogens in Indian diets. Her awards include: Dr. VN Patwardhan Prize; Dr. Kamala Menon Medical Res. Award, Internal Medicine; Shakuntala amir chand ward; Basant Devi Amirchand ,all 4 of ICMR, Glaxo oration, INSA; Chopra, IPS; BC Guha, IASc; Sita Mahalakshmi Memorial Orations; Best Medical Person Award, AP Akademi of Sciences; SG Srikantia Memorial Lecture Award, NSI; ASTC-Eminent Women Scientist Award; Cert. of Excellence, Indian Medical Assoc.; and Dr. Rajammal P. Devadas Annual Oration Award, Avinashilingam Deemed Univ., Honoured as eminent pharmacologist by IPS,Ramachandran oration of NFI She is fellow of several academies including IUNS.In 2022, she received the"living legend "from IUNS.