A method, comprising: (a) providing a microfluidic apparatus comprising: (i) a valve array comprising a series of N valves (2021, 2022, 2023, 2024, 2025) connected through unbranched fluidic connections, the series comprising, in order, a first terminal valve, at least three intermediate valves (2022, 2023, 2024) and a second terminal valve; (ii) at least one first port fluidically connected through a separate control valve to the first terminal valve; and (iii) at least one second port fluidically connected through a separate control valve to the second terminal valve; wherein each of said first terminal valve, said intermediate valves (2022, 2023, 2024) and said second terminal valve comprises a valve chamber; and (b) performing a biochemical reaction by: introducing a first reagent from a first reservoir into a first valve chamber of said first terminal valve; introducing a second reagent from a second reservoir into a second valve chamber of a valve in said series that is adjacent to said first terminal valve; and mixing said first and second reagents within said microfluidic apparatus to form a mixed reaction, wherein said mixing comprises moving both of said first reagent and said second reagent from said valve chambers of said first terminal valve and said valve adjacent to said first terminal valve in said series to a valve chamber of at least one additional valve in said series and flowing at least one of said first reagent and said second reagent in said series in a forward and in a reverse direction. (a) providing a microfluidic apparatus comprising: (i) a valve array comprising a series of N valves (2021, 2022, 2023, 2024, 2025) connected through unbranched fluidic connections, the series comprising, in order, a first terminal valve, at least three intermediate valves (2022, 2023, 2024) and a second terminal valve; (ii) at least one first port fluidically connected through a separate control valve to the first terminal valve; and (iii) at least one second port fluidically connected through a separate control valve to the second terminal valve; wherein each of said first terminal valve, said intermediate valves (2022, 2023, 2024) and said second terminal valve comprises a valve chamber; and (i) a valve array comprising a series of N valves (2021, 2022, 2023, 2024, 2025) connected through unbranched fluidic connections, the series comprising, in order, a first terminal valve, at least three intermediate valves (2022, 2023, 2024) and a second terminal valve; (ii) at least one first port fluidically connected through a separate control valve to the first terminal valve; and (iii) at least one second port fluidically connected through a separate control valve to the second terminal valve; (b) performing a biochemical reaction by: introducing a first reagent from a first reservoir into a first valve chamber of said first terminal valve; introducing a second reagent from a second reservoir into a second valve chamber of a valve in said series that is adjacent to said first terminal valve; and mixing said first and second reagents within said microfluidic apparatus to form a mixed reaction, wherein said mixing comprises moving both of said first reagent and said second reagent from said valve chambers of said first terminal valve and said valve adjacent to said first terminal valve in said series to a valve chamber of at least one additional valve in said series and flowing at least one of said first reagent and said second reagent in said series in a forward and in a reverse direction. introducing a first reagent from a first reservoir into a first valve chamber of said first terminal valve; introducing a second reagent from a second reservoir into a second valve chamber of a valve in said series that is adjacent to said first terminal valve; and mixing said first and second reagents within said microfluidic apparatus to form a mixed reaction, wherein said mixing comprises moving both of said first reagent and said second reagent from said valve chambers of said first terminal valve and said valve adjacent to said first terminal valve in said series to a valve chamber of at least one additional valve in said series and flowing at least one of said first reagent and said second reagent in said series in a forward and in a reverse direction.