1. Canonical protein dynamics d: Analytic solution and rise time

    11:02

    from David Liao / Added

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    We obtain an analytic solution for the relationship between the number of copies of protein and time for the differential equation qualitatively investigated in the previous video. We find that the rise time, T1/2, is ln(2) divided by the degradation rate coefficient, α. The fact that the rise time is independent of the translation rate β is sometimes used as a pedagogical example of the importance of quantitative reasoning for gaining insights into biological dynamics that would be difficult to develop through natural-language and vaguely-structured notional reasoning alone.

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    • Canonical protein dynamics c: Qualitative graphical solution to differential equation

      04:12

      from David Liao / Added

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      We sketch a slope field corresponding to the differential equation derived in the previous video. We use this slope field to draw a qualitative curve describing how the number of copies of protein is expected to rise over time, when starting from an initial value of zero.

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      • Canonical protein dynamics b: Differential equation and flowchart

        09:50

        from David Liao / Added

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        We derive a differential equation approximating the time-rate of change of the number of copies of protein in the cell modeled by the animation in the previous video. This differential equation reads, dx/dt = β - αx. We depict aspects of this differential equation with a flowchart. It is important to remember that this differential equation does not represent all aspects of the stochastic dynamics in the toy model presented in the previous video.

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        • Laura Mersini-Houghton - Q12

          01:42

          from Nautilus / Added

          597 Plays / / 0 Comments

          Your father was a mathematician. Was he an inspiration for you?

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          • C4 forming a differential equation using the chain rule

            04:16

            from Chalfonts Tube / Added

            42 Plays / / 0 Comments

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            • First order separable differential equation (2)

              03:38

              from Newcastle University Maths / Added

              22 Plays / / 0 Comments

              Solve dy/dx= (1+y^2)/(2+3x), y(-1/3)=0

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              • Chapter 16-3

                46:29

                from SAJC Math / Added

                22 Plays / / 0 Comments

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                • Chapter 16-2

                  51:14

                  from SAJC Math / Added

                  22 Plays / / 0 Comments

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                  • Chapter 16-1

                    48:49

                    from SAJC Math / Added

                    26 Plays / / 0 Comments

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                    • Resonance Example 3 - Maths-Aid

                      14:45

                      from Newcastle University Maths / Added

                      102 Plays / / 0 Comments

                      A worked solution to the third example in the Maths-Aid worksheet, "Resonance."

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