Table 1. Equations and fit functions... | American Society of Hematology

Table 1.

Equations and fit functions

Context	Formula	Variables and fit parameters	No.
Three-state transitions, probability top state	$P_{top} = \frac{1}{{(1 + e^{\frac{- Δ z• (F - F_{\frac{1}{2}})}{k_{B} T}})}^{2}}$	F Force k_B Boltzmann constant T Temperature Δz & F_1/2 fit parameters	1
Three-state transitions, probability middle state	$P_{middle} = \frac{1}{1 + \frac{1}{2} e^{\frac{- Δ z• (F - F_{\frac{1}{2}})}{k_{B} T}} + \frac{1}{2} e^{\frac{Δ z• (F - F_{\frac{1}{2}})}{k_{B} T}}}$	F Force k_B Boltzmann constant T Temperature Δz & F_1/2 fit parameters	2
Three-state transitions, probability bottom state	$P_{bottom} = \frac{1}{{(1 + e^{\frac{- Δ z• (F - F_{\frac{1}{2}})}{k_{B} T}})}^{2}}$	F Force k_B Boltzmann constant T Temperature Δz & F_1/2 fit parameters	3
Two-state transitions, probability top state	$P_{top} = \frac{1}{1 + e^{\frac{- Δ z• (F - F_{\frac{1}{2}})}{k_{B} T}}}$	F Force k_B Boltzmann constant T Temperature Δz & F_1/2 fit parameters	4
Two-state transitions, probability bottom state	$P_{bottom} = \frac{1}{1 + e^{\frac{Δ z• (F - F_{\frac{1}{2}})}{k_{B} T}}}$	F Force k_B Boltzmann constant T Temperature Δz & F_1/2 fit parameters	5
Dwell times open state	$τ_{open} (F) = τ_{0, open} e^{(\frac{Δ z_{o p e n} F}{k_{B} T})}$	F force k_B Boltzmann constant T Temperature τ_0,open, Δz_open fit parameters	6
Dwell times closed state	$τ_{closed} (F) = τ_{0, closed} e^{(- \frac{Δ z_{c l o s e d} F}{k_{B} T})}$	F force k_B Boltzmann constant T Temperature τ_0,closed, Δz_closed fit parameters	7
Gauss-fit, 1 term	$a • e^{- {(\frac{x - b}{c})}^{2}}$	a, b, c fit parameters	8
Gauss-fit, 2 terms	$a_{1} • e^{- {(\frac{x - b_{1}}{c_{1}})}^{2}} + a_{2} • e^{- {(\frac{x - b_{2}}{c_{2}})}^{2}}$	a₁, b₁, c₁, a₂, b₂, c₂ fit parameters	9
Gauss-fit, 3 terms	$a_{1} • e^{- {(\frac{x - b_{1}}{c_{1}})}^{2}} + a_{2} • e^{- {(\frac{x - b_{2}}{c_{2}})}^{2}} + a_{3} • e^{- {(\frac{x - b_{3}}{c_{3}})}^{2}}$	a₁, b₁, c₁, a₂, b₂, c₂, a₃, b₃, c₃ fit parameters	10

Context	Formula	Variables and fit parameters	No.
Three-state transitions, probability top state	$P_{top} = \frac{1}{{(1 + e^{\frac{- Δ z• (F - F_{\frac{1}{2}})}{k_{B} T}})}^{2}}$	F Force k_B Boltzmann constant T Temperature Δz & F_1/2 fit parameters	1
Three-state transitions, probability middle state	$P_{middle} = \frac{1}{1 + \frac{1}{2} e^{\frac{- Δ z• (F - F_{\frac{1}{2}})}{k_{B} T}} + \frac{1}{2} e^{\frac{Δ z• (F - F_{\frac{1}{2}})}{k_{B} T}}}$	F Force k_B Boltzmann constant T Temperature Δz & F_1/2 fit parameters	2
Three-state transitions, probability bottom state	$P_{bottom} = \frac{1}{{(1 + e^{\frac{- Δ z• (F - F_{\frac{1}{2}})}{k_{B} T}})}^{2}}$	F Force k_B Boltzmann constant T Temperature Δz & F_1/2 fit parameters	3
Two-state transitions, probability top state	$P_{top} = \frac{1}{1 + e^{\frac{- Δ z• (F - F_{\frac{1}{2}})}{k_{B} T}}}$	F Force k_B Boltzmann constant T Temperature Δz & F_1/2 fit parameters	4
Two-state transitions, probability bottom state	$P_{bottom} = \frac{1}{1 + e^{\frac{Δ z• (F - F_{\frac{1}{2}})}{k_{B} T}}}$	F Force k_B Boltzmann constant T Temperature Δz & F_1/2 fit parameters	5
Dwell times open state	$τ_{open} (F) = τ_{0, open} e^{(\frac{Δ z_{o p e n} F}{k_{B} T})}$	F force k_B Boltzmann constant T Temperature τ_0,open, Δz_open fit parameters	6
Dwell times closed state	$τ_{closed} (F) = τ_{0, closed} e^{(- \frac{Δ z_{c l o s e d} F}{k_{B} T})}$	F force k_B Boltzmann constant T Temperature τ_0,closed, Δz_closed fit parameters	7
Gauss-fit, 1 term	$a • e^{- {(\frac{x - b}{c})}^{2}}$	a, b, c fit parameters	8
Gauss-fit, 2 terms	$a_{1} • e^{- {(\frac{x - b_{1}}{c_{1}})}^{2}} + a_{2} • e^{- {(\frac{x - b_{2}}{c_{2}})}^{2}}$	a₁, b₁, c₁, a₂, b₂, c₂ fit parameters	9
Gauss-fit, 3 terms	$a_{1} • e^{- {(\frac{x - b_{1}}{c_{1}})}^{2}} + a_{2} • e^{- {(\frac{x - b_{2}}{c_{2}})}^{2}} + a_{3} • e^{- {(\frac{x - b_{3}}{c_{3}})}^{2}}$	a₁, b₁, c₁, a₂, b₂, c₂, a₃, b₃, c₃ fit parameters	10

Equations describing the equilibrium and the kinetics of the transitions in the D3 domains assuming independent processes.