EVOLUTION-MANAGER

Edit File: SSmicmen.html

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<table width="100%" summary="page for SSmicmen {stats}"><tr><td>SSmicmen {stats}</td><td style="text-align: right;">R Documentation</td></tr></table>

<h2>Self-Starting Nls Michaelis-Menten Model</h2>

<h3>Description</h3>

<p>This <code>selfStart</code> model evaluates the Michaelis-Menten model and
its gradient.  It has an <code>initial</code> attribute that
will evaluate initial estimates of the parameters <code>Vm</code> and <code>K</code>
</p>

<h3>Usage</h3>

<pre>
SSmicmen(input, Vm, K)
</pre>

<h3>Arguments</h3>

<table summary="R argblock">
<tr valign="top"><td><code>input</code></td>
<td>
<p>a numeric vector of values at which to evaluate the model.</p>
</td></tr>
<tr valign="top"><td><code>Vm</code></td>
<td>
<p>a numeric parameter representing the maximum value of the response.</p>
</td></tr>
<tr valign="top"><td><code>K</code></td>
<td>
<p>a numeric parameter representing the <code>input</code> value at
which half the maximum response is attained.  In the field of enzyme
kinetics this is called the Michaelis parameter.</p>
</td></tr>
</table>

<h3>Value</h3>

<p>a numeric vector of the same length as <code>input</code>.  It is the value of
the expression <code>Vm*input/(K+input)</code>.  If both
the arguments <code>Vm</code> and <code>K</code> are
names of objects, the gradient matrix with respect to these names is
attached as an attribute named <code>gradient</code>.
</p>

<h3>Author(s)</h3>

<p>José Pinheiro and Douglas Bates</p>

<p><code><a href="nls.html">nls</a></code>, <code><a href="selfStart.html">selfStart</a></code>
</p>

<h3>Examples</h3>

<pre>
PurTrt &lt;- Puromycin[ Puromycin$state == "treated", ]
SSmicmen(PurTrt$conc, 200, 0.05)  # response only
local({  Vm &lt;- 200; K &lt;- 0.05
  SSmicmen(PurTrt$conc, Vm, K)    # response _and_ gradient
})
print(getInitial(rate ~ SSmicmen(conc, Vm, K), data = PurTrt), digits = 3)
## Initial values are in fact the converged values
fm1 &lt;- nls(rate ~ SSmicmen(conc, Vm, K), data = PurTrt)
summary(fm1)
## Alternative call using the subset argument
fm2 &lt;- nls(rate ~ SSmicmen(conc, Vm, K), data = Puromycin,
           subset = state == "treated")
summary(fm2) # The same indeed:
stopifnot(all.equal(coef(summary(fm1)), coef(summary(fm2))))

## Visualize the SSmicmen()  Michaelis-Menton model parametrization :

xx &lt;- seq(0, 5, len = 101)
  yy &lt;- 5 * xx/(1+xx)
  stopifnot(all.equal(yy, SSmicmen(xx, Vm = 5, K = 1)))
  require(graphics)
  op &lt;- par(mar = c(0, 0, 3.5, 0))
  plot(xx, yy, type = "l", lwd = 2, ylim = c(-1/4,6), xlim = c(-1, 5),
       ann = FALSE, axes = FALSE, main = "Parameters in the SSmicmen model")
  mtext(quote(list(phi[1] == "Vm", phi[2] == "K")))
  usr &lt;- par("usr")
  arrows(usr[1], 0, usr[2], 0, length = 0.1, angle = 25)
  arrows(0, usr[3], 0, usr[4], length = 0.1, angle = 25)
  text(usr[2] - 0.2, 0.1, "x", adj = c(1, 0))
  text(     -0.1, usr[4], "y", adj = c(1, 1))
  abline(h = 5, lty = 3)
  arrows(-0.8, c(2.1, 2.9),
         -0.8, c(0,   5  ),  length = 0.1, angle = 25)
  text(  -0.8,     2.5, quote(phi[1]))
  segments(1, 0, 1, 2.7, lty = 2, lwd = 0.75)
  text(1, 2.7, quote(phi[2]))
  par(op)
</pre>

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