Im telling you I didnt do it! cried Mrs. Bleu. He just fell on my knife! The
Question:
“I’m telling you I didn’t do it!” cried Mrs. Bleu. “He just fell on my knife!” The detective smirked, turning away to hold back a chuckle. “I don’t know why,” she continued, “he ju—, he … he just sort of turned to me gasping and fell forward … I was just making dinner, chopping broccoli …” Mrs. Bleu trailed off and looked longingly at the floor of the interview room. They had been there for hours. “He was just standing at the end of the kitchen drinking his coffee and looking through the mail when it happened, but it was an accident. Why would I kill my husband?”
“We don’t know why,” the detective said calmly, “we’re hoping you’ll tell us. Your husband was found on the kitchen floor in a pool of blood … his blood. He had a knife wound, a wound from a kitchen knife that was lying on the floor just feet away covered in his blood. His blood … and your fingerprints! Moreover, you told the 911 operator that you stabbed him—”
“Accidentally!” she gasped.
“OK … OK, you admitted accidentally stabbing him … but do you really expect us to believe that he just fell onto your knife. Do you know how ridiculous that sounds?”
“I don’t care if it sounds ridiculous! It’s what happened!” she said, exasperated. “Look … I need to know what happened to my husband. One minute he was fine, and the next he was gasping! He had a heart attack I think, er—, I don't know, but he was MY husband. Why won’t you tell me?”
The detective looked annoyed. “We haven’t heard back yet from the coroner, Mrs. Bleu … but this is an active homicide investigation. We will share that information with you when we get it. Believe me, when we get confirmation of the cause of death, we will be talking again … soon.”
He stepped out. He had heard some good ones, but “he fell on my knife”? Really?? At that moment, the coroner stepped off the elevator and into the empty hallway … she was out of breath and appeared to be sweating. “Frank! Frank, listen! I just finished the autopsy. It missed!”
“What? What missed? Was it homicide?”
“No! I mean, maybe. Er—I don’t know for sure yet; we need the tox results.”
“Toxicology results? For a stabbing? And what do you mean it missed?”
“That’s just it, the knife! It missed the brachial artery! It was only muscle damage, mostly venous bleeding … seeping blood … comes out slow. It was halfway coagulated before he died and wasn’t even that deep.”
“What? Will you just calm down and start talking in plain English! What are you trying to say?”
"It was a flesh wound … plenty of blood, but not enough to kill a person. Without arterial damage it would take a long time to bleed out from this wound. But there is more to it … this guy died shortly after he was stabbed, but it wasn’t from the knife, that much is for sure!”
The detective cursed under his breath. It was going to be a long day. “OK, so the guy didn’t die from the knife wound, but he is dead, so from what?!”
Two weeks have passed, and you have been brought in to help investigate this case. You have heard the interrogation tapes and been briefed by both the lead detective and the coroner.
The coroner has ruled the cause of death of Dr. John Bleu a homicide, but by poisoning rather than because of the presumably accidental knife wound inflicted by Mrs. Bleu. Small quantities of an unknown substance, hereafter referred to as Compound X, were discovered in the decaf coffee Dr. Bleu was drinking shortly before he died. Dr. Bleu had brought the coffee home with him from work, as he did every day, according to his co‑workers and wife. His wife is still under suspicion, but it has not escaped the notice of the investigators that Dr. Bleu leads a large research group studying potentially lethal enzyme inhibitors for the drug company Hinesbiopharma.
The company is working with the U.S. government in a counter‑terrorism effort to study the effects of chemical weapons, so that potential treatments can be created in advance.
Three scientists who Dr. Bleu supervised, Dr. Greene, Dr. Gray, and Dr. Wight, are each running independent projects studying different inhibitors of the same enzyme, referred to in company documents only as XYZase. XYZase is critical to human metabolism, so development of chemical inhibitors of this enzyme by terrorist groups is viewed as a real and present threat by counter‑terrorism experts. According to company policies, only Dr. Bleu and the single scientist assigned to each project have access to the highly valuable, but extremely lethal, compounds.
INITIAL INVESTIGATION
Run kinetics experiments on XYZase without inhibitors and with Compound X.
Results: The compound found in Dr. Bleu's coffee (Compound X) has yet to be identified. Using a small amount of the compound extracted from the coffee, you have discovered that it is an inhibitor of XYZase. Given this revelation, it seems clear that this compound is the most likely murder weapon. The data you have gathered is shown in Table 1.
Table 1
[S] (nM) | V0 (no inhibitor) | V0 (Compound X) |
50 | 0.14 | 0.040 |
75 | 0.19 | 0.050 |
150 | 0.32 | 0.080 |
400 | 0.47 | 0.14 |
Note: [S] is given in nM; other values represent observed V0 values given in µmol/min of product formed.
Use the data collected to create Michaelis–Menten and Lineweaver–Burk plots with and without Compound X present.
From the limited data you have gathered, does it appear that XYZase follows Michaelis–Menten kinetics?
Now calculate the Michaelis constant, m,Km, of XYZase within two significant figures.
m= ________nM
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