JP2004093234A - Toxicity presence or absence determination method - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a method of determining the presence or absence of toxicity based on gene expression data (also called a gene expression profile) using DNA micro arrays, or the like. <P>SOLUTION: A set of simultaneous differential equations is prepared based on metabolic gene pathway information related to the metabolism or evacuation of toxic matter, a coefficient of reaction rate is determined, and a linear stability analysis and a Jacobian stability analysis are performed in advance to obtain a relation between the presence and absence of the toxicity in the values of the coefficients of reaction rate. The gene expression distribution data is substituted into the simultaneous differential equations to obtain the coefficients of the reaction rate, and the data thus obtained are collated with the relation on the presence or absence of the toxicity between the values of the coefficients of the reaction rate. Thus, the toxicity of chemical compounds can be predicted and the presence or absence of the toxicity can be determined by using the gene expression data. <P>COPYRIGHT: (C)2004,JPO

Description

図６は、薬毒物の代謝的活性化と毒性発現の関係図である。鎌滝、加藤編、薬物代謝学第２版、東京化学同人（２０００）参照。薬物が通常投与された場合、ほとんどの薬毒物はＰ４５０を始めとする代謝酵素群により、酸化、還元、加水分解、抱合を受け排泄される。表２にＰ４５０を始めとする薬物代謝酵素について整理した。表２の薬物代謝酵素群の組み合わせもしくは繰り返しの作用により、薬毒物は代謝される。図６で通常投与された薬物は、Ｐ４５０による代謝や抱合反応を受けて、排泄される。例えば、アセトアミノフェンはフェノール性のＯＨ基を有するので、グルクロン酸抱合と、硫酸抱合の両者により代謝される。一方図６では活性中間体が生成されることを示している。例えば、アセトアミノフェンでは大量投与時に、Ｎ−水酸化により、活性中間体が生成される。この活性中間体とは、薬毒物が代謝を受けることにより生じる薬理活性のある代謝物のことである。生体内で生成した反応性の高い活性中間体も多くの場合は、グルタチオン抱合などの代謝を受けて、解毒される。しかし活性中間体の量が多い場合や、その解毒に関与する酵素系が飽和したり、グルタチオンなどの生体成分の量が少ない場合には、解毒処理機構が機能しなくなり、最終的に生理機能の障害すなわち毒性の発現につながることになる。従って、薬毒物の毒性発現や毒性の程度は、活性中間体の生成速度と親化合物や代謝産物の解毒速度の均衡によって支配される。活性中間体は、その生成が促進されて解毒能が低下して均衡が崩れ、ＤＮＡやＲＮＡなど核酸と結合すると変異原性、発がん性、催奇形性など遺伝子毒性につながり、タンパク質などと結合すると臓器障害を発生する。一方、活性中間体と生体成分（特にタンパク質）との反応の結果、その複合体がハプテン抗原となり、免疫反応を導き出し、毒性を発現する場合もある。
【０００９】
【表２】

この活性中間体の生成速度や親化合物代謝産物の解毒速度の均衡を見る際、ＤＮＡチップやＦＤＤ，ＳＡＧＥ等を用いた発現分布解析が有効である。なぜなら、代謝や排泄に係わるタンパク質の遺伝子の発現状態が均衡している通常投与時と比較して、その均衡が有意に崩れている状態は、大量投与などによる毒性反応が生じていることを示唆するためである。この代謝や排泄にかかわるタンパク質を産生する複数の遺伝子の発現状態が均衡しているか否かを判定する際に、尿素サイクルとクエン酸回路に関連した遺伝子を解析するのが有効と考えられる。この理由の一つは、サイクル反応なので、関連遺伝子の変化が周期性を持つことである。周期性の変化、もしくは安定性を見ることで、複数遺伝子の発現状態が均衡しているか否かを数学的に解析することができる。もう一つの理由は両サイクルが、図６に示す各反応や現象と密接に係わっているためである。
図７に活性中間体の主要な解毒反応である、グルタチオン抱合とその代謝経路を示す。グルタチオンは生体内に最も多く存在するＳＨ化合物であり、肝内には数ｍＭのグルタチオンが存在する。薬毒物（化合物Ｒ−Ｘ；但しＲは基質、Ｃは脱離基）は、グルタチオン転移酵素により、グルタチオン抱合体を形成する。続いてγ―グルタミルトランスペプチダーゼ、システイニルグルシナーゼ、膜結合型Ｎ−アセチル転移酵素の作用により、メルカプツール酸抱合体が形成され、薬毒物は尿、糞中に排泄される。この代謝過程でグルタミン酸（Ｇｌｕ）とグリシン（Ｇｌｙ）の２種類のアミノ酸が生成される。
図８にグルタチオン抱合の過程で生成されるグリシンの代謝経路を示す。グリシンは、グリシンヒドロキシメチルトランスフェラーゼにより別のアミノ酸であるセリンになり、セリンデヒドラターゼにより、ピルビン酸になる。このピルビン酸生成過程で、産生されたアンモニア（ＮＨ_３）は、尿素サイクルを経て尿素に変換され尿中に排泄される。また、ピルビン酸は、糖代謝、脂質代謝、タンパク質代謝の多くで生成される化合物で、ピルビン酸デヒドロゲナーゼにより、アセチルＣｏＡになる。アセチルＣｏＡは、クエン酸回路の出発物質である。このピルビン酸からアセチルＣｏＡの過程で産生される二酸化炭素（ＣＯ_２）は、ピルビン酸生成過程で産出されたアンモニアと共に、尿素サイクルを経て尿素に変換され尿中に排泄される。このようにグルタチオン抱合により生成されたグリシンは、尿素サイクルとクエン酸回路に密接に関係している。
図９にグルタチオン抱合の過程で生成されるグルタミン酸の代謝経路を示す。なお、グルタミン酸は、アミノトランスフェラーゼによりアミノ酸代謝を行ったとき２オキソ酸と共に生成されるもので、アミノ酸代謝において中心的な化合物の一つである。グルタミン酸は、グルタミン酸ヒドロゲナーゼにより、２−オキソグルタル酸とアンモニアを生成する。またグルタミン酸は、アスパラギン酸アミノトランスフェラーゼにより、２−オキソグルタル酸とアスパラギン酸を生成する。アンモニアは尿素サイクルにより尿素に変換される。また２−オキソグルタル酸は、クエン酸回路中の化合物である。このようにグルタチオン抱合により生成されたグルタミン酸は、尿素サイクルとクエン酸回路に密接に関係している。図１０にクエン酸回路を示す。クエン酸回路はＴＣＡ回路ともよばれ、糖、脂肪酸、アミノ酸を酸化的に代謝する主要経路であり、同時にＮＡＤＨ（ニコチンアミドアデニンジヌクレオチド）等の各種生合成の原料を提供する経路である。具体的には、クエン酸回路で生成されるＮＡＤＨやＦＡＤＨ_２（還元型フラビンアデニンジヌクレオチド）の電子伝達系がＯ_２により再酸化されるとき酸化的リン酸化でＡＴＰを生成する。ＡＴＰは生体における主要なエネルギー伝達体である。
クエン酸回路と尿素サイクルは、グルタチオン抱合反応などと密接に関係していることが分かった。この抱合反応以外に、図６に示すように毒薬物がＤＮＡやタンパク質と共有結合を行うなどの反応を行う過程で、アミノ酸分解が起こることが考えられる。アミノ酸分解により生成される窒素（ＮＨ_３）や炭素（ＣＯ_２）は尿素サイクルにより尿素に変換される。またアミノ酸分解は尿素サイクルのみならずクエン酸回路とも関係している。図１１にアミノ酸分解とクエン酸回路との関係を示す。標準アミノ酸は、図１１に示すようにピルビン酸、２−オキソグルタル酸、スクシニルＣｏＡ、フマル酸、オキサロ酢酸、アセチルＣｏＡ、アセト酢酸のいずれかに分解される。このようにクエン酸回路も毒性発現に関連するアミノ酸分解と密接に関係している。
またクエン酸回路は、アミノ酸分解に留まらず、最も代表的な薬物代謝酵素であるＰ４５０の反応にも大きく係わっている。図１２に示すようにＰ４５０の代謝反応の補酵素であるヘムが、クエン酸回路中のスクシニル−ＣｏＡと、アミノ酸であるグリシンにより合成されるのである。ヘムは主に赤芽球と肝臓で合成されるが、肝臓が作るヘムは、主にＰ４５０の補因子となる。補因子とは、ある酵素の活性を向上させる因子で、その酵素反応に必須といえる因子である。このＰ４５０と補因子ヘムとの関係を図１３に示す。毒薬物の多くはＰ４５０により酸化もしくは還元を受け、代謝物となる。その過程でヘムを補因子として必要とするが、ヘムはクエン酸回路のスクシニル−ＣｏＡを合成の出発物質としている。このように、尿素サイクルとクエン酸回路は、Ｐ４５０を始めとする第Ｉ相代謝反応、グルタチオン抱合を始めとする第ＩＩ相代謝反応に関連する、薬物代謝において重要な代謝回路である。
尿素サイクルとクエン酸回路を構成する遺伝子の発現分布をＤＮＡチップ等の遺伝子発現分布測定法により測定し、その遺伝子発現分布を、予め遺伝子パスウェイ情報を元に作成されたモデルに代入し、そのモデルの連立微分方程式を解析することで、通常投与時の尿素サイクルやクエン酸回路の線形安定性、ヤコビ安定性を計算する。毒性が見られる場合は、尿素サイクルやクエン酸回路の線形安定性、ヤコビ安定性に乱れが生じると考えられる。その線形安定性、ヤコビ安定性の評価結果を用いて化合物の毒性の予測並びに毒性の有無について判定することができる。
本発明の本意は、薬物投与以前の安定状態にある細胞内の遺伝子発現や蛋白質発現の調和的振る舞いが、薬物投与後に変化する（崩れる）ことをシミュレーションにより判定することである。つまり薬物投与前と後とで、遺伝子発現やタンパク質発現の調和的振る舞いが変化したとき、薬物は何らかの毒性（もしくは薬効）を発揮したと判定できる。この調和的振る舞いの変化（崩れ）は、例えば線形安定解析やヤコビ安定性解析により評価することができる。
線形安定性解析による毒性判定の基準を以下にしめす。下記基準は線形安定性解析の意味を考えると自明である。
薬物投与前後で線形安定の場合、すなわち（イ）線形安定→線形安定の場合、遺伝子発現の調和的振る舞いが薬物投与前後で変化しないので、毒性なしと判定できる。
同様に、
（ロ）線形安定→線形不安定の場合、線形安定性解析では情報なし
（ハ）線形不安定→線形安定の場合、毒性有り
（ニ）線形不安定→線形不安定の場合、
振動子的（ｏｓｃｉｌｌａｔｏｒｙ）振る舞い→振動子的（ｏｓｃｉｌｌａｔｏｒｙ）　振る舞いならば、毒性無し
振動子的（ｏｓｃｉｌｌａｔｏｒｙ）振る舞い→カオス的（ｃｈａｏｔｉｃ）振る舞い　ならば、毒性有り
と判定できる。カオス的振る舞いとは将来的な振る舞いが予測できない振る舞いのことである。
なお振動子的振る舞いとカオス的振る舞いの判定には、線形安定性解析とヤコビ安定性解析の結果を組み合わせる必要がある。振動子振る舞いとは、数学的には線形不安定でかつヤコビ安定と同義である。またカオス的振る舞いとは、数学的には線形不安定でかつヤコビ不安定と同義である。
ヤコビ安定性解析による毒性判定の基準を以下に示す。下記基準はヤコビ安定性解析の意味を考えると自明である。薬物投与前後で、
（ホ）ヤコビ安定→ヤコビ安定の場合、毒性無し
（へ）ヤコビ安定→ヤコビ不安定の場合、毒性有り
（ト）ヤコビ不安定→ヤコビ安定の場合、ヤコビ安定性解析では情報なし
（チ）ヤコビ不安定→ヤコビ不安定の場合、ヤコビ安定性解析では情報なし
と判定できる。
本発明の特徴は、線形安定性解析やヤコビ安定性解析を同時に行うことにある。線形安定性解析のみ、もしくはヤコビ安定性解析のみでは毒性の判定がつかなくても、両者を同時に行うことで毒性判定が行える。また線形安定性解析とヤコビ安定性解析の判定結果とが矛盾した場合、連立微分方程式作成に用いたモデルが不適切、もしくは仮定したパスウエイが正しくないことを示唆しており、モデルを再構築するための情報を与えてくれる点でも優れている。
【００１０】
【発明の実施の形態】
以下、毒性予測に用いる具体的なアルゴリズムについて説明する。本実施例は、本発明を細胞分裂周期（Ｃｅｌｌ　ｄｉｖｉｓｉｏｎ　ｃｙｃｌｅ）モデルである細胞周期パスウェイモデル（論文執筆者の名前をとってタイソンモデル）に適用した例を示す。タイソンモデルについては図１４に示す。原著論文はＪ．Ｔｙｓｏｎ他、Ｍｏｄｅｌｉｎｇ　ｔｈｅ　ｃｅｌｌ　ｄｅｖｉｓｉｏｎ　ｃｙｃｌｅ：　ｃｄｃ２　ａｎｄ　ｃｙｃｌｉｎ　ｉｎｔｅｒａｃｔｉｏｎｓ，　Ｐｒｏｃ．　Ｎａｔａｌ．　Ａｃａｄ．　ＵＳＡ，　ｖｏｌ．８８，　ｐｐ．７３２８−７３３２　（１９９１）である。本実施例と同様の方法で、細胞分裂周期パスウェイを、尿素サイクルもしくはクエン酸回路に置き換えることで、遺伝子発現解析結果を用いた毒性予測が可能となる。
図１４について説明する。図１４のモデルは細胞周期に関連する遺伝子サイクリン（Ｃｙｃｌｉｎ）とｃｄｃ２の二種類のタンパク質と、サイクリンとｃｄｃ２の結合体であるＭＰＦ（Ｍａｔｕｒａｔｉｏｎ　ｐｒｏｍｏｔｉｎｇ　ｆａｃｔｏｒ）より構成される。なお、ｃｄｃ２はプロテインキナーゼによりリン酸化（Ｐｈｏｓｐｈｏｒｙｌａｔｉｏｎ）され、リン酸化ｃｄｃ２となる。また活性型ＭＰＦはプロテインキナーゼによりリン酸化され通常型ＭＰＦになる。単純なモデルであるが図１４のモデルを用いて細胞増殖時の振る舞いをよく説明できることが知られている。定式化のため、図１４の活性化ＭＰＦをＭ，通常型（リン酸化）ＭＰＦをｐＭ、サイクリンをＹ，リン酸化サイクリンをＹＰ、ｃｄｃ２をＣ２，リン酸化ｃｄｃ２をＣＰと呼ぶ。また図１４でリン酸化を行う酵素、プロテインキナーゼをＰと呼ぶ。図１４中のａ．ａは、蛋白質の構成要素であるアミノ酸（Ａｍｉｎｏ　Ａｃｉｄ）を意味する。また図１４中の各タンパク質間をつなぐ矢印は、反応の方向を意味し、その矢印の横に記載されたｋ１からｋ９までの値は、各反応の反応速度係数を示す。図１４の反応速度係数ｋは濃度÷時間の次元を持ち、ｋが大きいほど、矢印の向きの反応量（反応速度）が大きいことを意味する。
図１５は図１４のモデルをもとに作成した連立微分方程式である。図１５の一番上の式は、時刻ｔにおけるｃｄｃ２（Ｃ２）の濃度（例えばモル／リットル）に関する微分方程式である。ｃｄｃ２は、活性型ＭＰＦ（Ｍ）とリン酸化ｃｄｃ２（ＣＰ）の両者から生成され、その反応速度係数はそれぞれｋ６、ｋ９である。またＣ２自身がプロテインキナーゼ（Ｐ）により反応速度係数ｋ８でリン酸化されＣＰとなる。生成される場合の符号をプラス、消滅する場合の符号をマイナスとすると図１５に示す微分方程式ができる。図１４の反応をすべて上記のように定式化することで、図１５の連立微分方程式が作成される。図１５の連立微分方程式を解くことで、図１４に示すパスウェイにおける各タンパク質の濃度の時間変化をシミュレートすることができる。
図１６に図１５の連立微分方程式の反応速度係数に対する仮定をまとめた。またＣ２とＣＰとｐＭとＭの総和は一定と仮定した。これらの値は、他の実験結果、生物知識、文献情報に基づき、出来るだけ確実な値とした。このように連立微分方程式における反応速度係数の値は可能な限り確実な値とすることが望ましい。
図１７に線形安定性解析の具体例について記す。まず図１５の連立微分方程式を簡略化し、一次微分の値がゼロになる条件を探す。それらの式の符号を見ることで、式１〜式３の定義に従って、線形安定、線形不安定を判定する。
図１８にヤコビ安定性解析の具体例について記す。図１５の連立微分方程式を更に微分して、二次微分方程式を得る。その二次微分方程式からヤコビ安定性に用いる判定式Ｐを得る。Ｐの符号により、ヤコビ安定、ヤコビ不安定を判定する。
図１９に本発明のアルゴリズムをフローチャート図で示す。図１４に示すようなパスウェイモデルを作成した後、そのパスウェイモデルから図１５に示すような連立微分方程式を作成する。パスウェイモデル作成にあたっては、文献情報や生物知識を参照して、可能限り妥当なモデルを作成する。続いて、数学分野における線形安定性解析（図１７）とヤコビ安定性解析（図１８）の両者を、図１５のような連立微分方程式に対して行う。数学の分野では線形安定性解析とヤコビ安定性解析はそれぞれよく知られた解析方法であるが、それら両者を、同一のパスウェイモデルに適応した例はない。しかし、線形安定性解析とヤコビ安定性解析の両者を行うことで、遺伝子発現の振動子的（ｏｓｃｉｌｌａｔｏｒｙ）　振る舞いの変化をより詳細に解析することが可能であり、精度の高い判定（例えば毒性判定）が行える。また仮に線形安定性解析とヤコビ安定性解析の結果が矛盾している場合は、計算の出発点であるパスウェイモデルそのものに矛盾があることが示唆されるので、パスウェイモデルに対して変更を加える必要がある。結果が矛盾していない場合、線形安定性解析とヤコビ安定性解析の結果から、遺伝子発現の振動子的振る舞いの変化の有無、すなわち毒性の有無について判定を行うことができる。図２０に本発明における遺伝子発現の振動子的振る舞いの変化の有無を評価する一例を示した。図２０は、図１４と図１５の細胞周期パスウェイモデルの解析結果の一例である。図１５の連立微分方程式に含まれる反応速度係数ｋ６の値を図１６の範囲で変化させつつ線形安定性解析（図１７）およびヤコビ安定性解析（図１８）を行ったところ、ｋ６の値によって細胞周期の様子が、図２０に示すような３種類に分類できることが分かった。
例えばＭからＣ２を生成する反応速度係数ｋ６の値を０から１０まで変化させたとき、図２０に示すような３つの領域Ａ、Ｂ、Ｃに分類できた。この３分類は、線形安定性解析（図１７）の結果から分類された。線形安定性解析の符号が領域Ａではマイナス（すなわち線形安定）、領域Ｂではプラス（すなわち線形不安定）、領域Ｃではマイナス（すなわち線形安定）であった。線形安定性解析の結果が安定とは、その系が定常解近傍から変化しない傾向にあることを意味する。生物学的には領域Ａは、Ｍの濃度が高濃度であり続ける結果、細胞周期の回転にブレーキがかかる。この状態は細胞分裂期（Ｍｅｔａｐｈａｓｅ）において細胞周期が一時停止した（Ｍｅｔａｐｈａｓｅ　Ａｒｒｅｓｔ）状態に相当する。それに対し、領域Ｂは、ＭやＣ２の濃度が変化する結果、細胞周期が回転し、細胞増殖が行われる状態に相当する。また領域Ｃは、Ｍの濃度が低濃度であり続けるので、細胞間期（Ｉｎｔｅｒｐｈａｓｅ）において細胞周期が一時停止した（Ｉｎｔｅｒｐｈａｓｅ　Ａｒｒｅｓｔ）に相当する。但し、領域Ａの内、ｋ６の値が０．１から０．１９２の時、ヤコビ安定性解析（図１８）の符号はプラス（すなわちヤコビ不安定）である。ヤコビ不安定とは、定常解近傍以外を含む領域では変化が起ころうとしていることを意味する。そこで、ｋ６の値が０．１から０．１９２の間では、定常解近傍ではその定常解に留まろうとするが、系全体は動こうとしているといえる。細胞周期は一時停止しているだけであり、いずれ動くので、その細胞は正常である。しかし、ｋ６の値が０．１９２から０．２の間では、線形安定であると同時にヤコビ安定である。この場合は、定常解近傍のみならず系の全体に渡って停止しようとしており、細胞周期が将来に渡って動くことはない。従って、ｋ６の値が０．１９２から０．２の間では、その細胞は一時停止しているだけでなく、死んでいることを意味する。同様に領域Ｃでも、ｋ６の値が１．９から１０では、細胞は一時停止しているだけだが、ｋ６の値が１．５から１．９の間では、細胞は死んでいることを意味する。
このように連立微分方程式のパラメータに相当する、反応速度係数ｋの値を変化させるシミュレーションすることで、ｋの値とその細胞の状態との関係を予め評価することができる。その後、ＤＮＡチップなどを用いて時間ごと計測した発現分布値より、Ｍ，Ｃ２等の各物質の濃度値（あるいはその相対値）を連立微分方程式に代入し、実際のｋの値を計算する。
なお、領域Ｂ（ｋ６の値が０．２から１．５の間）は、線形不安定、ヤコビ安定である。この場合は、細胞は安定した周期で増殖する。なぜなら、現時点ではＭとＣ２の濃度が変化しているが、系全体ではいずれ安定するためである。すなわち振動子的（ｏｓｃｉｌｌａｔｏｒｙ）な振る舞いであり、細胞は正常である。しかし、仮に線形不安定でかつヤコビ不安定であった場合、現時点でもそして系全体でも不安定なため、将来的にどのような状態になるか予測がつかない。すなわちカオス（Ｃｈａｏｔｉｃ）な振る舞いであり、細胞ががん化したことを示唆する。このように連立方程式を線形安定性解析のみならずヤコビ安定性解析を行うことで、細胞が増殖しているのか、一時停止しているのか、それとも死んでいるのか、ガン化しているのかを判定できる。線形安定性解析もしくはヤコビ安定性解析のいずれか一方を行うだけでは不可能な判定を、本方法では行うことができる。本法を尿素サイクルもしくはクエン酸サイクルに適用することで細胞周期と同様に毒性の有無などの判定を行うことができる。
すなわち予め、尿素サイクルとクエン酸サイクルに基づきパスウェイモデルを作成し、連立微分方程式を得る。その連立微分方程式に用いる反応速度係数等のパラメータは文献情報や生物知識に基づき可能な限り妥当な値とする。その後、反応速度係数の値に基づき、統合したり消去できる連立微分方程式を探して整理する。続いて、線形安定性解析（図１７）とヤコビ安定性解析（図１８）を行い、図２０のように反応速度係数の値と細胞異常（毒性あり）、細胞正常（毒性なし）の関係を予め得ておく。その後、実験より得られた発現分布データから各遺伝子の濃度もしくはその相対値の実測値を、連立微分方程式に代入し、実験値に基づく反応速度係数を計算する。最後に、実験により得られた反応速度係数の値と、図２０のような反応速度係数の値と毒性との値の関連表とを照らし合わせ、毒性の有無を判定する。
本発明の実施形態のソフトウェアを実行するために利用されうるコンピュータシステムの一例を図２１に、そのシステムブロック図を図２２に示す。
図２１は、本発明の実施形態のソフトウェアを実行するために使用されうるコンピュータシステムの例である。図２１はキーボード１８１、ディスプレイ１８２、ＣＰＵ１８３、記憶装置１８４および記憶媒体１８５を示す。キーボード以外に、マウス等のグラフィカルユーザーインターフェースと対話するためのデバイスを備えても良い。記憶装置１８４および記憶媒体１８５は、本発明を実行するコンピュータコードに組み込まれるソフトウェアプログラム、本発明と共に使用するためのデータなどを記憶および読み出すために利用され得る。
図２２は、本発明の実施形態のソフトウェアを実行するための使用される、コンピュータシステムのブロック図である。図２１に示すようにコンピュータシステムは、キーボード１８１、ディスプレイ１８２、ＣＰＵ１８３、記憶装置１８４および記憶媒体１８５を備える。またコンピュータシステムは、例えばシステムメモリ、固定ディスク（ハードディスク）、ＣＤ−ＲＯＭ、ＤＶＤ等の着脱式ディスク、ディスプレイアダプタ、サウンドカード、スピーカーおよびネットワークインタフェースを更に備える。本発明は共に使用するのに適切なコンピュータシステムはまた、測定機器に組み込まれ得る。
【００１１】
【発明の効果】
本発明により、薬物投与時のＤＮＡチップ等の遺伝子発現分布データから、その薬物の毒性予測、毒性の有無について判定することができる。
【図面の簡単な説明】
【図１】尿素サイクルの概念図。
【図２】薬物代謝の概念図。
【図３】ＤＮＡチップの概念図。
【図４】ＤＮＡチップ解析のフローチャート。
【図５】アセトアミノフェンの代謝経路図。
【図６】薬毒物の代謝的活性化と毒性発現の説明図。
【図７】グルタチオン抱合の代謝経路図。
【図８】グリシン代謝経路図。
【図９】グルタミン代謝経路とアミノ酸代謝経路図。
【図１０】クエン酸回路の概念図。
【図１１】アミノ酸分解とクエン酸回路の関連図。
【図１２】ヘム生合成経路図。
【図１３】Ｐ４５０と補因子ヘムの関係図。
【図１４】細胞周期パスウェイモデル図。
【図１５】細胞周期パスウェイモデルの連立微分方程式。
【図１６】図１５の反応速度係数に対する仮定の一例。
【図１７】線形安定性解析の一例。
【図１８】ヤコビ安定性解析の一例。
【図１９】遺伝子発現の振動子的振る舞い変化（例えば毒性判定）の有無を判定するフローチャート図。
【図２０】遺伝子発現の振動子的振る舞いの変化の評価法の概念図。
【図２１】本発明の実施形態のソフトウェアを実行するために利用され得るコンピュータシステムの一例。
【図２２】図１８のコンピュータシステムのシステムブロック図。
【符号の説明】
３１．検出器、３２．ＤＮＡプローブ、３３．蛍光標識された遺伝子、３４．支持体、５１．アセトアミノフェン、１８１．キーボード、１８２．ディスプレイ、１８３．ＣＰＵ、１８４．記憶装置、１８５．記憶媒体。[0001]
TECHNICAL FIELD OF THE INVENTION
The present invention relates to a method and an apparatus for predicting drug toxicity and efficacy based on gene expression distribution data (also referred to as gene expression profile) using a DNA microarray or the like.
[0002]
[Prior art]
Toxicology is the study of elucidating the harmful effects of drug toxicants on living organisms and the mechanism of action, and evaluating the risk and safety based on this information. General toxicity tests (single-dose, repeated-dose toxicity tests) and special toxicity tests (carcinogenicity, reproductive / developmental toxicity, allergenicity, teratogenicity) have been conducted to elucidate the adverse effects of toxicants. Was. However, the toxicity test described above is a test using experimental animals such as rats and dogs, and there is a limit to a method for evaluating human toxicity. Toxicogenomics is one of the approaches to overcome the limitations of conventional methods by incorporating a genomics approach into this toxicology. Toxicogenomics uses the genomic information obtained through human genome analysis and other genomic analysis techniques developed in the process to apply the toxic substances contained in the environment and the response of organisms to compounds such as stressors or drugs. And a new field of toxicology to study interactions at the genetic level. Toxicogenomics includes microarray (DNA chip) analysis of messenger RNA (mRNA) expression, protein expression analysis in cells and tissues, and gene sensitivity analysis (single nucleotide polymorphism analysis). Is an attempt to determine toxicity using a computer algorithm from the expression analysis results using a microarray (to calculate the presence or absence of toxicity and the amount thereof). Castle AL, et al., Toxicogenomics: \ a \ new \ revolution \ in \ drug \ safety, \ DDT \ vol. 7, @pp. 728-736 (2002). However, there is no defined method for determining toxicity based on microarray data. Therefore, development of a method for determining toxicity based on microarray data has been awaited.
[0003]
[Problems to be solved by the invention]
An object of the present invention is to provide a method and an apparatus for determining toxicity using data of a microarray (DNA chip). More specifically, it is an object of the present invention to determine the toxicity of a compound based on a set of gene expression distribution data (gene expression profile) and information on gene pathways and enzyme / metabolism pathways.
[0004]
[Means for Solving the Problems]
In order to solve the above-mentioned problems, a simultaneous differential equation is created based on pathway information related to metabolism and excretion (excretion or drug @elimination) of a toxic drug, and then the simultaneous differential equation using gene expression distribution data is created. The toxicity of the compound is determined by calculating the stability of the solution (linear stability, Jacobi stability).
Pathway information related to the metabolism and excretion of toxic drugs refers to the interrelationship between genes and proteins on pathways that control amino acid synthesis and amino acid excretion, for example, urea cycle and citric acid cycle. FIG. 1 shows the urea cycle. The urea cycle, also called the ortinine cycle, is a metabolic pathway that exists in the liver of mammals and other urea excreting animals and purifies urea. Ammonia (NH) generated in the metabolic process of sugar, protein, lipid, etc.₃) And carbon dioxide (CO₂Or carbonate ion HCO₃ ⁻) Is finally excreted as urea by the urea cycle as shown in FIG. The gene expression distribution data includes, for example, a DNA chip method (DNA Chip), a differential display method (Differential Display), a quantitative PCR method (Quantitative PCR), a SAGE (Serial Analysis of Gene Expression) method, and a protein method. It refers to the expression level of a plurality of genes (or proteins) obtained by a method for measuring the change in expression of a plurality of genes or proteins, or a ratio between the expression levels.
Linear stability (Linear Stability) refers to the mathematically defined stability for the differential equation for time t shown in Equation 1.
[0005]
(Equation 1)
C (dT / dt) = f (θ)
Where C is a constant. f (θ) is a function. The solution of the equation in which the right side of Equation 1 is zero is called a steady solution (SteadyａｄState).₀It represents. Stationary solution T₀Given a small perturbation ΔT around₀Expanding as + ΔT,
[0006]
[Equation 2]
d (ΔT) / dt = −λ ΔT (t)
In the form of Then
[0007]
[Equation 3]
ΔT (t) = T₀Exp (-λt)
Becomes
If λ> 0, the perturbation decays, that is, the stationary solution is stable
If λ <0, the perturbation is amplified, that is, the stationary solution is unstable
Is obtained. This stability or instability is called linear stability. Mathematically, the linear stability can be determined from the sign of the real part (real @ part) of the eigenvalue of the Jacobian of the system in the stationary solution.
Jacobi stability refers to the second derivative x (t) of an equation such as Equation 1. A set of values of x (t) in the section α ≦ t ≦ β is called a trajectory. Some initial time t₀X (t) at x (t)₀) And t ≧ t₀Trajectory values x (t; where t ≧ t₀) Is sufficiently close (sufficiently close), x (t) is said to be Jacobi stable. Mathematically, Jacobi stability can be determined from the sign of the eigenvalue of the Berwald deviation tensor or the curvature deviation tensor.
A limit cycle is a continuous cycle of continuous movement or vibration, such as a watch, a human, or a gasoline engine, provided that fuel or energy is supplied from the outside, regardless of its initial state. State. The limit cycle has a property of continuing while being affected by an external factor such as deceleration or acceleration.
A singular point refers to a state that stands out from other points, and a state that is significantly different from a normal state, such as a point that changes from a steady state or an equilibrium state to a fluctuating state.
The phase change refers to a change in the phase of a sin function or a cos function when a phenomenon indicating a certain periodicity is represented by a linear combination such as a sin function or a cos function (such as a Fourier expansion).
FIG. 2 is a conceptual diagram showing a route from drug absorption to metabolism. When the drug enters the digestive tract orally, it is absorbed from the intestine while being metabolized by enzymes of the intestinal bacteria and transported to the liver. The drug is administered not only orally but also parenterally such as intravenously, intramuscularly, and subcutaneously. Some of these drugs are metabolized in the liver and excreted into bile (bile excretion). The drug excreted in bile is excreted in the intestinal tract and excreted as it is with the feces. In addition to bile and intestinal tract, the drug is excreted from the kidney as urine or mother's milk. Above all, it is known that the urinary route from the kidney is important as a drug excretion route (urinary excretion).
Water-soluble drugs are usually excreted in urine or bile without being metabolized. However, common drugs are fat-soluble. If these fat-soluble substances are not converted into water-soluble metabolites, they may accumulate in the body and threaten cell functions. Therefore, these fat-soluble substances first undergo metabolism of oxidation, reduction, and hydrolysis by P450 in microsomes (Phase I metabolic reaction: Phase I). Although this treatment may excrete the body as it is, in many cases, it is excreted in urine and bile after being conjugated with a more polar, ie water-soluble substance (Phase II metabolic reaction: Phase II). Conjugation includes glucuronidation, sulfate conjugation, glutathione conjugation, and the like.
FIG. 3 is a diagram showing a general structure of a DNA chip. FIG. 4 shows a flowchart of a measurement method using a DNA chip. First, the DNA probe 32 is immobilized on the support 34. Subsequently, the gene fragment extracted from the sample to be measured is labeled with a fluorescent label or the like. The fluorescently labeled gene 33 is hybridized with the DNA probe 32. After that, the fluorescence derived from the fluorescent label is detected by the detector 31. As a result of this detection, the amount of the fluorescently labeled gene 33 hybridized to each DNA probe 32 is obtained. This is called expression distribution.
Acetaminophen, a drug widely used as a nonsteroidal antipyretic analgesic, causes strong central necrosis in the liver of animals (rats, mice, hamsters) when administered in large doses. The acute toxicity of acetaminophen is also observed in humans, and hepatotoxicity is enhanced by alcohol drinking. Acetaminophen is a pharmacologically active substance of acetanilide and phenacetin, and its metabolism is as shown in FIG. See Kamataki and Kato, Ed., Drug Metabolism, Second Edition, Tokyo Kagaku Doujin (2000). Acetaminophen is detoxified and excreted by glucuronidation or sulfate conjugation when the normal dose is taken (normal administration). However, when administered in large doses, both conjugates are saturated and undergo N-hydroxylation (NH group → NOH group) by P450, producing a reactive and unstable active intermediate. This active intermediate is glutathione conjugated and detoxified, with the result that as the amount of glutathione in the cell decreases, the production of covalent conjugates, such as proteins, increases, ultimately inducing hepatocyte death.
According to a study using a DNA chip, arginase (Arginase; Unigene symbols ARG1 and ARG2) and ornithine carbamoyltransferase (Ornithine carbamoyltransferase) were obtained by administering hepatotoxicants such as acetaminophen to human cultured cells (HepG2) while changing the dosage. (Unigene symbol OTC), the expression level of a gene related to the urea cycle was significantly (more than twice) significantly increased during large-dose administration as compared to normal administration. The dose of acetaminophen administered was HepG2 cells (（5 × 10⁶Normal administration (0.2 mM) and large-volume administration (5 mM) for cells / 10 cc). The reason why the gene on the urea cycle fluctuates when a large amount of the drug is administered, not limited to acetaminophen, and the possibility that the gene on the metabolic pathway such as the citrate cycle fluctuates, will be described below. In addition, since large doses of many drugs are toxic, the following description is generally considered to be effective when administering toxic substances. Therefore, it is highly likely that the following description is also effective for general hepatotoxic drugs shown in Table 1.
[0008]
[Table 1]

FIG. 6 is a diagram showing the relationship between metabolic activation of a toxicant and the onset of toxicity. See Kamataki and Kato, Ed., Drug Metabolism, Second Edition, Tokyo Kagaku Doujin (2000). When a drug is administered normally, most toxic substances are excreted by oxidation, reduction, hydrolysis, and conjugation by metabolic enzymes such as P450. Table 2 summarizes drug metabolizing enzymes including P450. The drug toxicant is metabolized by the combination or repeated action of the drug metabolizing enzyme groups in Table 2. The drug normally administered in FIG. 6 undergoes metabolism and conjugation by P450 and is excreted. For example, since acetaminophen has a phenolic OH group, it is metabolized by both glucuronidation and sulfate conjugation. On the other hand, FIG. 6 shows that an active intermediate is produced. For example, in the case of acetaminophen, at the time of large dose administration, an active intermediate is generated by N-hydroxylation. The active intermediate is a pharmacologically active metabolite produced by metabolism of a drug toxicant. In many cases, highly reactive active intermediates produced in vivo are detoxified by metabolism such as glutathione conjugation. However, when the amount of the active intermediate is large, or when the enzyme system involved in the detoxification is saturated, or when the amount of biological components such as glutathione is small, the detoxification treatment mechanism does not function, and eventually the physiological function This will lead to injury or toxicity. Therefore, the onset and degree of toxicity of a drug toxicant is governed by the balance between the rate of production of the active intermediate and the rate of detoxification of the parent compound or metabolite. The production of active intermediates is promoted, detoxification ability is reduced and the balance is disrupted, and binding to nucleic acids such as DNA and RNA leads to genotoxicity such as mutagenicity, carcinogenicity, teratogenicity, and binding to proteins etc. Causes organ damage. On the other hand, as a result of a reaction between the active intermediate and a biological component (particularly, a protein), the complex may become a hapten antigen, induce an immune reaction, and develop toxicity.
[0009]
[Table 2]

When observing the balance between the production rate of the active intermediate and the detoxification rate of the parent compound metabolite, expression distribution analysis using a DNA chip, FDD, SAGE, or the like is effective. This is because a state in which the expression of protein genes related to metabolism and excretion is significantly out of balance compared with that in normal administration suggests that a toxic reaction caused by large doses or the like is occurring. To do that. In determining whether or not the expression states of a plurality of genes that produce proteins involved in metabolism and excretion are balanced, it is effective to analyze genes related to the urea cycle and the citric acid cycle. One of the reasons for this is that changes in related genes have a periodicity because they are cycle reactions. By observing the change or stability of the periodicity, it is possible to mathematically analyze whether or not the expression states of a plurality of genes are balanced. Another reason is that both cycles are closely related to each reaction and phenomenon shown in FIG.
FIG. 7 shows glutathione conjugation and its metabolic pathway, which are the main detoxification reactions of active intermediates. Glutathione is the most abundant SH compound in the living body, and several mM of glutathione is present in the liver. A drug toxicant (compound RX; where R is a substrate and C is a leaving group) forms a glutathione conjugate by glutathione transferase. Subsequently, a mercapturic acid conjugate is formed by the action of γ-glutamyl transpeptidase, cysteinyl glucinase, and membrane-bound N-acetyltransferase, and the toxicant is excreted in urine and feces. In this metabolic process, two kinds of amino acids, glutamic acid (Glu) and glycine (Gly), are produced.
FIG. 8 shows the metabolic pathway of glycine produced during glutathione conjugation. Glycine is converted to another amino acid, serine by glycine hydroxymethyltransferase, and to pyruvate by serine dehydratase. In this pyruvate production process, the ammonia (NH₃) Is converted to urea via the urea cycle and excreted in urine. Pyruvate is a compound produced in many of glucose metabolism, lipid metabolism and protein metabolism, and is converted into acetyl-CoA by pyruvate dehydrogenase. Acetyl-CoA is the starting material for the citric acid cycle. Carbon dioxide (CO2) produced from this pyruvate in the process of acetyl-CoA₂) Is converted to urea via the urea cycle together with the ammonia produced in the pyruvate production process and excreted in urine. Glycine produced by glutathione conjugation in this way is closely related to the urea cycle and the citric acid cycle.
FIG. 9 shows the metabolic pathway of glutamate produced during glutathione conjugation. Glutamic acid is produced together with 2-oxo acid when amino acid metabolism is performed by aminotransferase, and is one of the main compounds in amino acid metabolism. Glutamate produces 2-oxoglutarate and ammonia by glutamate hydrogenase. Glutamate produces 2-oxoglutarate and aspartate by aspartate aminotransferase. Ammonia is converted to urea by a urea cycle. 2-oxoglutaric acid is a compound in the citric acid cycle. Glutamate produced by glutathione conjugation in this way is closely related to the urea cycle and the citric acid cycle. FIG. 10 shows a citric acid circuit. The citric acid cycle, also called the TCA cycle, is a main pathway for oxidatively metabolizing sugars, fatty acids, and amino acids, and at the same time, a pathway for providing various biosynthetic raw materials such as NADH (nicotinamide adenine dinucleotide). Specifically, NADH or FADH generated in the citric acid cycle₂(Reduced flavin adenine dinucleotide)₂Produces ATP by oxidative phosphorylation when reoxidized by ATP is a major energy carrier in living organisms.
It was found that the citric acid cycle and the urea cycle are closely related to glutathione conjugation reaction and the like. In addition to this conjugation reaction, it is conceivable that amino acid degradation occurs in the process of performing a reaction such as a covalent bond of a toxic drug with DNA or protein as shown in FIG. Nitrogen (NH₃) And carbon (CO₂) Is converted to urea by the urea cycle. Amino acid degradation is related not only to the urea cycle but also to the citric acid cycle. FIG. 11 shows the relationship between amino acid degradation and the citric acid cycle. The standard amino acid is decomposed into any of pyruvic acid, 2-oxoglutaric acid, succinyl-CoA, fumaric acid, oxaloacetic acid, acetyl-CoA, and acetoacetic acid as shown in FIG. Thus, the citric acid cycle is also closely related to amino acid degradation related to toxicity.
In addition, the citric acid cycle is not only involved in amino acid decomposition but also greatly involved in the reaction of P450, which is the most typical drug metabolizing enzyme. As shown in FIG. 12, heme, which is a coenzyme of the metabolic reaction of P450, is synthesized by succinyl-CoA in the citric acid cycle and glycine, which is an amino acid. Heme is mainly synthesized in erythroblasts and the liver, but heme produced by the liver is mainly a cofactor for P450. A cofactor is a factor that improves the activity of a certain enzyme, and is a factor that can be said to be essential for the enzyme reaction. FIG. 13 shows the relationship between P450 and cofactor heme. Many toxic drugs undergo oxidation or reduction by P450 and become metabolites. Heme requires heme as a cofactor in the process, but heme uses succinyl-CoA from the citric acid cycle as the starting material for the synthesis. As described above, the urea cycle and the citric acid cycle are important metabolic cycles in drug metabolism related to the phase I metabolic reaction including P450 and the phase II metabolic reaction including glutathione conjugation.
The expression distribution of the genes constituting the urea cycle and the citric acid cycle is measured by a gene expression distribution measuring method such as a DNA chip, and the gene expression distribution is substituted into a model created in advance based on gene pathway information, and the model By analyzing the simultaneous differential equations, the linear stability and Jacobi stability of the urea cycle and the citric acid cycle during normal administration are calculated. If toxicity is observed, it is considered that the linear stability and the Jacobi stability of the urea cycle and the citric acid cycle are disturbed. The toxicity of the compound can be predicted and the presence or absence of toxicity can be determined using the evaluation results of the linear stability and the Jacobi stability.
The intent of the present invention is to determine by simulation that the harmonious behavior of gene expression and protein expression in cells in a stable state before drug administration changes (disrupts) after drug administration. That is, when the harmonious behavior of gene expression or protein expression changes before and after drug administration, it can be determined that the drug has exerted some toxicity (or medicinal effect). The change (collapse) of the harmonic behavior can be evaluated by, for example, a linear stability analysis or a Jacobi stability analysis.
The criteria for toxicity determination by linear stability analysis are as follows. The following criteria are self-evident considering the significance of linear stability analysis.
In the case of linear stability before and after drug administration, that is, (a) in the case of linear stability → linear stability, it can be determined that there is no toxicity because the harmonious behavior of gene expression does not change before and after drug administration.
Similarly,
(B) In the case of linear stability → linear instability, there is no information in linear stability analysis
(C) Toxic if linear unstable → linear stable
(D) In the case of linear instability → linear instability,
Oscillatory behavior → Oscillatory behavior, no toxicity
Oscillatory behavior → Chaotic behavior 毒性 if toxic
Can be determined. Chaotic behavior is behavior where future behavior is unpredictable.
It is necessary to combine the results of the linear stability analysis and the Jacobi stability analysis to determine the oscillatory behavior and the chaotic behavior. Oscillator behavior is mathematically synonymous with linear instability and Jacobi stability. Also, chaotic behavior is mathematically synonymous with linear instability and Jacobi instability.
The criteria for judging toxicity by Jacobi stability analysis are shown below. The following criteria are self-evident considering the meaning of the Jacobi stability analysis. Before and after drug administration,
(E) In case of Jacobi stable → Jacobi stable, no toxicity
(J) Jacobi stable → If Jacobi is unstable, toxic
(G) In case of Jacobi instability → Jacobi stability, there is no information in Jacobi stability analysis
(H) In case of Jacobi instability → Jacobi instability, there is no information in Jacobi stability analysis
Can be determined.
A feature of the present invention resides in that a linear stability analysis and a Jacobi stability analysis are simultaneously performed. Even if the toxicity is not determined by only the linear stability analysis or the Jacobi stability analysis alone, the toxicity can be determined by performing both at the same time. If the results of the linear stability analysis and the Jacobi stability analysis contradict each other, it indicates that the model used to create the simultaneous differential equations is inappropriate or the assumed pathway is incorrect, and the model is rebuilt. It is also excellent in giving information for
[0010]
BEST MODE FOR CARRYING OUT THE INVENTION
Hereinafter, a specific algorithm used for toxicity prediction will be described. This embodiment shows an example in which the present invention is applied to a cell cycle pathway model (a Tyson model taking the name of the author of a dissertation), which is a cell division cycle (Cell division cycle) model. FIG. 14 shows the Tyson model. The original paper was published by Tyson et al., Modeling the cell division cycle: cdc2 and cyclin interactions, Proc. {Natal. {Acad. USA, vol. 88, @pp. 7328-7332} (1991). By replacing the cell division cycle pathway with a urea cycle or a citrate cycle in the same manner as in this example, it is possible to predict toxicity using the results of gene expression analysis.
FIG. 14 will be described. The model of FIG. 14 is composed of two kinds of proteins, cyclin and cdc2, which are related to the cell cycle, and MPF (Maturation Promoting Factor) which is a conjugate of cyclin and cdc2. In addition, cdc2 is phosphorylated (Phosphorylation) by protein kinase to become phosphorylated cdc2. Active MPF is phosphorylated by protein kinase to become normal MPF. Although it is a simple model, it is known that the behavior at the time of cell growth can be well explained using the model of FIG. For the purpose of formulation, the activated MPF in FIG. 14 is called M, the normal (phosphorylated) MPF is called pM, the cyclin is Y, the phosphorylated cyclin is YP, cdc2 is C2, and the phosphorylated cdc2 is CP. In FIG. 14, the enzyme that performs phosphorylation, protein kinase, is referred to as P. A. a means an amino acid (Amino Acid) which is a component of a protein. The arrows connecting the proteins in FIG. 14 indicate the direction of the reaction, and the values k1 to k9 described beside the arrows indicate the reaction rate coefficients of the respective reactions. The reaction rate coefficient k in FIG. 14 has a dimension of concentration / time, and the larger the k, the greater the reaction amount (reaction rate) in the direction of the arrow.
FIG. 15 shows a simultaneous differential equation created based on the model of FIG. The uppermost equation in FIG. 15 is a differential equation relating to the concentration of cdc2 (C2) at time t (for example, mol / liter). cdc2 is produced from both activated MPF (M) and phosphorylated cdc2 (CP), and the reaction rate coefficients are k6 and k9, respectively. Further, C2 itself is phosphorylated by protein kinase (P) at a reaction rate coefficient of k8 to become CP. If the sign of generation is plus and the sign of disappearance is minus, the differential equation shown in FIG. 15 is obtained. By formulating all the reactions in FIG. 14 as described above, the simultaneous differential equations in FIG. 15 are created. By solving the simultaneous differential equations in FIG. 15, it is possible to simulate the time-dependent change in the concentration of each protein in the pathway shown in FIG.
FIG. 16 summarizes assumptions for the reaction rate coefficient of the simultaneous differential equations in FIG. The sum of C2, CP, pM, and M was assumed to be constant. These values were set as reliable as possible based on other experimental results, biological knowledge, and literature information. As described above, it is desirable that the value of the reaction rate coefficient in the simultaneous differential equations be a value as reliable as possible.
FIG. 17 shows a specific example of the linear stability analysis. First, the simultaneous differential equations in FIG. 15 are simplified, and a condition for the value of the first derivative to be zero is searched. By looking at the signs of these equations, linear stability and linear instability are determined according to the definitions of Equations 1 to 3.
FIG. 18 shows a specific example of the Jacobi stability analysis. The system of differential equations in FIG. 15 is further differentiated to obtain a quadratic differential equation. From the quadratic differential equation, a decision formula P used for Jacobi stability is obtained. Jacobi stability and Jacobi instability are determined based on the sign of P.
FIG. 19 is a flowchart illustrating the algorithm of the present invention. After creating the pathway model as shown in FIG. 14, a simultaneous differential equation as shown in FIG. 15 is created from the pathway model. When creating a pathway model, a model that is as appropriate as possible is created with reference to literature information and biological knowledge. Subsequently, both the linear stability analysis (FIG. 17) and the Jacobi stability analysis (FIG. 18) in the mathematical field are performed on the simultaneous differential equations as shown in FIG. In the field of mathematics, linear stability analysis and Jacobi stability analysis are well-known analysis methods, respectively, but there is no example in which both are applied to the same pathway model. However, by performing both the linear stability analysis and the Jacobi stability analysis, it is possible to analyze in more detail the oscillating behavior change of gene expression, and it is possible to perform highly accurate determination (for example, toxicity determination). ) Can be performed. Also, if the results of the linear stability analysis and the Jacobi stability analysis are inconsistent, it is suggested that the pathway model itself, which is the starting point of the calculation, is inconsistent. There is. If the results are not contradictory, it can be determined from the results of the linear stability analysis and the Jacobi stability analysis whether there is a change in the oscillatory behavior of gene expression, that is, whether there is toxicity. FIG. 20 shows an example of evaluating the presence / absence of a change in the oscillatory behavior of gene expression in the present invention. FIG. 20 is an example of an analysis result of the cell cycle pathway model of FIGS. 14 and 15. The linear stability analysis (FIG. 17) and the Jacobi stability analysis (FIG. 18) were performed while changing the value of the reaction rate coefficient k6 included in the simultaneous differential equations in FIG. 15 within the range of FIG. It was found that the state of the cell cycle can be classified into three types as shown in FIG.
For example, when the value of the reaction rate coefficient k6 for generating C2 from M was changed from 0 to 10, it could be classified into three regions A, B, and C as shown in FIG. These three classifications were classified based on the results of the linear stability analysis (FIG. 17). The sign of the linear stability analysis was minus in region A (ie, linear stability), plus in region B (ie, linear instability), and minus in region C (ie, linear stability). When the result of the linear stability analysis is stable, it means that the system tends to remain unchanged from near the steady solution. Biologically, region A brakes cell cycle rotation as a result of the continued high concentration of M. This state corresponds to a state where the cell cycle is temporarily stopped (Metaphase @ Arrest) in the cell division phase (Metaphase). On the other hand, the region B corresponds to a state in which the cell cycle is rotated and the cell proliferation is performed as a result of the change in the concentration of M or C2. In the region C, since the concentration of M continues to be low, the cell cycle is temporarily stopped in the intercellular phase (Interphase) (Interphase Arrest). However, when the value of k6 in the region A is 0.1 to 0.192, the sign of the Jacobi stability analysis (FIG. 18) is plus (ie, Jacobi instability). Jacobi instability means that a change is about to occur in a region including other than the vicinity of the steady solution. Therefore, when the value of k6 is between 0.1 and 0.192, the system tries to stay at the steady solution near the steady solution, but it can be said that the whole system is moving. The cell cycle is only paused and moves, so the cell is normal. However, when the value of k6 is between 0.192 and 0.2, it is both linearly stable and Jacobi stable. In this case, the cell cycle is stopped not only in the vicinity of the stationary solution but also in the whole system, and the cell cycle does not move in the future. Therefore, when the value of k6 is between 0.192 and 0.2, it means that the cell is not only paused but also dead. Similarly, in the region C, when the value of k6 is 1.9 to 10, the cells are only suspended, but when the value of k6 is 1.5 to 1.9, the cells are dead. I do.
As described above, by performing a simulation in which the value of the reaction rate coefficient k corresponding to the parameter of the simultaneous differential equation is changed, the relationship between the value of k and the state of the cell can be evaluated in advance. Then, the actual k value is calculated by substituting the concentration values (or their relative values) of the respective substances such as M and C2 into the simultaneous differential equations from the expression distribution values measured over time using a DNA chip or the like.
Region B (where k6 is between 0.2 and 1.5) is linearly unstable and Jacobi stable. In this case, the cells proliferate in a stable cycle. This is because although the concentrations of M and C2 are changed at the present time, the whole system eventually becomes stable. That is, the behavior is oscillatory, and the cells are normal. However, if the system is linearly unstable and Jacobi unstable, it is not possible to predict what state it will be in the future because it is unstable at this time and also in the whole system. That is, the behavior is chaotic and suggests that the cells have become cancerous. In this way, by performing not only linear stability analysis but also Jacobi stability analysis of simultaneous equations, it is possible to determine whether cells are growing, paused, dead, or cancerous it can. This method can make a determination that cannot be made by simply performing either the linear stability analysis or the Jacobi stability analysis. By applying this method to the urea cycle or the citric acid cycle, it is possible to determine the presence or absence of toxicity as in the cell cycle.
That is, a pathway model is created in advance based on the urea cycle and the citric acid cycle, and a simultaneous differential equation is obtained. The parameters such as the reaction rate coefficient used in the simultaneous differential equations are set as appropriate as possible based on literature information and biological knowledge. After that, based on the value of the reaction rate coefficient, a simultaneous differential equation that can be integrated or eliminated is searched for and arranged. Subsequently, linear stability analysis (FIG. 17) and Jacobi stability analysis (FIG. 18) were performed, and as shown in FIG. 20, the relationship between the value of the reaction rate coefficient and cell abnormalities (toxic) and cell normality (no toxicity) was determined. Get it in advance. Then, the measured values of the concentrations of the respective genes or their relative values are substituted into the simultaneous differential equations from the expression distribution data obtained from the experiment, and the reaction rate coefficients based on the experimental values are calculated. Finally, the value of the reaction rate coefficient obtained by the experiment is compared with a table of the relationship between the value of the reaction rate coefficient and the value of toxicity as shown in FIG. 20 to determine the presence or absence of toxicity.
FIG. 21 shows an example of a computer system that can be used to execute the software of the embodiment of the present invention, and FIG. 22 shows a system block diagram thereof.
FIG. 21 is an example of a computer system that can be used to execute software of an embodiment of the present invention. FIG. 21 shows a keyboard 181, a display 182, a CPU 183, a storage device 184, and a storage medium 185. In addition to the keyboard, a device for interacting with a graphical user interface such as a mouse may be provided. The storage device 184 and the storage medium 185 may be used to store and read out software programs embedded in computer code for executing the present invention, data for use with the present invention, and the like.
FIG. 22 is a block diagram of a computer system used to execute the software of the embodiment of the present invention. As shown in FIG. 21, the computer system includes a keyboard 181, a display 182, a CPU 183, a storage device 184, and a storage medium 185. The computer system further includes, for example, a system memory, a fixed disk (hard disk), a removable disk such as a CD-ROM and a DVD, a display adapter, a sound card, a speaker, and a network interface. A computer system suitable for use with the present invention can also be incorporated into a measurement instrument.
[0011]
【The invention's effect】
According to the present invention, it is possible to predict the toxicity of a drug and determine the presence or absence of toxicity from gene expression distribution data of a DNA chip or the like at the time of drug administration.
[Brief description of the drawings]
FIG. 1 is a conceptual diagram of a urea cycle.
FIG. 2 is a conceptual diagram of drug metabolism.
FIG. 3 is a conceptual diagram of a DNA chip.
FIG. 4 is a flowchart of DNA chip analysis.
FIG. 5 is a metabolic pathway diagram of acetaminophen.
FIG. 6 is an explanatory view of metabolic activation of a toxicant and manifestation of toxicity.
FIG. 7 is a metabolic pathway diagram of glutathione conjugation.
FIG. 8 is a glycine metabolism pathway diagram.
FIG. 9 is a diagram showing a glutamine metabolism pathway and an amino acid metabolism pathway.
FIG. 10 is a conceptual diagram of a citric acid cycle.
FIG. 11 is a diagram showing the relationship between amino acid degradation and the citric acid cycle.
FIG. 12 is a diagram of a heme biosynthesis pathway.
FIG. 13 is a diagram showing the relationship between P450 and cofactor heme.
FIG. 14 is a diagram of a cell cycle pathway model.
FIG. 15 shows simultaneous differential equations of a cell cycle pathway model.
FIG. 16 shows an example of an assumption for the reaction rate coefficient in FIG.
FIG. 17 shows an example of a linear stability analysis.
FIG. 18 shows an example of a Jacobi stability analysis.
FIG. 19 is a flowchart for judging the presence / absence of oscillatory behavior change (for example, toxicity determination) of gene expression.
FIG. 20 is a conceptual diagram of a method for evaluating a change in oscillatory behavior of gene expression.
FIG. 21 is an example of a computer system that can be used to execute software of an embodiment of the present invention.
FIG. 22 is a system block diagram of the computer system shown in FIG. 18;
[Explanation of symbols]
31. Detector, 32. DNA probe, 33. 34. a fluorescently labeled gene; Support, 51. Acetaminophen, 181. Keyboard, 182. Display, 183. CPU, 184. Storage device, 185. Storage medium.

Claims (7)

Simultaneous differential equations based on gene pathway information related to the metabolism or sequence of the toxic drug, a reaction rate coefficient of the simultaneous differential equations, a relationship between linear stability and Jacobi stability according to the reaction rate coefficient, and the reaction Storage means for storing the determination of the presence or absence of toxicity of the toxic drug in the value of the speed coefficient,
Input means for inputting gene expression distribution data to the simultaneous differential equations,
A display means for obtaining the reaction rate coefficient by inputting the gene expression distribution data to the simultaneous differential equation and displaying a determination of the presence or absence of toxicity of the toxic drug. Create simultaneous differential equations based on gene pathway information related to the metabolism or excretion of toxic drugs,
Determine the reaction rate coefficient of the simultaneous differential equations based on literature information and biological knowledge,
Perform linear stability analysis and Jacobi stability analysis using the simultaneous differential equations,
Determine the relationship between linear stability and Jacobi stability according to the reaction rate coefficient,
By obtaining the relationship between the presence or absence of the toxic drug in the value of the reaction rate coefficient,
A toxicity determining method for determining the presence or absence of toxicity by substituting gene expression distribution data obtained from an experiment into the simultaneous differential equation to determine the reaction rate coefficient and collating with the relationship of the presence or absence of toxicity. 3. The method according to claim 2, wherein the gene expression distribution data is data before and after administration of the toxic drug, and when the reaction rate coefficient changes from linear instability to linear stability, it is determined that there is toxicity. A method for determining the presence or absence of toxicity. 3. The method according to claim 2, wherein the gene expression distribution data is data before and after administration of the toxic drug, and when the reaction rate coefficient changes from Jacobi stable to Jacobi unstable, it is determined that there is toxicity. A method for determining the presence or absence of toxicity. 3. The method according to claim 2, wherein the metabolic gene pathway related to the metabolism or excretion of the toxic drug is a metabolic pathway related to a urea cycle or a citric acid cycle. 3. The method according to claim 2, wherein the gene expression distribution data is gene expression distribution data obtained by any of a DNA chip method, a differential display method, a quantitative PCR method, a SAGE method, and a protein chip method. A method for determining the presence or absence of toxicity. Create simultaneous differential equations based on gene pathway information related to the metabolism or excretion of toxic drugs,
Determine the reaction rate coefficient of the simultaneous differential equations based on literature information and biological knowledge,
Perform linear stability analysis and Jacobi stability analysis using the simultaneous differential equations,
Determine the relationship between linear stability and Jacobi stability according to the reaction rate coefficient,
A method for predicting the presence or absence of toxicity, comprising predicting the presence or absence of toxicity of the toxic drug.

Images