ActiveSciBench-Chem: Enzyme Kinetics Benchmark

• ActiveSciBench-Chem is a closed-loop benchmark for enzyme kinetics that discovers symbolic enzyme rate laws via adaptive experiment selection.
• It uses a fixed seven-dimensional assay space to simulate enzyme reactions and challenges agents to identify mechanistically relevant variables across easy, medium, and hard task tiers.
• The benchmark integrates active query policies, symbolic hypothesis generation, and rigorous evaluation metrics to distinguish true mechanistic recovery from mere interpolation.

ActiveSciBench-Chem, denoted $\chem$, is the active enzyme-kinetic law discovery component of ActiveSciBench, a two-dataset benchmark suite for closed-loop scientific discovery. Rather than presenting a fixed supervised dataset, it exposes a queryable oracle with hidden mechanisms and parameters, and evaluates whether an agent can use a limited experiment budget to design informative assays, identify which variables are mechanistically relevant, and recover the underlying symbolic enzyme rate law rather than merely interpolate observed responses (Kabra et al., 21 May 2026).

1. Benchmark formulation

ActiveSciBench is defined around a common closed-loop discovery formalism. Let $\mathcal{M}$ be a set of candidate mechanisms, let $m \in \mathcal{M}$ define a mapping $f_m : \mathcal{X} \to \mathcal{Y}$, and let $m^\star$ be the fixed but unknown ground-truth mechanism. At round $t$, the learner selects an experiment $x_t \in \mathcal{X}$ and receives an observation

$y_t \sim p(\cdot \mid x_t, m^\star).$

After $t$ rounds, the accumulated data are

$D_t = \{(x_i, y_i)\}_{i=1}^t,$

and the benchmark state is

$\mathcal{M}$0

where $\mathcal{M}$1 is structured memory and $\mathcal{M}$2 is the current hypothesis set. A discovery policy $\mathcal{M}$3 chooses the next experiment by

$\mathcal{M}$4

and the objective is to output $\mathcal{M}$5 after budget $\mathcal{M}$6 so as to minimize

$\mathcal{M}$7

Within this framework, $\mathcal{M}$8 is paired with ActiveSciBench-GRN as one of the two benchmark datasets in the suite. $\mathcal{M}$9 specializes the abstract formulation to enzyme kinetics: the input space $m \in \mathcal{M}$0 is a seven-dimensional assay space, the output space $m \in \mathcal{M}$1 is centered on the measured initial reaction rate $m \in \mathcal{M}$2, and the central target is mechanistic recovery under adaptive data acquisition rather than passive curve fitting. This design encodes the identifiability problem emphasized in the paper: distinct rate laws can exhibit similar local behavior under limited conditions, so informative perturbations become part of the task definition rather than an external experimental convenience (Kabra et al., 21 May 2026).

2. Task structure and assay interface

ActiveSciBench-Chem contains 57 curated tasks. Each task corresponds to one enzyme-catalyzed reaction system with a hidden kinetic mechanism family and a hidden parameterization. The benchmark organizes these tasks into three difficulty tiers. The Easy tier contains standard families such as Michaelis–Menten and competitive inhibition. The Medium tier contains structured compositions such as mixed inhibition, substrate inhibition, and combinations with temperature dependence. The Hard tier contains extended or nonstandard mechanisms such as cooperative binding, allosteric regulation, and related extensions.

All tasks share a fixed seven-dimensional experimental interface,

$m \in \mathcal{M}$3

where $m \in \mathcal{M}$4 is substrate concentration, $m \in \mathcal{M}$5 inhibitor concentration, $m \in \mathcal{M}$6 second-substrate concentration, $m \in \mathcal{M}$7 product concentration, $m \in \mathcal{M}$8 enzyme loading, $m \in \mathcal{M}$9 temperature, and $f_m : \mathcal{X} \to \mathcal{Y}$0 solution pH. For a chosen $f_m : \mathcal{X} \to \mathcal{Y}$1, the oracle returns the initial reaction rate $f_m : \mathcal{X} \to \mathcal{Y}$2 and auxiliary mass-balance observables. A central benchmark feature is that each task depends only on a subset of these seven variables; the remainder are distractor dimensions. Variable selection is therefore intrinsic to the benchmark, not a preprocessing convenience.

An experiment in $f_m : \mathcal{X} \to \mathcal{Y}$3 is a single oracle query at a point in this seven-dimensional space. Budgets are explicit and fixed. The main comparison table uses $f_m : \mathcal{X} \to \mathcal{Y}$4, while ablations consider $f_m : \mathcal{X} \to \mathcal{Y}$5. All methods are evaluated under equal budgets, and the cost model assigns one unit per query. This makes the benchmark a direct test of adaptive experimental efficiency: performance depends not only on the symbolic hypothesis class but also on whether the agent spends queries on conditions that actually separate candidate mechanisms.

3. Mechanism space and simulator construction

The mechanism library is deliberately broad. The benchmark is organized around nine canonical base families: Michaelis–Menten saturation, competitive inhibition, product inhibition, Arrhenius temperature dependence, ping–pong bisubstrate kinetics, uncompetitive inhibition, substrate inhibition, Hill cooperativity, and noncompetitive inhibition (Kabra et al., 21 May 2026).

Representative forms include the Michaelis–Menten law

$f_m : \mathcal{X} \to \mathcal{Y}$6

competitive inhibition

$f_m : \mathcal{X} \to \mathcal{Y}$7

ping–pong bisubstrate kinetics

$f_m : \mathcal{X} \to \mathcal{Y}$8

substrate inhibition

$f_m : \mathcal{X} \to \mathcal{Y}$9

Hill cooperativity

$m^\star$0

and noncompetitive inhibition

$m^\star$1

Temperature dependence is represented through Arrhenius-like modulation, for example

$m^\star$2

Beyond these base families, $m^\star$3 includes structured composite mechanisms such as Michaelis–Menten with competitive inhibition and Arrhenius modulation,

$m^\star$4

ping–pong bisubstrate kinetics with noncompetitive inhibition, Hill cooperativity with product feedback, and substrate inhibition with temperature dependence. It also includes extended families: ordered sequential bisubstrate kinetics, allosteric activation, anti-cooperative Hill behavior, fractal or anomalous kinetics, mixed inhibition, cooperative inhibition, monotonic pH dependence, metal-ion activation, product activation or autocatalytic feedback, and dual inhibition by inhibitor plus product.

The oracle is simulator-based. Parameters such as $m^\star$5, $m^\star$6, $m^\star$7, Hill coefficients, and activation energies are sampled from physically reasonable ranges. Main experiments use zero-noise or controlled Gaussian noise settings, and the authors note that even under conservative discretization the number of distinct instantiations exceeds $m^\star$8. This suggests that retrieval from a small predefined library is structurally inadequate: the benchmark rewards agents that can generate, refine, and falsify mechanisms rather than merely rank a closed menu.

4. Symbolic hypothesis representation and interaction protocol

In $m^\star$9, both the hidden ground truth and the agent’s candidate explanations are represented as symbolic kinetic laws. A discovered mechanism is expressed as a symbolic expression or Python function, with an interface of the form discovered_law(C_A, C_I, C_B, C_P, Enz, T, pH). The allowable function set consists of arithmetic operations, exponentials, powers, Arrhenius-style exponentials, and rational functions typical of enzyme kinetics. The benchmark therefore targets equation-structured reasoning with continuous parameter estimation.

The reported leading agent, LLM-AutoSciLab, interacts with $t$0 through a closed-loop procedure. At iteration $t$1, it forms the state $t$2, generates multiple candidate hypotheses with a small LLM, groups them by structural “skeleton,” and continues sampling until structural diversity entropy stabilizes, with an adaptive ensemble up to $t$3. A larger LLM then synthesizes the ensemble, selects a primary hypothesis, and proposes search regions in the experimental space (Kabra et al., 21 May 2026).

Experiment selection switches between Disambiguate and Refine modes according to a confidence threshold $t$4, given as 0.9 in the paper. In disambiguation mode, candidate experiments are scored by inter-hypothesis disagreement,

$t$5

and the policy prefers regions where plausible mechanisms diverge most strongly. In refinement mode, acquisition concentrates on improving the parameter fit of the current primary mechanism.

After each oracle call, candidate structures are numerically fitted and further refined with a PySR symbolic regression backend run for 800 iterations. Stability is estimated by bootstrap refitting, using the confidence statistic

$t$6

Stable hypotheses are retained, brittle ones are pruned, and the final answer after budget exhaustion is selected from the surviving symbolic candidates. This interaction protocol makes explicit that $t$7 is not simply an equation-discovery dataset; it is a benchmark for adaptive hypothesis generation, targeted experimentation, and mechanistic discrimination.

5. Evaluation criteria and reported performance

ActiveSciBench-Chem evaluates candidate laws with three primary metrics. The first is RMSLE,

$t$8

which measures predictive fit over multiple orders of magnitude. The second is Exact Accuracy,

$t$9

a strict numeric criterion for near-exact recovery. The third is Symbolic Accuracy (SA), determined by an LLM judge that asks whether there exists any choice of constant parameters making the predicted and true expressions equivalent up to algebraic simplification and variable renaming. Symbolic Accuracy is the benchmark’s most mechanism-sensitive metric, because it distinguishes true law recovery from merely close numerical approximation (Kabra et al., 21 May 2026).

The main reported results at budget $x_t \in \mathcal{X}$0 are as follows:

Method	SA / Ex.	RMSLE
PySR	7.89 / 15.79	1.212
BO+PySR	5.26 / 6.98	1.960
BED+PySR	31.58 / 39.47	0.249
LLM-only / Code-assisted LLM	0 / 0	$x_t \in \mathcal{X}$1–0.82
LLM-AutoSciLab	35.09 / 50.88	0.189

The abstract reports this as 35.1% symbolic accuracy on ActiveSciBench-Chem. Difficulty-stratified numbers for LLM-AutoSciLab are also reported: on Easy tasks it reaches SA 55.56%, Ex. 88.89%, RMSLE 0.298; on Medium tasks SA 22.22% and Ex. 37.04%; on Hard tasks SA 42.86% and Ex. 52.38%. The strongest non-LLM baseline, BED+PySR, remains competitive overall but is described as limited on the hard tier.

The benchmark also quantifies sample efficiency. For $x_t \in \mathcal{X}$2, the strongest active baseline, BED+PySR, requires roughly 2.33–2.47× more oracle queries to match the symbolic accuracy obtained by LLM-AutoSciLab at a given budget. The paper further summarizes the gain on $x_t \in \mathcal{X}$3 as about 2.3–2.5× versus the strongest non-LLM baselines, with larger advantages over naïve LLM-only approaches. This suggests that the benchmark rewards experiment selection policies that target mechanism disagreement rather than generic uncertainty reduction.

6. Design choices, limitations, and practical use

Several design choices define the benchmark’s character. It is fully simulator-based, which yields a reproducible environment with exact hidden mechanisms and controllable noise. It uses a shared seven-variable interface across all tasks, with hidden relevant-variable structure, so agents must discover both the kinetic law and which perturbation axes matter. Its mechanism space includes canonical textbook forms, structured compositions, and extended nonstandard families, which prevents simple fixed-library methods from covering the entire task set.

The reported baselines reveal corresponding failure modes. LLM-only and simple code-assisted LLM systems exhibit strong prior knowledge about enzyme kinetics but tend to default to generic textbook equations such as canonical Michaelis–Menten and achieve 0% symbolic accuracy under the benchmark’s strict equivalence criterion. BED+PySR performs strongly on easier cases but is reported to collapse on the hard tier, where extended families fall outside a fixed library. For LLM-AutoSciLab itself, the paper identifies dependence on the quality and diversity of generated hypotheses, and on the coverage of the parser and symbolic regression backend.

The benchmark’s limitations are explicit. Because it is synthetic, it abstracts away real-laboratory complications such as heterogeneous experiment costs, assay failures, and more complex noise structures. The shared cost model assigns one unit to every query, regardless of whether conditions involve high temperature or unusual reagents. The paper therefore proposes extensions including non-uniform condition costs, experimental failures, heteroscedastic noise, more exotic enzyme mechanisms, interacting pathways, and eventual integration with self-driving laboratory hardware.

Practically, ActiveSciBench-Chem is distributed with the broader LLM-AutoSciLab codebase at https://github.com/scientific-discovery/LLM-AutoSciLab. The environment exposes an active-query oracle interface in which an algorithm proposes a vector $x_t \in \mathcal{X}$4, calls the oracle, receives $x_t \in \mathcal{X}$5 and optional auxiliary observables, and after exhausting the budget outputs a symbolic law in executable or symbolic form. In that sense, $x_t \in \mathcal{X}$6 functions simultaneously as a benchmark, a simulation environment, and a standardized testbed for budget-constrained mechanistic discovery in enzyme kinetics.