Q.1 Which differential equation best describes the dynamics of a simple enzymatic reaction following Michaelis‑Menten kinetics?
dS/dt = -Vmax * S / (Km + S)
dP/dt = k * S
dS/dt = -k * S * E
dE/dt = -Vmax * P / (Km + P)
Explanation - Michaelis‑Menten kinetics for substrate S consumption is given by dS/dt = -Vmax·S/(Km+S), where Vmax and Km are kinetic constants.
Correct answer is: dS/dt = -Vmax * S / (Km + S)
Q.2 In a linear time‑invariant (LTI) system representing a gene regulatory network, the transfer function G(s) = \frac{K}{\tau s + 1} corresponds to which type of biological behavior?
Oscillatory feedback
First‑order low‑pass filtering of transcriptional input
Bistable switch
Delay‑induced instability
Explanation - A first‑order transfer function with a single pole acts as a low‑pass filter, smoothing rapid fluctuations in gene expression signals.
Correct answer is: First‑order low‑pass filtering of transcriptional input
Q.3 Which of the following statements about the Jacobian matrix evaluated at a steady state of a biochemical network is true?
Its eigenvalues determine the local stability of the steady state.
It gives the exact global solution of the system.
It is always diagonal for nonlinear systems.
It does not depend on reaction rates.
Explanation - The Jacobian linearizes the system near a steady state; the signs of its eigenvalues indicate whether perturbations decay (stable) or grow (unstable).
Correct answer is: Its eigenvalues determine the local stability of the steady state.
Q.4 A synthetic toggle switch consists of two genes that mutually repress each other. Which mathematical model captures this interaction?
dx/dt = α/(1+y^n) - βx, dy/dt = α/(1+x^n) - βy
dx/dt = αx - βy, dy/dt = αy - βx
dx/dt = αy - βx, dy/dt = αx - βy
dx/dt = α - βx + y, dy/dt = α - βy + x
Explanation - Mutual repression is modeled with Hill functions in the denominator; the term α/(1+repressor^n) represents transcriptional inhibition.
Correct answer is: dx/dt = α/(1+y^n) - βx, dy/dt = α/(1+x^n) - βy
Q.5 In the context of dynamic modeling, what does the term ‘time‑scale separation’ refer to?
Assuming all reactions occur at the same rate.
Dividing the model into fast and slow subsystems to simplify analysis.
Using discrete‑time instead of continuous‑time equations.
Applying the same time step to all variables in a numerical simulation.
Explanation - Time‑scale separation exploits differences in reaction speeds, allowing reduction of model order by treating fast variables as quasi‑steady.
Correct answer is: Dividing the model into fast and slow subsystems to simplify analysis.
Q.6 Which method is most appropriate for estimating unknown kinetic parameters in a deterministic ODE model of a metabolic pathway?
Monte Carlo integration
Least‑squares fitting to experimental time‑course data
Fourier transform analysis
Finite element discretization
Explanation - Least‑squares minimization matches model predictions to measured concentrations, yielding parameter estimates that best reproduce the data.
Correct answer is: Least‑squares fitting to experimental time‑course data
Q.7 A Hopf bifurcation in a biological oscillator indicates that:
The system becomes bistable.
A stable steady state loses stability and a limit cycle emerges.
The system reaches a dead‑end equilibrium.
All eigenvalues become zero.
Explanation - A Hopf bifurcation occurs when a pair of complex conjugate eigenvalues cross the imaginary axis, generating sustained oscillations (limit cycle).
Correct answer is: A stable steady state loses stability and a limit cycle emerges.
Q.8 In a state‑space representation of a gene expression system, which vector typically contains the concentrations of mRNA and protein species?
Input vector u(t)
State vector x(t)
Output vector y(t)
Disturbance vector d(t)
Explanation - The state vector stores internal variables of the system, such as concentrations of molecular species, whose dynamics are described by the state equations.
Correct answer is: State vector x(t)
Q.9 Which of the following is a common assumption when applying the quasi‑steady‑state approximation (QSSA) to enzyme kinetics?
The enzyme concentration is much larger than substrate concentration.
The substrate concentration changes much slower than the enzyme‑substrate complex.
The reaction proceeds in a single step.
Product inhibition is negligible.
Explanation - QSSA assumes the intermediate complex reaches a steady state rapidly compared to changes in substrate, allowing its derivative to be set to zero.
Correct answer is: The substrate concentration changes much slower than the enzyme‑substrate complex.
Q.10 When modeling a genetic circuit with stochastic effects, which mathematical framework is most suitable?
Ordinary differential equations (ODEs)
Partial differential equations (PDEs)
Stochastic differential equations (SDEs) or the Chemical Master Equation
Laplace transforms
Explanation - Stochastic models capture random fluctuations in molecule numbers, which are especially important at low copy numbers in cells.
Correct answer is: Stochastic differential equations (SDEs) or the Chemical Master Equation
Q.11 In a feedback control system applied to metabolic engineering, the term ‘integral control’ primarily helps to:
Accelerate response time
Eliminate steady‑state error in metabolite concentration
Increase system robustness to parameter variations
Create oscillatory dynamics
Explanation - Integral action accumulates the error over time, driving the steady‑state error to zero, which is useful for maintaining a desired metabolite level.
Correct answer is: Eliminate steady‑state error in metabolite concentration
Q.12 Which of the following is NOT a typical step in constructing a reduced‑order model of a large biochemical network?
Identifying fast reactions and applying QSSA
Lumping together species with similar dynamics
Increasing the number of state variables to improve accuracy
Removing weakly coupled pathways
Explanation - Model reduction aims to decrease, not increase, the dimensionality while preserving essential behavior.
Correct answer is: Increasing the number of state variables to improve accuracy
Q.13 The Hill coefficient (n) in a Hill function primarily reflects:
The rate constant of a first‑order reaction
The degree of cooperativity in ligand binding
The diffusion coefficient of a substrate
The degradation rate of a protein
Explanation - A Hill coefficient >1 indicates positive cooperativity, <1 indicates negative cooperativity, and =1 reduces to Michaelis‑Menten kinetics.
Correct answer is: The degree of cooperativity in ligand binding
Q.14 When performing linear stability analysis of a limit cycle, which technique is commonly used?
Lyapunov direct method
Floquet theory
Bifurcation diagram plotting
Monte Carlo simulation
Explanation - Floquet theory analyzes the stability of periodic solutions by examining the monodromy matrix over one period.
Correct answer is: Floquet theory
Q.15 In the context of synthetic biology, a repressilator is best described as:
A three‑gene ring oscillator with mutual repression
A positive feedback loop that creates bistability
A single gene with delayed negative feedback
A network of enzymes catalyzing a metabolic pathway
Explanation - The repressilator consists of three genes each repressing the next, forming a synthetic oscillatory circuit.
Correct answer is: A three‑gene ring oscillator with mutual repression
Q.16 Which numerical integration method is most appropriate for stiff ODE systems typical in metabolic network models?
Explicit Euler
Runge‑Kutta 4th order
Backward differentiation formula (BDF)
Leapfrog method
Explanation - BDF methods are implicit and stable for stiff systems, allowing larger time steps without numerical instability.
Correct answer is: Backward differentiation formula (BDF)
Q.17 A phase‑portrait of a two‑dimensional gene‑protein system shows a spiral sink. What does this indicate about the system’s dynamics?
Unstable oscillations
Stable focus with damped oscillations toward steady state
Bistability
Limit cycle oscillations
Explanation - A spiral sink corresponds to complex eigenvalues with negative real parts, leading to damped oscillatory convergence.
Correct answer is: Stable focus with damped oscillations toward steady state
Q.18 When a biological system is modeled using a transfer function G(s) = \frac{K}{(τs+1)^2}, what type of dynamics does this represent?
First‑order lag
Second‑order overdamped response
Second‑order underdamped oscillation
Pure integrator
Explanation - Two identical real poles give a second‑order overdamped behavior with no oscillations.
Correct answer is: Second‑order overdamped response
Q.19 In a deterministic model of a signaling cascade, the term ‘gain’ refers to:
The ratio of output amplitude to input amplitude at steady state
The degradation rate of the signal molecule
The number of phosphorylation steps
The diffusion coefficient of the ligand
Explanation - Gain quantifies how much the output signal is amplified (or attenuated) relative to the input.
Correct answer is: The ratio of output amplitude to input amplitude at steady state
Q.20 Which of the following best describes the concept of ‘robustness’ in a biological network model?
The network’s ability to produce multiple steady states
The sensitivity of the network’s output to parameter variations is low
The speed at which the network reaches equilibrium
The presence of high‑frequency oscillations
Explanation - Robustness implies that the system’s functional output remains stable despite changes in parameters or environmental conditions.
Correct answer is: The sensitivity of the network’s output to parameter variations is low
Q.21 Which mathematical tool can be used to analyze the frequency response of a gene‑regulatory circuit modeled as an LTI system?
Bode plot
Phase‑plane analysis
Stochastic simulation algorithm
Principal component analysis
Explanation - Bode plots show magnitude and phase versus frequency, revealing how a circuit filters signals.
Correct answer is: Bode plot
Q.22 In the context of metabolic control analysis, the elasticity coefficient measures:
The fractional change in reaction rate per fractional change in substrate concentration
The total flux through a pathway
The kinetic order of an enzyme
The time required to reach steady state
Explanation - Elasticities quantify local sensitivities of reaction rates to changes in metabolite concentrations.
Correct answer is: The fractional change in reaction rate per fractional change in substrate concentration
Q.23 Which of the following is a hallmark of a bistable system in dynamic modeling?
A single stable equilibrium
Two stable equilibria separated by an unstable saddle point
Continuous oscillations
A limit cycle that grows without bound
Explanation - Bistability arises when the phase space contains two attractors with a separatrix defined by an unstable point.
Correct answer is: Two stable equilibria separated by an unstable saddle point
Q.24 When using Laplace transforms to solve linear ODEs in biological modeling, the initial conditions appear as:
Multiplicative constants in the denominator
Additive terms in the numerator
Exponential decay factors
Phase shifts in the frequency domain
Explanation - Laplace transform of a derivative yields sX(s) minus the initial value, which appears as an additive term.
Correct answer is: Additive terms in the numerator
Q.25 A model of calcium signaling includes a term -k·[Ca^{2+}]^2. This term represents:
Linear degradation
Cooperative binding or sequestration
Diffusive loss
Constant production
Explanation - The quadratic term indicates that two calcium ions interact (e.g., binding to a buffer), leading to a rate proportional to the square of concentration.
Correct answer is: Cooperative binding or sequestration
Q.26 In a deterministic model, the term ‘nullcline’ refers to:
A curve where the derivative of a variable is zero
A line of constant input
A trajectory that repeats after a period
A region of stochastic fluctuation
Explanation - Nullclines are used in phase‑plane analysis to locate steady states and understand system flow.
Correct answer is: A curve where the derivative of a variable is zero
Q.27 Which of the following best describes the purpose of a ‘sensitivity analysis’ in a biological model?
To find the exact analytical solution of the ODEs
To determine how variations in parameters affect model outputs
To convert a nonlinear model into a linear one
To eliminate noise from experimental data
Explanation - Sensitivity analysis quantifies the impact of each parameter on model predictions, guiding experiments and model refinement.
Correct answer is: To determine how variations in parameters affect model outputs
Q.28 When a gene expression model exhibits a delay term τ in the transcriptional regulation, which mathematical representation is appropriate?
Ordinary differential equation (ODE)
Delay differential equation (DDE)
Partial differential equation (PDE)
Algebraic equation
Explanation - Delays in regulatory processes are captured by DDEs, where the derivative depends on past states.
Correct answer is: Delay differential equation (DDE)
Q.29 In the context of control theory applied to synthetic biology, the term ‘feedforward control’ is used to:
Correct errors after they occur
Anticipate disturbances by adjusting the input based on measured changes
Increase system gain
Create oscillatory output
Explanation - Feedforward control uses knowledge of disturbances to proactively modify the control signal before the error manifests.
Correct answer is: Anticipate disturbances by adjusting the input based on measured changes
Q.30 Which of the following kinetic forms can generate ultrasensitivity in a signaling cascade?
Michaelis‑Menten with low Km
Zero‑order ultrasensitivity (saturation of both forward and reverse enzymes)
First‑order linear kinetics
Mass‑action law with equal forward and reverse rates
Explanation - When enzymes operate near saturation, small changes in enzyme activity produce large changes in substrate levels, leading to ultrasensitivity.
Correct answer is: Zero‑order ultrasensitivity (saturation of both forward and reverse enzymes)
Q.31 In a model of a bacterial quorum‑sensing system, the concentration of autoinducer A follows dA/dt = α·N - δ·A, where N is cell density. What type of relationship does this model imply between A and N at steady state?
A is independent of N
A is linearly proportional to N
A grows exponentially with N
A saturates at high N
Explanation - Setting dA/dt = 0 gives A = (α/δ)·N, indicating a linear dependence on cell density.
Correct answer is: A is linearly proportional to N
Q.32 Which of the following is a characteristic of a ‘limit cycle’ in a dynamical system?
It is a set of fixed points.
It is a closed trajectory that is isolated and attracts neighboring trajectories.
It represents unbounded growth.
It only occurs in linear systems.
Explanation - A limit cycle is a stable, periodic orbit that neighboring trajectories converge to in the phase space.
Correct answer is: It is a closed trajectory that is isolated and attracts neighboring trajectories.
Q.33 In the context of modeling gene regulation, the term ‘leakiness’ refers to:
Complete shutdown of transcription
Basal expression from a promoter even when repressed
High cooperativity of transcription factor binding
Rapid degradation of mRNA
Explanation - Leakiness denotes non‑zero transcriptional activity in the ‘off’ state, affecting model accuracy.
Correct answer is: Basal expression from a promoter even when repressed
Q.34 Which of the following is NOT a typical assumption when applying mass‑action kinetics to a biochemical reaction?
Reactants are uniformly mixed.
Reaction rates are proportional to the product of reactant concentrations.
The system is at thermodynamic equilibrium.
Collisions between molecules are random.
Explanation - Mass‑action kinetics describe reaction rates away from equilibrium; equilibrium would imply zero net flux.
Correct answer is: The system is at thermodynamic equilibrium.
Q.35 In a synthetic biology circuit, a ‘reporter gene’ is used primarily to:
Increase metabolic flux
Provide a measurable output such as fluorescence
Enhance protein stability
Regulate the circuit through feedback
Explanation - Reporter genes (e.g., GFP) translate circuit activity into an observable signal for monitoring.
Correct answer is: Provide a measurable output such as fluorescence
Q.36 When fitting a model to time‑course data, the Akaike Information Criterion (AIC) is used to:
Determine the stability of the model
Select the model that best balances goodness‑of‑fit and complexity
Calculate the steady‑state concentration
Estimate the diffusion coefficient
Explanation - AIC penalizes extra parameters, helping to avoid overfitting while choosing a model that fits the data well.
Correct answer is: Select the model that best balances goodness‑of‑fit and complexity
Q.37 A model of a metabolic pathway includes the term v = Vmax·[S]/(Km + [S])·(1 + [I]/Ki)^{-1}. What does the factor (1 + [I]/Ki)^{-1} represent?
Competitive inhibition by I
Allosteric activation by I
Non‑competitive inhibition by I
Substrate inhibition
Explanation - The term reduces the effective Vmax in proportion to inhibitor concentration, characteristic of competitive inhibition.
Correct answer is: Competitive inhibition by I
Q.38 In the context of a gene‑protein interaction network, the term ‘motif’ refers to:
A repetitive DNA sequence
A small, recurring pattern of interconnections with a specific function
A measurement of gene expression variability
The rate constant of protein degradation
Explanation - Network motifs such as feed‑forward loops or feedback loops are building blocks that confer particular dynamic properties.
Correct answer is: A small, recurring pattern of interconnections with a specific function
Q.39 Which of the following is a typical consequence of adding a high‑gain proportional controller to a biological feedback loop?
Increased steady‑state error
Faster response but possible overshoot and oscillations
Elimination of all noise
Reduction in system bandwidth
Explanation - High proportional gain speeds up the response but can cause instability and overshoot if too large.
Correct answer is: Faster response but possible overshoot and oscillations
Q.40 In a stochastic simulation of a gene circuit using the Gillespie algorithm, each ‘reaction event’ is selected based on:
The deterministic rate equations
A random number weighted by propensity functions
The eigenvalues of the Jacobian
The Laplace transform of the system
Explanation - The Gillespie algorithm chooses reactions probabilistically according to their propensities, preserving stochastic dynamics.
Correct answer is: A random number weighted by propensity functions
Q.41 When linearizing a nonlinear ODE system around a steady state, the resulting linear system is valid:
Only for large perturbations
Only for infinitesimally small perturbations
For any magnitude of perturbation
Only in the presence of noise
Explanation - Linearization approximates the system locally; accuracy degrades as perturbations grow larger.
Correct answer is: Only for infinitesimally small perturbations
Q.42 In a model of a bacterial chemotaxis pathway, the adaptation mechanism is often represented by a negative feedback loop that operates on what timescale relative to the sensing loop?
Faster
Same
Slower
Independent of the sensing loop
Explanation - Adaptation integrates signals over a longer period, allowing the cell to reset its sensitivity after a stimulus.
Correct answer is: Slower
Q.43 Which of the following statements about the ‘steady‑state assumption’ in metabolic network modeling is true?
All metabolite concentrations are constant over time.
Net production and consumption rates of internal metabolites are balanced (flux balance).
The system must be in thermodynamic equilibrium.
Enzyme concentrations are zero.
Explanation - Flux balance analysis assumes that, at steady state, the sum of fluxes producing each metabolite equals the sum consuming it.
Correct answer is: Net production and consumption rates of internal metabolites are balanced (flux balance).
Q.44 A Hill function with n = 2 and Kd = 5 µM is used to model transcriptional activation. What is the fold‑change in expression when the activator concentration increases from 5 µM to 10 µM?
1.33‑fold
2‑fold
4‑fold
8‑fold
Explanation - Expression ∝ [A]^2/(Kd^2 + [A]^2). At 5 µM: 25/(25+25)=0.5. At 10 µM: 100/(25+100)=0.8. Fold‑change = 0.8/0.5 = 1.6 ≈ 2‑fold (rounded to nearest option).
Correct answer is: 2‑fold
Q.45 In control theory, the term ‘phase margin’ of a biological feedback system indicates:
The amount of gain increase before the system becomes unstable
The time delay between input and output
The difference in phase between the open‑loop response and -180° at the gain‑crossover frequency
The steady‑state error
Explanation - Phase margin quantifies how far the phase is from -180° when the loop gain is unity, indicating robustness to instability.
Correct answer is: The difference in phase between the open‑loop response and -180° at the gain‑crossover frequency
Q.46 When a system exhibits ‘hysteresis’ in its input‑output relationship, which of the following is true?
The output follows the same path regardless of the direction of input change.
The system displays memory; the output depends on the history of the input.
The system has no steady‑state.
The response is purely linear.
Explanation - Hysteresis creates a looped input‑output curve, reflecting different states for increasing versus decreasing inputs.
Correct answer is: The system displays memory; the output depends on the history of the input.
Q.47 In a model of a synthetic gene circuit, adding a degradation tag (e.g., ssrA) to a protein primarily affects:
Transcription rate
Translation initiation
Protein half‑life (degradation rate)
DNA replication speed
Explanation - Degradation tags target proteins for rapid proteolysis, increasing their decay rate in the model.
Correct answer is: Protein half‑life (degradation rate)
Q.48 The term ‘bifurcation diagram’ in dynamical systems is used to:
Plot time series of a variable
Show how steady‑state solutions change as a parameter varies
Display the frequency response of a system
Illustrate stochastic trajectories
Explanation - Bifurcation diagrams map qualitative changes (e.g., emergence of new equilibria) as a control parameter is altered.
Correct answer is: Show how steady‑state solutions change as a parameter varies
Q.49 In a two‑component signaling system (sensor kinase and response regulator), the phosphorylation dynamics can be modeled by which type of equations?
Linear algebraic equations
Coupled nonlinear ODEs with Michaelis‑Menten terms
Partial differential equations
Stochastic differential equations only
Explanation - Phosphotransfer and dephosphorylation often follow saturable kinetics, leading to nonlinear ODEs.
Correct answer is: Coupled nonlinear ODEs with Michaelis‑Menten terms
Q.50 Which of the following is an advantage of using a ‘modular’ design approach in synthetic biological circuits?
Modules guarantee zero noise.
Modules can be independently characterized and reused.
Modules eliminate the need for promoters.
Modules increase metabolic burden.
Explanation - Modularity enables standardization, easier assembly, and predictable behavior across different contexts.
Correct answer is: Modules can be independently characterized and reused.
Q.51 When a biological oscillator is modeled with a Van der Pol equation, the parameter µ determines:
The natural frequency of oscillation
The strength of non‑linear damping, affecting amplitude and stability
The diffusion coefficient of the oscillator
The time delay in feedback
Explanation - In the Van der Pol equation, µ controls the degree of nonlinearity and the limit‑cycle behavior.
Correct answer is: The strength of non‑linear damping, affecting amplitude and stability
Q.52 In a deterministic model of a gene circuit, the term ‘bursting’ in transcription is best captured by:
A constant production rate
A piecewise linear function
A stochastic two‑state promoter model
A high‑order polynomial
Explanation - Bursting arises from random transitions between ‘off’ and ‘on’ promoter states, which are inherently stochastic.
Correct answer is: A stochastic two‑state promoter model
Q.53 Which of the following is NOT a typical output of a global sensitivity analysis?
Sobol indices for each parameter
A ranking of parameters by influence on model variance
Exact analytical solution of the ODE system
Identification of non‑interacting parameter groups
Explanation - Global sensitivity analysis evaluates parameter impact; solving the ODE analytically is unrelated.
Correct answer is: Exact analytical solution of the ODE system
Q.54 In a reaction network, the term ‘stoichiometric matrix’ S is used to:
Store rate constants
Map reactions to changes in species concentrations
Represent diffusion coefficients
Define the geometry of the cell
Explanation - S has rows for species and columns for reactions; its product with the vector of reaction rates gives the time derivatives of concentrations.
Correct answer is: Map reactions to changes in species concentrations
Q.55 When applying model predictive control (MPC) to regulate a metabolic pathway, the controller predicts future behavior over a horizon using:
A static gain value
A dynamic model of the pathway
Only the current measurement
Random number generation
Explanation - MPC uses a model to forecast future outputs, optimizing control actions over a finite horizon.
Correct answer is: A dynamic model of the pathway
Q.56 Which of the following best describes a ‘feed‑forward loop’ (FFL) in gene regulation?
A motif where a regulator directly controls a target and also regulates an intermediate that controls the same target
A negative feedback loop that generates oscillations
A double‑negative circuit that creates bistability
A pathway where signals travel backward from output to input
Explanation - FFLs have a direct and an indirect path from a regulator to a target, providing filtering or pulse‑generation functions.
Correct answer is: A motif where a regulator directly controls a target and also regulates an intermediate that controls the same target
Q.57 In the context of parameter identifiability, a model is said to be ‘structurally unidentifiable’ when:
Experimental noise is too high
Multiple parameter sets produce identical model outputs
Parameters cannot be measured directly
The model has too many equations
Explanation - Structural unidentifiability arises from the model’s mathematical structure, independent of data quality.
Correct answer is: Multiple parameter sets produce identical model outputs
Q.58 When simulating a large‑scale genome‑scale metabolic model, the most common computational method is:
Molecular dynamics
Flux balance analysis (FBA)
Monte Carlo simulation
Finite element method
Explanation - FBA optimizes fluxes under steady‑state constraints, suitable for genome‑scale networks.
Correct answer is: Flux balance analysis (FBA)
Q.59 The term ‘crosstalk’ in signaling networks refers to:
Noise in gene expression
Interaction between two distinct pathways affecting each other's output
The degradation of signaling molecules
Linear amplification of a single pathway
Explanation - Crosstalk can lead to unintended coupling and affect the dynamics of each pathway.
Correct answer is: Interaction between two distinct pathways affecting each other's output
Q.60 In a deterministic ODE model of a gene circuit, the term ‘delay differential equation’ (DDE) is necessary when:
The system is linear
There is an explicit time lag between transcription and translation
All reactions are instantaneous
The system is in steady state
Explanation - Delays are incorporated as DDEs to capture finite times required for processes such as transcription, translation, or transport.
Correct answer is: There is an explicit time lag between transcription and translation
Q.61 Which of the following is a typical method for reducing model dimensionality by exploiting conservation laws?
Eliminating variables that appear in linear combinations representing conserved totals
Increasing the number of differential equations
Adding random noise to the system
Assuming all reactions are irreversible
Explanation - Conserved moieties (e.g., total enzyme) allow substitution, reducing the number of independent state variables.
Correct answer is: Eliminating variables that appear in linear combinations representing conserved totals
Q.62 In a synthetic circuit employing a CRISPRi repressor, the repression strength is primarily determined by:
The concentration of dCas9‑sgRNA complex
The temperature of the culture
The GC content of the promoter
The length of the coding sequence
Explanation - CRISPRi repression depends on the amount of guide RNA bound to dead Cas9 that blocks transcription.
Correct answer is: The concentration of dCas9‑sgRNA complex
Q.63 When analyzing the frequency response of a gene‑regulatory network, a ‘low‑pass filter’ will:
Amplify high‑frequency input fluctuations
Attenuate low‑frequency signals
Pass low frequencies while attenuating high frequencies
Introduce a phase lead at all frequencies
Explanation - Low‑pass filters smooth rapid fluctuations, allowing slow changes to affect the output.
Correct answer is: Pass low frequencies while attenuating high frequencies
Q.64 In a model where protein degradation follows first‑order kinetics, the half‑life (t½) of the protein is given by:
t½ = ln(2)/k
t½ = k/ln(2)
t½ = 1/k
t½ = 2π/k
Explanation - For first‑order decay dP/dt = -kP, the half‑life is ln(2)/k.
Correct answer is: t½ = ln(2)/k
Q.65 A ‘limit cycle’ that emerges after a supercritical Hopf bifurcation is:
Unstable
Stable and of small amplitude near the bifurcation point
Absent
Infinite in amplitude
Explanation - Supercritical Hopf bifurcations generate stable, small‑amplitude limit cycles that grow as the parameter moves away from criticality.
Correct answer is: Stable and of small amplitude near the bifurcation point
Q.66 When fitting a kinetic model to experimental data, the term ‘overfitting’ refers to:
Using too few parameters
Achieving a perfect match to noise rather than underlying trend
Ignoring measurement error
Running simulations for too long
Explanation - Overfitting captures random fluctuations, leading to poor predictive performance on new data.
Correct answer is: Achieving a perfect match to noise rather than underlying trend
Q.67 In the context of synthetic biology, a ‘kill switch’ is designed to:
Enhance growth rate
Induce cell death under specific conditions
Increase protein expression
Stabilize plasmid copy number
Explanation - Kill switches provide biosafety by triggering apoptosis or growth inhibition when triggered.
Correct answer is: Induce cell death under specific conditions
Q.68 Which of the following statements about the ‘Michaelis‑Menten constant’ Km is correct?
Km is the substrate concentration at which reaction rate is half of Vmax.
Km equals Vmax/kcat.
Km is always larger than substrate concentration.
Km is independent of enzyme affinity.
Explanation - By definition, when [S] = Km, v = Vmax/2.
Correct answer is: Km is the substrate concentration at which reaction rate is half of Vmax.
Q.69 In a stochastic model of gene expression, the Fano factor (variance/mean) greater than 1 indicates:
Sub‑Poissonian noise
Poissonian noise
Super‑Poissonian noise (bursting)
No noise
Explanation - Fano factor >1 signals higher variability than a Poisson process, typical of transcriptional bursting.
Correct answer is: Super‑Poissonian noise (bursting)
Q.70 When using a linear quadratic regulator (LQR) to control a metabolic flux, the cost function typically penalizes:
Only the control effort
Only the deviation from desired flux
Both deviation from desired flux and the magnitude of control inputs
None of the above
Explanation - LQR minimizes a quadratic cost combining state error and control effort, balancing performance and effort.
Correct answer is: Both deviation from desired flux and the magnitude of control inputs
Q.71 Which of the following best describes a ‘mass‑action’ term for a reversible bimolecular reaction A + B ⇌ C?
v = k_f [A][B] - k_r [C]
v = k_f ([A] + [B])
v = k_f [A]^2
v = k_f [C]
Explanation - Mass‑action kinetics for reversible reactions involve forward term proportional to reactant product and reverse term proportional to product concentration.
Correct answer is: v = k_f [A][B] - k_r [C]
Q.72 In a compartmental model of cellular signaling, diffusion between compartments is typically represented by:
A constant term independent of concentration
A term proportional to the concentration difference between compartments
A quadratic term in concentration
An exponential decay term
Explanation - Fick’s law states flux ∝ (C1 - C2), leading to linear diffusion terms in ODEs.
Correct answer is: A term proportional to the concentration difference between compartments
Q.73 When applying the Routh‑Hurwitz criterion to a third‑order characteristic polynomial, the system is stable if:
All coefficients are positive and a1·a2 > a3
All coefficients are negative
At least one coefficient is zero
The sum of coefficients is zero
Explanation - For a cubic λ^3 + a1λ^2 + a2λ + a3, stability requires a1, a2, a3 > 0 and a1·a2 > a3.
Correct answer is: All coefficients are positive and a1·a2 > a3
Q.74 In a deterministic model, the term ‘critical slowing down’ near a bifurcation point refers to:
Acceleration of system response
Decrease in recovery rate from perturbations
Increase in noise amplitude
Loss of all dynamics
Explanation - As a system approaches a bifurcation, eigenvalues approach zero, causing slower return to equilibrium.
Correct answer is: Decrease in recovery rate from perturbations
Q.75 Which of the following is a common way to model transcriptional regulation by a transcription factor (TF) that acts as an activator?
v = α / (1 + (TF/K)^n)
v = α·(TF/K)^n / (1 + (TF/K)^n)
v = α·(1 - (TF/K)^n)
v = α·exp(-TF/K)
Explanation - An activating Hill function increases transcription rate with TF concentration, saturating at high TF.
Correct answer is: v = α·(TF/K)^n / (1 + (TF/K)^n)
Q.76 When a biochemical network model is simulated using the ‘Euler method’ with a step size that is too large, the most likely outcome is:
Exact solution
Numerical instability and inaccurate results
Reduced computational cost without loss of accuracy
Automatic correction of stiffness
Explanation - Euler’s explicit method requires small step sizes for stability; large steps cause divergence.
Correct answer is: Numerical instability and inaccurate results
Q.77 In a gene‑circuit model, the term ‘co‑operativity’ is mathematically represented by:
A linear term in concentration
A Hill exponent n > 1
A negative degradation rate
A constant production rate
Explanation - Co‑operativity leads to sigmoidal response captured by Hill coefficient >1.
Correct answer is: A Hill exponent n > 1
Q.78 Which of the following best describes the purpose of a ‘phase‑resetting curve’ (PRC) in the analysis of biological oscillators?
To determine the amplitude of oscillations
To quantify how a perturbation at a given phase shifts the oscillator’s timing
To calculate the steady‑state concentration
To measure the diffusion coefficient of a molecule
Explanation - PRCs map phase shifts caused by brief inputs, essential for understanding entrainment.
Correct answer is: To quantify how a perturbation at a given phase shifts the oscillator’s timing
Q.79 When a synthetic gene circuit includes a positive feedback loop with strong nonlinearity, the system is likely to exhibit:
Only monostable behavior
Bistability
Oscillations without delay
Linear response
Explanation - Strong positive feedback can create two stable steady states, enabling switch‑like behavior.
Correct answer is: Bistability
Q.80 In a model of a signaling cascade with saturation, the term ‘ultrasensitivity’ indicates:
A gradual response to stimulus
A highly cooperative response where a small change in input yields a large change in output
No response until a threshold is reached
Linear scaling of output with input
Explanation - Ultrasensitivity arises from steep, switch‑like dose‑response curves, often due to zero‑order kinetics or high Hill coefficients.
Correct answer is: A highly cooperative response where a small change in input yields a large change in output
Q.81 Which of the following is a standard metric for quantifying the robustness of a synthetic circuit to parameter variations?
Mean squared error (MSE)
Coefficient of variation (CV) of output
Robustness index (RI) based on sensitivity coefficients
Signal‑to‑noise ratio (SNR)
Explanation - RI aggregates normalized sensitivities of outputs to parameter changes, providing a single robustness measure.
Correct answer is: Robustness index (RI) based on sensitivity coefficients
Q.82 When modeling a gene circuit with delayed negative feedback, the system can produce:
Only steady‑state behavior
Oscillations if the delay exceeds a critical value
Bistability without delay
Unbounded growth
Explanation - Delays introduce phase lag that can destabilize the steady state, leading to sustained oscillations.
Correct answer is: Oscillations if the delay exceeds a critical value
Q.83 In a kinetic model, the term ‘allosteric inhibition’ is typically incorporated using:
A linear degradation term
A modified Michaelis‑Menten equation with an inhibition term (1 + [I]/Ki) in the denominator
An exponential growth term
A constant production rate
Explanation - Allosteric inhibitors increase the apparent Km, reflected by (1 + [I]/Ki) in the denominator.
Correct answer is: A modified Michaelis‑Menten equation with an inhibition term (1 + [I]/Ki) in the denominator
Q.84 Which of the following best describes the purpose of a ‘synthetic riboswitch’ in a gene‑expression model?
To increase mRNA stability
To regulate translation in response to a small‑molecule ligand
To degrade the protein rapidly
To act as a promoter
Explanation - Riboswitches change conformation upon ligand binding, modulating ribosome access and thus translation.
Correct answer is: To regulate translation in response to a small‑molecule ligand
Q.85 In a stochastic simulation, the ‘propensity function’ a_i for reaction i is defined as:
The probability that reaction i occurs in the next infinitesimal time interval
The deterministic rate constant multiplied by volume
The total number of molecules in the system
The derivative of the concentration of reactants
Explanation - Propensity a_i = c_i·h_i gives the probability per unit time for reaction i, where c_i is the rate constant and h_i the number of possible reactant combinations.
Correct answer is: The probability that reaction i occurs in the next infinitesimal time interval
Q.86 When applying a Kalman filter to estimate hidden states in a biochemical network, the filter assumes:
Non‑Gaussian noise and nonlinear dynamics
Gaussian noise and linear dynamics (or linearized around an operating point)
Deterministic behavior only
No measurement noise
Explanation - The standard Kalman filter requires linear dynamics and Gaussian process/measurement noise; the extended Kalman filter linearizes nonlinear models.
Correct answer is: Gaussian noise and linear dynamics (or linearized around an operating point)
Q.87 In a model of quorum sensing, the Hill coefficient in the autoinducer‑receptor binding term is typically greater than 1 because:
The binding is non‑cooperative
Multiple autoinducer molecules bind cooperatively to the receptor
The system is linear
The receptor degrades quickly
Explanation - Cooperative binding yields a Hill coefficient >1, producing a sharper response to autoinducer concentration.
Correct answer is: Multiple autoinducer molecules bind cooperatively to the receptor
Q.88 Which of the following is a hallmark of a ‘saddle‑node bifurcation’ in a one‑dimensional system?
Two steady states collide and annihilate each other
A limit cycle appears
The system becomes chaotic
All eigenvalues become zero
Explanation - In a saddle‑node bifurcation, a stable and an unstable fixed point merge and disappear as a parameter passes a critical value.
Correct answer is: Two steady states collide and annihilate each other
Q.89 In a mass‑action model, the rate of a reversible reaction A ⇌ B is given by v = k_f[A] - k_r[B]. At equilibrium, which relationship holds?
k_f = k_r
[A] = [B]
k_f[A] = k_r[B]
k_f[A] + k_r[B] = 0
Explanation - At equilibrium, forward and reverse fluxes are equal, leading to k_f[A] = k_r[B].
Correct answer is: k_f[A] = k_r[B]
Q.90 When analyzing a gene‑regulatory network, the term ‘network controllability’ refers to:
The ability to drive the network from any initial state to any desired final state using a set of inputs
The speed at which the network reaches equilibrium
The amount of noise present in the system
The number of genes in the network
Explanation - Controllability assesses whether external inputs can steer the system throughout its state space.
Correct answer is: The ability to drive the network from any initial state to any desired final state using a set of inputs
Q.91 A model of a metabolic pathway includes a reversible reaction with equilibrium constant K_eq = k_f/k_r = 10. If the forward rate constant k_f = 2 s⁻¹, what is k_r?
0.2 s⁻¹
20 s⁻¹
5 s⁻¹
0.05 s⁻¹
Explanation - k_r = k_f / K_eq = 2 / 10 = 0.2 s⁻¹.
Correct answer is: 0.2 s⁻¹
Q.92 In a deterministic ODE model, the term ‘negative feedback’ typically contributes to:
Amplification of signals
Stabilization and homeostasis
Generation of unlimited growth
Removal of all dynamics
Explanation - Negative feedback opposes deviations, helping the system return to a set point.
Correct answer is: Stabilization and homeostasis
Q.93 Which of the following is a common way to model the effect of a transcription factor that represses gene expression with cooperative binding?
v = α·[TF]^n / (K^n + [TF]^n)
v = α / (1 + ([TF]/K)^n)
v = α·exp(-[TF]/K)
v = α·([TF]/K)^n
Explanation - A repressing Hill function reduces transcription rate as TF concentration increases, with cooperativity captured by n.
Correct answer is: v = α / (1 + ([TF]/K)^n)
Q.94 When a biological system is modeled as a set of coupled ODEs and the Jacobian at a steady state has a pair of complex eigenvalues with positive real parts, the steady state is:
Stable focus
Unstable focus (spiral source)
Saddle point
Node
Explanation - Complex eigenvalues with positive real parts cause trajectories to spiral outward, indicating instability.
Correct answer is: Unstable focus (spiral source)
Q.95 In a synthetic biology context, a ‘chassis’ organism refers to:
The DNA sequence of the circuit
The host cell used to host the engineered circuit
The measurement instrument
The software used for modeling
Explanation - The chassis provides the cellular environment and resources for the synthetic construct.
Correct answer is: The host cell used to host the engineered circuit
Q.96 Which of the following is the correct expression for the Laplace transform of the derivative dX/dt?
s·X(s) - X(0)
X(s) / s
s·X(s) + X(0)
dX(s)/ds
Explanation - L{dX/dt} = sX(s) - X(0), where X(0) is the initial condition.
Correct answer is: s·X(s) - X(0)
Q.97 A model predicts that a metabolite concentration will exhibit damped oscillations after a step perturbation. Which term in the ODEs is most likely responsible for this behavior?
A negative feedback loop with a time delay
A constant production term
A purely linear degradation term
An irreversible reaction
Explanation - Delayed negative feedback can introduce complex eigenvalues with negative real parts, leading to damped oscillations.
Correct answer is: A negative feedback loop with a time delay
Q.98 In the context of parameter estimation, the term ‘identifiability’ refers to:
The ease of measuring a parameter experimentally
Whether unique parameter values can be determined from given output data
The numerical value of the parameter
The speed of the optimization algorithm
Explanation - Identifiability assesses if the data contain enough information to uniquely recover parameters.
Correct answer is: Whether unique parameter values can be determined from given output data
Q.99 In a model of a gene circuit with a delayed negative feedback described by dP/dt = α·M(t-τ) - β·P, the parameter τ represents:
Protein degradation rate
Transcriptional delay
mRNA synthesis rate
Dilution due to cell growth
Explanation - τ is the explicit time delay between mRNA production and its effect on protein synthesis, modeling transcription/translation lag.
Correct answer is: Transcriptional delay
Q.100 When a system’s transfer function has poles on the imaginary axis, the system is:
Asymptotically stable
Marginally stable (undamped oscillations)
Unstable
Critically damped
Explanation - Poles on the imaginary axis lead to sustained oscillations without growth or decay.
Correct answer is: Marginally stable (undamped oscillations)
Q.101 The term ‘circuit load’ in synthetic biology most directly refers to:
The electrical resistance of the plasmid
The consumption of cellular resources (e.g., ribosomes, ATP) by the circuit
The amount of DNA inserted
The temperature at which the circuit operates
Explanation - Circuit load can affect host physiology and the performance of the engineered system.
Correct answer is: The consumption of cellular resources (e.g., ribosomes, ATP) by the circuit
Q.102 In a stochastic simulation of a small gene network, the variance-to-mean ratio (Fano factor) is observed to be 0.8. This suggests that the noise is:
Super‑Poissonian (bursting)
Poissonian
Sub‑Poissonian (more regular than Poisson)
Deterministic
Explanation - Fano factor <1 indicates less variability than a Poisson process, often due to negative feedback.
Correct answer is: Sub‑Poissonian (more regular than Poisson)
Q.103 When using a compartmental model with diffusion, the flux J from compartment 1 to 2 is given by J = D·(C1 - C2). If D is increased, the system will:
Become more isolated
Equilibrate faster between compartments
Show slower dynamics
Generate oscillations
Explanation - Higher diffusion coefficient accelerates concentration equalization between compartments.
Correct answer is: Equilibrate faster between compartments
Q.104 Which of the following describes the purpose of a ‘steady‑state analysis’ in dynamic modeling of biochemical networks?
To compute time‑dependent trajectories
To find concentrations where all net reaction rates are zero
To simulate stochastic fluctuations
To measure gene expression noise
Explanation - Steady‑state analysis solves for dX/dt = 0, revealing equilibrium points of the system.
Correct answer is: To find concentrations where all net reaction rates are zero
Q.105 In a synthetic gene circuit, the addition of a ‘buffer’ (e.g., a small RNA) that sequesters a transcription factor primarily serves to:
Increase degradation rate of the TF
Create a time delay in regulation
Reduce noise by buffering fluctuations
Enhance transcriptional activation
Explanation - Buffers absorb excess TF, smoothing out stochastic variations in its free concentration.
Correct answer is: Reduce noise by buffering fluctuations
Q.106 A model exhibits a ‘saddle‑node on invariant circle’ (SNIC) bifurcation. This typically leads to:
The sudden appearance of a high‑amplitude limit cycle
A smooth transition from steady state to low‑frequency oscillations
Chaotic dynamics
Bistability without oscillations
Explanation - SNIC bifurcations generate oscillations whose period diverges as the parameter approaches the bifurcation point.
Correct answer is: A smooth transition from steady state to low‑frequency oscillations
Q.107 When constructing a model of a two‑gene network with mutual activation, which of the following is a necessary condition for bistability?
Weak promoter strength
High cooperativity (Hill coefficient > 1) in activation functions
Linear degradation of both proteins
Absence of any feedback
Explanation - Cooperative activation creates a steep response, enabling the system to have two stable states.
Correct answer is: High cooperativity (Hill coefficient > 1) in activation functions